McMaster University Dr. Chris Swartz Department of Chemical Engineering Telephone: (905) 525 9140 × 27945 1280 Main Street West Fax: (905) 521 1350 Hamilton, Ontario E-mail: [email protected] Canada, L8S 4L7 Website: http://macc.mcmaster.ca/

McMaster Advanced Control Consortium (MACC)

Summary of Research Projects

May 2012

Table of Contents

1 Yanan Cao 1

2 Pedro A. Castillo 5

3 Zhiwen Chong ‡ 9

4 Brandon Corbett 17

5 Buddhadeva Das 21

6 Miao Du ‡ 25

7 Yasser Ghobara 29

8 Jaffer H. Ghouse 33

9 Nor Farida Harun 37

10 Mohammad Zamry Jamaludin 41

11 Yaser Khojasteh Salkuyeh 45

12 Richard Mastragostino ‡ 49

13 Jake Nease 53

14 Alicia Pascall 57

15 Shailesh Patel 61

16 Mudassir M. Rashid 65

17 Ali M. Sahlodin ‡ 69

18 Matt Wallace 73

19 Ian Washington 77

‡This student is about to graduate and is available for interviews for future employment. His/her contact details appear on the MACC webpages: http://macc.mcmaster.ca/ 1 Yanan Cao

Research title: Design for Dynamic Performance: Application to Air Sepa- ration Units Advisor: Dr. C.L.E. Swartz Date: May 2012 Industrial Collaboration: Praxair, Inc.

Research Goals

This project is an extension of a previous study on the implementation of a dynamic optimization- based framework for identifying bottleneck constraints for plant performance, and evaluation of design modifications to improve plant agility. The previous work completed focused on a nitrogen plant. In this project, the research scope will be expanded to include a multi-product cryogenic air separation plant. Simultaneous design and control under uncertainties and/or disturbances will be applied on both nitrogen and multi-product plants. While considering uncertainties in the process, the problem will be formulated as multi-scenario optimization problem with an economic objective function. Various process designs and control schemes will be evaluated. Operating policies (i.e. production and scheduling) with fixed process design will also be explored with and without startup and shutdown.

Background

Energy consumption is the dominant source of operation costs for air separation units (ASUs) (Zhu et al. [2001]). Traditionally, air separation plants had infrequent changes in production rate, hence operation conditions, due to a steady electricity price and customer demands. However, the situation has changed after electricity price deregulation, and operation of ASUs is subject to time-of-day or real-time electricity price fluctuations and varying customer demand. Frequent changes in operating conditions and/or startup/shutdown would be required to gain economic benefits from utility price fluctuations (Zhu et al. [2001]).

This project is motivated by the need for a systematic approach for operation, and integrated design and control of ASUs to obtain improvements in process performance (i.e. switchablility and agility) and associated potential economic gain subject to time-of-day or real-time electricity price and varying customer demand. Systematic approaches to the design of dynamically operable plants have been the subject of many research studies over the past three decades. Studies on operation and design of ASUs are typically limited, with one or a couple of the following considerations: (1) dynamic behavior (i.e. through implementing rigorous dynamic model), (2) design modification, (3) uncertainty and disturbances, (4) multi-period operation policy and (5) control structure (e.g. Schenk et al. [2002], Zhu et al. [2010], Mitra et al. [2012]).

1 Research Plan gPROMS will be used as one of the main platforms in this project. Other commercially available software may also be used. This project will investigate 4 main research directions:

1. Operation Policy – The previous study demonstrated that switching between different operating points according to varying electricity price and demand can increase a plant’s profitability with a single period problem formulation. In this study, the operation policy problem will be studied using a multi-period preemptive approach with a dynamic plant model. Multiple variations (known/forecasted) in product demand and/or electricity price will be introduced. The objective is to follow the demand closely by utilizing available electricity price and demand information, and plant capacities (production and storage) wisely so that economic gain can be achieved. No operation/safety constraints violations are allowed and unnecessary variations in the inputs should be eliminated.

2. Integrated Design and Control – It was shown previously that design modifications can improve plant performance during transitions, which may lead to potential economical gains. In this study, a dynamic optimization based approach similar to Schenk et al. [2002] will be followed with detailed economic analysis. The focus will be on design and operational decisions such as the location of introducing reflux during transitions and the corresponding feeding profile. The optimization problem will be solved under open-loop considerations. In the area of our interest, uncertainties could be in customer demand or electricity price or both.

3. Control Dynamics – Open-loop studies provide benchmarks on system responses under perfect control. Control delay and measurement lag can degrade plant performance with certain design configurations. Consequently, adjustments may be required in the design and operation policy to accommodate the effect of control dynamics and to maintain the desired performance. This study will be based on the conventional PI control structure. Following the mixed integer dynamic optimization approach for integrated design and control, the optimal control structure and corresponding tuning parameters can be obtained simultaneously as in Schenk et al. [2002].

4. Start-up of Multi-product Plant – Miller [2008] demonstrated that collecting and dis- tributing process liquid (i.e. with fixed feeding profile) during start-up can improve plant agility through manual optimization. It was unclear what would be the economically optimal operating trajectories of the collected liquid. Also, the design modification of having multiple external/internal storages may also be applied for the upper and lower columns in the process so that the overall startup time of the plant can be further reduced. To answer these questions, in this project, the problem will be solved through optimization based methodologies.

2 Current Status

Our current focus is on model modifications. The dynamic model of the nitrogen plant that will be used in this study is based on the one developed in the previous study with two major modifications:

Varying pressure drop in the distillation column In the previous study, the pressure drop in the distillation column was assumed to be constant. This leads to a high index problem under the assumption of negligible vapor holdup. In this study, the pressure drop at each tray is expressed as a function of the corresponding vapor velocity and liquid hold up.

Variable Scaling Variables, including state and algebraic variables, in the revised model are scaled by the corresponding steady state value or a factor so that the range of variables after scaling is between 0.1 and 10.

It has been observed that the execution time required to perform a dynamic simulation reduced by at least 25 % from the base case model.

Industrial Collaboration

We will be interacting closely with Praxair Inc. during all phases of the project.

Literature Cited

Miller, J. (2008). Rapid startup of cryogenic air separation plants by collection and distribution of process liquid. PhD thesis, Chemical Engineering, Lehigh University, United States.

Mitra, S., Grossmann, I. E., Pinto, J. M., and Arora, N. (2012). Robust Scheduling under Time-sensitive Electricity Prices for Continous Power-intensive Processes. In FOCAPO 2012: Foundations of Computer-Aided Process Operations, Savannah, Georgia January 8 - 11. Foundations of Computer-AidedProcess Operations.

Schenk, M., Sakizlis, V., Perkins, J. D., and Pistikopoulos, E. N. (2002). Optimization- Based Methodologies for Integrating Design and Control in Cryogenic Plants. In Grievink, J. and van Schijndel, J. (Eds.), European Symposium on Computer Aided Process Engineering - 12, pp. 331 – 336, The Hague, The Netherlands, 26 - 29 May. ESCAPE, Elsevier.

Zhu, G., Henson, M. A., and Megan, L. (2001). Low-order dynamic modeling of cryogenic distillation columns based on nonlinear wave phenomenon. Separation and Purification Technology, 24, 467 – 487.

Zhu, Y., Legg, S., and Laird, C. D. (2010). Optimal design of cryogenic air separation columns under uncertainty. Computers & Chemical Engineering, 34(9), 1377 – 1384.

3 Poster Slides

Motivation and Objective Research Directions I. Operation Policy Motivation and Objective Operation Policy – Production and Scheduling Background: the cryogenic air separation process is Observed: switching between different operating points according to varying a widely used technology for producing high purity O ,N and Ar electricity price and demand can increase a plant’s profitability • 2 2 a large consumer of electrical energy • Objective: follow the demand closely by utilizing available electricity price subject to variations in customer demand as well as electricity price • and demand information, and plant capacities (production and storage) Motivation: the need for a systematic approach for operation, and wisely so that economic gain can be achieved integrated design and control of ASU to obtain: Methodology: improvement in process performance multi-period formulation reactive vs. preemptive • • potential economic gain decomposition approach: economical operation + move suppression • • subject to (1) time-of-day or real-time electricity price and (2) varying customer demand Remarks: Related studies on ASU Ierapetritou et al. [2002] Objectives: for N2 and multi-product plants: • 1 obtain the optimal long-term operation policy with economic analysis Zhu et al. [2011] • 2 apply the simultaneous design and control framework to large-scale Mitra et al. [2012] dynamic systems with and without uncertainties and disturbances • None of these studies implemented a 3 investigate the effect of control dynamics on the design and operation rigorous dynamic model. 4 determine the design and operation policy for improving plant agility during start-up

Y. Cao & C.L.E. Swartz Simultaneous Design and Control: Application to ASU Y. Cao & C.L.E. Swartz Simultaneous Design and Control: Application to ASU McMaster University MACC Annual Meeting (May 14, 2012) 1 / 6 McMaster University MACC Annual Meeting (May 14, 2012) 2 / 6 Slide 1 Slide 2

Research Directions II. Integrated Design and Control Research Directions III. Effects of Control Dynamics Integrated Design and Control Effects of Control Dynamics Observed: design modification can improve plant performance during Motivation: transitions, which may lead to potential economical gains open-loop studies provide benchmarks on system responses under perfect • Objective: apply dynamic optimization based framework for the control control delay and measurement lag can degrade plant performance with simultaneous plant and control system design of large-scale dynamic systems • with and without uncertainties and disturbances certain design configurations Decision variables: discrete and continuous Objective: determine the design and operation policy to accommodate the Methodology: effect of control dynamics and to maintain the desired performance open-loop Methodology: • study with proportional integral control structure (i.e. pairing and multi-scenario and mixed-integer dynamic optimization • • tuning) Uncertainties: electricity price and customer demand apply mixed-integer dynamic optimization framework Disturbances: ambient temperature • Remarks: Related studies on ASU Remarks: Related studies on ASU Schenk et al. [2002]: no design, control structure for disturbance rejection Schenk et al. [2002]: dynamic model, no design modification, no uncertainties • • Miller [2008]: steady state gain matrix, relative gain array matrix and Zhu et al. [2010]: steady-state model, no design modification, uncertainties • • Niederlinski index

Y. Cao & C.L.E. Swartz Simultaneous Design and Control: Application to ASU Y. Cao & C.L.E. Swartz Simultaneous Design and Control: Application to ASU McMaster University MACC Annual Meeting (May 14, 2012) 3 / 6 McMaster University MACC Annual Meeting (May 14, 2012) 4 / 6 Slide 3 Slide 4

Research Directions IV. Start-up of Multi-product Plants Current Status and Future Work Start-up of Multi-product Plants Current Status and Future Work

Motivation: having multiple external/internal storage for the argon columns together with the operating policy of collecting and distributing process liquid during start-up can improve plant agility Current Status: introduced two major modifications in the N2 plant Objective: dynamic model determine the optimal operating strategy during plant start-up and its Varying pressure drop in the distillation column: pressure drop at • • corresponding design modifications with economic analysis each tray is expressed as a function of the corresponding vapor velocity and liquid hold up multi-period operation problem with plant start-up allowed • Variable Scaling: the range of variables is between 0.1 and 10. Methodology: dynamic optimization based integrated design and control • and working on model validation with available plant data. Pre-requirement: dynamic multi-product plant model with start-up and normal operation phases Future Work: study each of the four research directions for N2 and multi-product plants starting with the N2 plant. Remarks: Related studies on ASU Miller [2008]: design modifications with corresponding operation policy, • simulation based

Y. Cao & C.L.E. Swartz Simultaneous Design and Control: Application to ASU Y. Cao & C.L.E. Swartz Simultaneous Design and Control: Application to ASU McMaster University MACC Annual Meeting (May 14, 2012) 5 / 6 McMaster University MACC Annual Meeting (May 14, 2012) 6 / 6 Slide 5 Slide 6

4 2 Pedro A. Castillo

Research title: Pinch Point Algorithm for Gasoline Blend Planning Advisor: Dr. V. Mahalec Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

The objective of this research is to develop a Pinch Point algorithm that simplifies the gasoline blend planning optimization problem with the capability to calculate global optimal solutions keeping the blend recipes as constant as possible along the planning time horizon.

Background

The petroleum refining industry has to deal with a dynamic market environment where product demands and crude prices oscillate very often and environmental regulations are continuously becoming stricter (Li and Karimi [2011]). These are some of the reasons why optimization has been a main part of the decision-making in oil refineries and has a great impact in their net profit. Over the years, several mathematical programming techniques have been developed and used for planning refinery operations.

The gasoline blend operation represents the major profitable operation in a refinery, accounting for 60-70 percent of the total profit. The gasoline blend planning optimization aims to find the best possible way to mix different intermediate products from the refinery in order to minimize the blending cost subject to meeting the quality and demand requirements of the final products (C.A. Mendez and Karobe [2006]). The relation of the volumes to be blended is called the blend recipe. Given a planning time horizon, and demand and supply profiles, one way to solve this optimization problem is as an aggregate model using the cumulative demands and supplies. The aggregate solution will provide a unique blend recipe but it is usually infeasible at some point in the time horizon. In order to avoid this, multi-time period models have been used, but this approach leads to multiple global optima solutions and the blend recipe for the same product is not uniform along the time horizon which raises operational common sense questions. Additionally, the multi-time period model has a larger number of equations than the aggregate model which increases the requirements and time to solve the model. Moreover, recent EPA regulations have made the model significantly more nonlinear and more difficult to converge.

A Pinch Point algorithm is proposed here to solve the gasoline blend planning optimization problem. This algorithm consists in solving aggregate models between pinch points encountered in the gasoline blend planning system. The pinch point is defined as the point in time where the demand of at least one component is greater than its supply (Figure 9.1).

5 Figure 2.1: Pinch Point graphical description

6 Research Plan

The research will proceed as follows, taken into consideration that improving the algorithm is an iterative process.

1. Developing the Pinch Point algorithm – Starting with preliminary hypothesis and ideas, building with results, and finishing with well-defined concepts.

2. Testing the algorithm – The following cases will be studied for at least 3 different scenarios: a) Blending 1 product, b) blending 3 products with decision variables, and c) blending 4 products with decision variables.

3. Introducing non-linear constraints – Once having a revised algorithm for the ideal linear blending of the components’ properties (research octane number, Reid vapor pressure, etc.), non-linear equations that predict these properties will be integrated to the model.

4. Determining the limitations of the method – This is an important step because it is used to improve the algorithm.

Current Status

The algorithm currently being used has been able to solve gasoline blend planning optimization problems where 1 product is blended, giving the same objective function as the multi-time period solution. Right now, the algorithm is being tested on a gasoline blend system that produces 3 different grades of gasoline and is subject to minimum and maximum blending rates of each one.

Literature Cited

C.A. Mendez, I.E. Grossman, I. H. and Karobe, P. (2006). A Simultaneous Optimization Approach for Off-line Blending and Scheduling of Oil Refinery Operations. Computers and Chemical Engineering, 30, 614–634.

Kelly, J. (2003). Supply and Demand-Order Event Handling in Discrete Time Closed-Shop Schedule.

Li, J. and Karimi, I. (2011). Scheduling Gasoline Bending Operations from Recipe Determination to Shipping Using Unit Slots. Industrial and Engineering Chemistry Research, 50, 9156–9174.

Thakral, A. (2009). Optimal Sequencing of Gasoline Blending with Agent Based Modelling and Simulation. In Master thesis project report, GMC Centre for Engineering Design, McMaster University, Canada.

7 Poster Slides

Slide 1 Slide 2

Slide 3 Slide 4

Slide 5 Slide 6

8 3 Zhiwen Chong ‡

Research title: Dynamic Optimization under Partial Plant Shutdowns Advisor: Dr. C.L.E. Swartz Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

A systematic control strategy is proposed for the optimal operation of multi-unit systems undergoing a partial shutdown. This entails manipulating the degrees-of-freedom available during (and after) the shutdown, such that production is restored in a cost-optimal fashion, while meeting all safety and operational constraints.

In this work, we investigate the coordination of buffer tanks, production rates and recycle streams during a partial shutdown. The problem is cast as a differential-algebraic-equation (DAE) based dynamic optimization problem. A multi-tiered economics-based Model Predictive Control (MPC) scheme serves as the basis for implementing the optimal policies in the presence of disturbances and plant-model mismatch. A nonlinear observer, the Constrained Unscented Kalman Filter (CUKF), is used to estimate states and fictitious disturbance terms in order to moderate the effects of mismatch. In related work, we also propose efficient integer formulations for handling switched behavior arising from induced shutdowns and other discontinuities associated with partial shutdowns.

Background

In a typical chemical plant, raw materials are transported through a number of processing units to be fashioned into some end-product. A shutdown in an intermediate unit constitutes an disruption in the processing chain, which can adversely affect the plant’s ability to continue operating. A partial shutdown is a type of circumscribed plant unit shutdown that permits the rest of the plant to continue operating to some degree. Under such a scenario, it is frequently possible for an operator to pursue a certain course of action to mitigate its effects, including reconfiguration of the process pathways, re-routing material streams, slowing down production, making use of buffer capacities and so on. The severity of a disruption is typically a function of the configuration of the processing units, the redundancies available and the extent of remedial actions taken.

Our aim is to systematize the procedure for handling partial shutdowns by designing an optimal control scheme that will compute control trajectories for equipment in unaffected parts of the plant, during (and after) a shutdown, with the view of restoring the system to its pre-shutdown state in a cost-optimal way. Restoration is accomplished via adjustments of production rates, recycles and buffer levels.

‡This student will be graduating in the near future and is available for employment interviews.

9 Formulations for representing the partial shutdown are presented in Chong and Swartz [2009]. A multi-tiered optimization method is introduced to handle the problem of nonunique optimal trajectories. An MPC-type feedback controller was used to implement the computed strategies. This controller represents a transient “partial-shutdown controller” which takes over from the nominal control system at the beginning of a shutdown, implements control policies to restore the system to its nominal operation, and then transfers control back to the production control system.

All the mathematical modeling in this work was accomplished using an in-house modeling tool, a Modeling Language for Dynamic Optimization, MLDO (Chong and Swartz [2006]).

State Estimation and Plant Model Mismatch In a complex plant, the full states of the system are often not directly measurable. State estimation techniques offer a model-based approach for reconstructing the current state of the system from available plant measurements. The Extended Kalman Filter (EKF) is one such technique that is widely applied in industry. In this work, we employ a novel configuration of a filter known as the Constrained Unscented Kalman Filter (CUKF), due to Julier and Uhlmann [1997]. The CUKF is a modern derivative-free nonlinear observer with comparable computational complexity vis-`a-visthe EKF, but produces estimates with a higher order of accuracy for nonlinear models by eschewing the latter’s model linearization step. The bound constraints on the states are handled by solving a Quadratic Program (QP) that projects the estimated states into the feasible space.

In order to moderate the effects of plant-model mismatch, we simultaneously estimate states and uncertain parameters by means of a standard augmentation of the filter’s state vector with a parameter vector. For cases in which the sources of the mismatch are unknown (e.g. structural mismatch, persistent stochastic disturbances, etc.), the additive state disturbances are recursively estimated (MacGregor et al. [1988]). These disturbances are then incorporated back into the nonlinear controller model as biases. This provides a correction of the controller’s notion of the plant.

In our control framework, an economics optimization problem is solved in which hard endpoint target constraints are enforced in order to drive the plant to its original operating point post-shutdown. However, if a sufficiently large disturbance enters during the period of transience, it may render such endpoint targets infeasible. We attempt to address this problem by introducing a “dynamic feasibility” tier in our multi-tiered approach in which we solve for feasible endpoint targets in the first tier, fix them, and solve an economics problem in the next tier. This strategy is intended to enable the controller to move toward the next best feasible endpoint, with as little compromise in the economics as possible. This represents a general technique for handling terminal constraints and one-step ahead estimates in MPC control optimization problems.

Discontinuous Formulations for Shutdowns The optimizer will on occasion produce an operating policy that prescribes the shutting off of

10 material flows to upstream/downstream units–effectively shutting them down–to accommodate the original shutdown. This phenomenon we refer to as an “induced shutdown”. Induced shutdowns usually occur in response to long shutdown durations. A single buffer tank has the capacity to buffer shutdowns for a limited time before it overflows or empties. Therefore, when a long shutdown occurs, it is sometimes necessary to throttle down the production upstream (or downstream) in order to keep from violating the level constraints in the buffer tanks. In doing so, inlet flowrates to a process unit may dip below their thresholds and induce a shutdown. Also, instead of gradually reducing material flows over time, the optimizer may find it more profitable to suddenly shut down upstream/downstream production for a short period of time. In order for the optimizer to properly disincentivize this scenario, it is necessary to penalize induced shutdowns in the objective function by accounting for their true cost. This gives rise to a discontinuous economic term, which we handle using a parsimonious mixed-integer formulation based on work by Kelly and Zyngier [2007]. Constraints are also proposed for enforcing a minimum shutdown duration (a limit arising from the physical constraints of the plant). This simultaneously serves as an aggregation strategy, which can improve the solution efficiency of the mixed-integer problem. A proof-of-concept mixed-integer model-based control framework was proposed for demonstrating the above formulations (Chong and Swartz [2011]).

Literature Cited

Chong, Z. and Swartz, C. (2006). A modeling language for dynamic optimization. In 56th CSChE Canadian Chemical Engineering Conference, Sherbrooke QC.

Chong, Z. and Swartz, C. (2009). Model-based control of multi-unit systems under partial shutdown conditions. In Proceedings of the American Control Conference, St Louis MO.

Chong, Z. and Swartz, C. (2011). Discontinuous modeling formulations for the optimal control of partial shutdowns. In IFAC World Congress. Milan, Italy.

Julier, S. J. and Uhlmann, J. K. (1997). A new extension of the Kalman Filter to nonlinear systems. In AeroSense: the 11th Int. Symp. on Aerospace/Defence Sensing, Simulation and Controls.

Kelly, J. and Zyngier, D. (2007). An improved MILP modeling of sequence-dependent switchovers for discrete-time scheduling problems. Industrial and Engineering Chemistry Research, 46, 4964–4974.

MacGregor, J., Kozub, D., Penlidis, A., and Hamielec, A. (1988). State estimation for polymerization reactors. In Dynamics and Control of Chemical Reactors and Distillation Columns. Selected Papers from the IFAC Symposium,, pp. 147 – 52, Oxford, UK.

11 Poster Slides

Dynamic Optimization of Partial Shutdowns - Z. Chong & C.L.E. Swartz Dynamic Optimization

Definition (Partial Shutdown) Terminal Constraints – Restoration Shutdowns that can be decoupled from the rest of the plant (through the use of Dynamic Optimization Problem

redundancies, production rate control and reconfiguration of process pathways). xss

max state Delignification Φecon (Objective) d x Hi-Q Header Drumwasher s.t. f x, z, u, θ (Model) F1 d t = ( ) u ! g x, z, u, θ 0, input ss !shut !shut shut ( ) (Constraints) F6 F7 ≤ y = C x + Dz, (Outputs) Digester ! shut where x, z = state variables, u = control : Screening Suppose !shut variable, y = output variables, Blowtank #1 Blowtank #2 disturbance renders original 2 3 θ = parameters. m F 5 m F 1 F 2 steady-state targets (xss, uss)

m3 MPC scheme solves dynamic infeasible in model. Sealtank optimization problem repeatedly. estimated (unconverged) F4 parameter θ drives MPC reconstructed States & parameters prediction infeasible if held from plant measurements on-line constant throughout horizon. using Constrained Unscented Kalman Strategies Filter (CUKF). Recourse: relax using a feasibility optimization problem! (dynamic Manual way: operator takes compensatory action during the shutdown and used for restoring Terminal constraints feasibility tier) restoration periods. May lead to significant resource wastage. a plant to pre-shutdown targets. Systematic way: computer algorithm activates and calculates an optimal set of control actions that will keep the plant operational during the shutdown. Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium Slide 1 Slide 2

Multi-Tiered Optimization – for Multiple Objectives, Non-Unique Solutions Optimization of Shutdown Restoration Time

Plant measurements 45 24.01 60 Estimated states, Application 40 parameters Dynamic Feasibility Tier Find minimum restoration 24 40 35 23.99 20 min x(N) xss (Relax terminal state) 0 5 10 0 5 10 0 5 10 time for preparedness to future H vs. time H vs. time H vs. time Tier 1: Dynamic Feasibility (Φfeas) || − || 1 2 3 u N u Solve for dynamic feasibility. Find ( ) ss (Relax terminal controls) 20 75 77 || − || upsets. feasible terminal constraints. Relax θ(k + 1) θest (Relax parameters) 18 parameter estimate. || − || 70 76.5 s.t. θ k θest Mixed Integer problem due to 16 ( ) = 65 76 Feasible terminal endpoints 0 5 10 0 5 10 0 5 10 H vs. time H vs. time H vs. time Feasible parameter estimate discrete nature of time. 4 5 6 200 (fixed) Tier 2: Economics (Φecon) 150 100 Find maximum economics MIP cuts proposed for 100 achievable. 100 increased solution efficiency. 50 0 50 0 5 10 0 5 10 0 5 10 F vs. time F vs. time F vs. time Optimal Economics (fixed) Kelly-Zyngier constraints used 1 2 6 Tier 3: Off-spec products (Φqlty) 200 40 Find minimum tolerable deviation for efficient formulation. 80 100 20 from product quality targets. 60 40 0 0 Multi-tiered optimization used. 0 5 10 0 5 10 0 5 10 F vs. time F vs. time F vs. time 4 8 10 Minimum target deviation (fixed) Tier 4: Input Effort (Φeff) 1000 Find an input trajectory Minimize restoration time 60 80 500 Why not use a weighted objective? whose movements are pe- 40 60 nalized. 20 40 0 max(w1Φfeas + w1Φecon + w1Φqlty + w1Φeff) Optimal time 0 5 10 0 5 10 0 5 10 F vs. time F vs. time I vs. time 12 14 out Not obvious how to select w1, w2, w3, and w1; optimizer may trade-off objectives in unpredictable Smooth control Maximize economics ways. profiles For fast restoration, production To plant: u Optimal economics Why multi-tiered? throttled down drastically during Progressively searches for solutions within optimal shutdown, and up during restoration. spaces. Control trajectories (u) embody all objec- Minimize input movement tives, prioritized systematically.

Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium Slide 3 Slide 4

State, Parameter and Disturbance Estimation Constrained UKF Estimation Results (Kraft Plant subset)

Full-state Feedback, no estimation, Profit = $29,644 CUKF State and Parameter Estimation, Profit = $30,178

23.5 23 65 85

Constrained Unscented Kalman Filter 60 23 80 22.5 CUKF Online Estimator 55 22.5 75 22 No derivatives needed, Black box 70 Nonlinear estimator 50 22 65 21.5 45 / simulator / hybrid / DAE 21.5 Constraint handling 60 40 0 2 4 6 8 10 0 2 4 6 8 10 models OK. Easy to implement. 0 2 4 6 8 10 0 2 4 6 8 10

x1 x2 x1 x2 Computationally complexity low, State, parameter, disturbance 25 25 3 16.5 16.5 same as as EKF, O(n ). estimates. 24.5 24 24 16 16 23.5

23 23 15.5 No linearization performed, better MPC Controller 15.5 22.5 22 15 accuracy than EKF on nonlinear 22 15 Partial shutdown 21.5 21 14.5 systems. 21 14.5 handling 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 z1 z z1 z 2 Bound constraints handled by Multi-tiered dynamic 2 optimizer −9.4 solving a quadratic optimization 3.1 −9.5 −9.6 3.08 problem. Control trajectories −9.7 3.06 −9.8 −9.9 States, parameters, disturbance 3.04 Plant undergoing Partial Shutdown −10 3.02 −10.1 terms estimated simultaneously 0 2 4 6 8 10 0 2 4 6 8 10

No measurements from offline p1 p (given observability, sufficient 2 units Plant-model mismatch in parameters p1 and p2. Plant-model mismatch in parameters p1 and p2. measurements). State x unmeasured. CUKF estimates x , p and p . Certain states, parameters Sensor 2 2 1 2 Novel configurations of the CUKF hard to measure (e.g. heat measurements used – augmented system or exchanger fouling factor) Estimation moderates plant-model mismatch by correcting model simple RLS-type parameter Plant-model mismatch parameters and reconstructs missing states. estimation. If set of mismatched parameters unknown, can estimate biases. Similar results can be achieved.

Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium Slide 5 Slide 6

12 Zhiwen Chong

Research title: Project: A Modeling Language for Dynamic Optimization (MLDO) Advisor: Dr. C.L.E. Swartz Date: May 2012

Research Goals

The goal of this project is the development of a Modeling Language for Dynamic Optimization (MLDO) (Chong and Swartz [2006]), a minimalist language for process modeling that can easily generate computer code in different languages, with the desired mathematical transformations applied.

Background

MLDO is a domain-specific language for describing first-principles dynamic optimization problems (that is, optimal control problems involving systems of differential and algebraic equations). Its syntax is minimalist and resembles mathematical notation by design. At the core of the modeling system is a software program that parses a description of a problem (in the MLDO language) and automatically produces code in various computer languages. Depending on the target language selected, the output code can be variously used for simulation, optimization, visualization, analysis or documentation. Support for various (computer) language targets is an important feature, because in a typical nonlinear process modeling/optimization workflow, a single software tool is rarely sufficient for performing all the tasks necessary to obtain a satisfactory solution. Frequently, an entire ecosystem of software programs and libraries (used in some concerted fashion) is required by the modeler.

The MLDO code generator is built on the concept of “metaprogramming”, a technique in which code in one programming language is used to generate code in another. There has been some interest in the process systems engineering community in employing these techniques for improving the quality and speed of software development. An example of a metaprogramming application is ControlH (Englehart [1994]), a control specifications language developed at Honeywell that is capable of generating C or Ada code.

In contrast to conventional programming languages like FORTRAN or C, high-level modeling languages like MLDO are usually declarative rather than imperative; that is, they contain a problem definition rather than the explicit computer instructions required to solve the problem. This effectively decouples the model description from the underlying solution proces. This is an important attribute that enables MLDO to output computer code that is clean, concise and readable. Furthermore, because the MLDO language has almost a one-to-one mapping to pure mathematical

13 notation, it represents a single, universal, and canonical form that is easily transformed into any number of standard computer languages and modeling platforms. Table 3 shows target languages that the software implementation of MLDO is capable of generating code for.

Task Languages/Platforms Dynamic optimization (simulta- AMPL (orthogonal collocation, Euler), FORTRAN/C++ (using neous) DAEOC libraries), MATLAB (using INTLAB or complex-step derivatives for automatic differentiation) Simulation/DAE integration gPROMS, MATLAB (.m file), C (mex code), AMPL Symbolic analysis Maple (algebraic-only) Documentation LATEX Visualization MATLAB (.m plotfile), HTML (Sparklines), Python (Matplotlib) Solution Storage Format JSON

Table 3.1: MLDO language targets

By adopting a one-to-many (as in one model definition, many target languages) approach, MLDO represents a single entry point to process modeling. From a business perspective, this approach allows organizations to protect their investments in modeling effort and time—and to some extent, prevent vendor lock-in—by enabling them to switch to newer modeling platforms as they emerge. With the code processing and generation infrastructure already present in MLDO, new target languages can be added to the MLDO code generator’s repertoire with relatively little effort. This flexibility leads to easier migrations, without entailing the manual re-development of an entire model on the new platform of choice (which, in the context of very large models, may require significant effort and is prone to human errors). Any transformations done at the mathematical level (e.g. numerical variable/equation scaling, algebraic transformations, etc.) are preserved, which is also an advantage from a model maintenance and sustainability point of view. Figure 3.1 shows the transcription of a mathematical model into the MLDO language.

Mathematical Notation MLDO Notation Optimization of a semi-batch reactor model Optimization of a semi-batch reactor model

min [−x2(tf )] minimize: -x2(tf); dae: $x1 = -k1*x1; s.t. x˙ = −k x 1 1 1 $x2 = k1*x1 - k2*x2; x˙ 2 = k1x1 − k2x2 k1 = k10*exp( -E1/(R*T) ); k1 = k10 exp (−E1/(RT )) ⇒ k2 = k20*exp( -E2/(R*T) ); k2 = k20 exp (−E2/(RT )) init: x1(0) = 0.53; x2(0) = 0.43; x1(0) = 0.53 x2(0) = 0.43 diffvars: x1; x2; controlvars: T; where x , x = differential variables; T = control 1 2 algvars: k1; k2; variable; k , k = algebraic variables; and E , E , 1 2 1 2 params: E1; E2; k10; k20; R; k10, k20,R = parameters, tf = final time.

Figure 3.1: Transcription of a mathematical model into MLDO form – from which computer code in various languages can be automatically generated.

14 MLDO can also serve as a platform that allows for experimentation with various numerical software configurations and formulation ideas. It enables the user to focus on modeling aspects without having to repeatedly deal with the lower-level boilerplate code. MLDO also has a extensible architecture for applying custom mathematical transformations on MLDO models, and can be used as a reformulation engine to alter model formulations.

A variety of dynamic optimization software exists in the market (ACADO, DAETools, PROPT, APMonitor, gPROMS, JModelica, DAEOC, TACO etc.), but MLDO is currently unique in its aim to be a modeling system that targets other modeling systems. The MLDO modeling system is written entirely in Python, a multi-paradigm programming language.

Current Status

Work is currently under way to convert the internals of the MLDO language into an object- based system, which would allow for more intelligent code transformations and will make the model more amenable to analysis (e.g. graph-theoretic routines for analyzing variable/equation dependency, degrees-of-freedom, etc.). A real-time, cross-platform, web-based (using AJAX/Comet web technologies) front-end for the modeling system is currently under development. Language features such as support for multidimensional array variables are currently in the testing phase. Generation of code for multiple-shooting is planned. A prototype version of MLDO was used to solve large-scale dynamic optimization problems in Chong [2012]. Availability is currently limited to specialized deployments within the research group.

Literature Cited

Chong, Z. (2012). Dynamic Optimization Formulations for Plant Operation under Partial Shutdown Conditions. PhD thesis, McMaster University.

Chong, Z. and Swartz, C. L. E. (2006). A modeling language for dynamic optimization. In 56th CSChE Canadian Chemical Engineering Conference, Sherbrooke QC.

Englehart, M. (1994). High quality automatic code generation for control applications. In Proceedings., IEEE/IFAC Joint Symposium on 7-9 March 1994, pp. 363 – 367, Tucson, AZ, USA.

15 Poster Slides

A Modeling Language for Dynamic Optimization MLDO Language

Mathematical Notation Optimization of a semi-batch reactor model MLDO Notation Code Generated Optimization of a semi-batch reactor model

MLDO min x2(t ) − f minimize: -x2(tf); MATLAB (.m and mex C) s.t. x˙ 1 = k1x1 dae: $x1 = -k1*x1; −  $x2 = k1*x1 - k2*x2; What is it? x˙ 2 = k1x1 k2x2 AMPL (IPOPT, CPLEX, − k1 = k10*exp( -E1/(R*T) ); A minimalist math-like k1 = k10 exp ( E1/(RT )) Gurobi, KNITRO, − k2 = k20*exp( -E2/(R*T) ); k2 = k20 exp ( E2/(RT )) init: x1(0) = 0.53; optimization modeling language. CONOPT, Bonmin) − x1(0) = 0.53 x2(0) = 0.43; Generates code in other languages Maple x2(0) = 0.43 for solution, visualization, and diffvars: x1; x2; gPROMS where x1, x2 = differential variables; T = controlvars: T; documentation. control variable; k1, k2 = algebraic variables; algvars: k1; k2; and E1, E2, k10, k20,R = parameters, tf = params: E1; E2; k10; k20; R; Complicated mathematical DAEOC final time. transformations easily applied. (FORTRAN/C++) LAT X, JSON, Sparklines, Why? E Object Matplotlib, SUNDIALS Object Transformations with code Parser Code Assembly Single entry point to modeling. DAE MLDO with tokens Custom Mathematical blocks Output code in Tokenization via a Using a template DAE interface etc. Model Model Transformations (add-ons) target language formal grammar tool Avoid tool lockdown. In nonlinear Text transformations Step 1: Parsing Step 3: Code Assembly optimization, 1 or 2 software Step 2: Transformations packages rarely adequate – need MLDO Code Generator an ecosystem of tools.

Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium

Slide 1 Slide 2

Code Visualization of optimal solution

Generated MATLAB code Generated C code MATLAB Sparklines

f u n c t i o n [res , f l a g , n d a t a ] = DAE ramirez (... #include

Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium

Slide 3 Slide 4

Web-based Interface Current status/Future work

Move to a more intelligent internal object-based system for language elements. Permits future analysis of variable/equation dependencies, degrees-of-freedom etc. Multidimensional arrays of arbitrary dimensions, using set constructor notation. For instance:

xi,j = 2yi where i = 1, . . . , m, j = 1, . . . , n, and i 2j ≥ can be written in MLDO as:

x[i,j] = 2*y[i], i in 1..m, j in 1..n: i >= 2*j { } Generation of code for multiple-shooting dynamic optimization. Preliminary work on cross-platform Run locally or from the cloud. web interface. Built with CherryPy, Cheetah and Real-time interaction through jQuery. AJAX/Comet technologies.

Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium Zhiwen Chong & C.L.E. Swartz McMaster Advanced Control Consortium

Slide 5 Slide 6

16 4 Brandon Corbett

Research title: Model Predictive Quality Control of Batch Processes Advisor: Dr. P. Mhaskar Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

Batch processes present interesting challenges from a controls perspective. Some of these challenges include the inability to obtain online measurements and the nonlinear nature of batch dynamics. With these factors in mind, the first goal of this work was to develop a data-driven modeling approach to both describe nonlinear batch dynamics and also infer unmeasurable quality values. Having theses models, the subsequent goal was to implement a control scheme to utilize the process insight provided by the models. Next this work will be expanded upon by developing techniques to explicitly handle mid-batch events (such as ingredient addition).

Background

Batch operations are industrially important in the production of many high valued and quality critical products. Examples of such products include pharmaceutical, bio-chemicals, and high quality polymers. In batch processes, a reaction vessel is first charged with ingredients, which are subsequently reacted for some finite duration. By nature, this type of process moves through a large range of operating conditions. The goal for these process is to reach some predefined terminal batch quality. Controllers are used to alter the progress of the reaction. By manipulating inputs such as heating, mixing, and ingredient addition, etc. the final quality can be influenced. Because of the high value nature of the products, controllers which can improve batch success (ability to reach the target final quality) have high economic value.

The control of batch systems presents a number of unique challenges. Unlike continuous process, batch processes inherently lack equilibrium operation conditions. As a result, many traditional control techniques, which focus on stabilizing and maintaining operations at an equilibrium point, are not applicable. Unavailability of process measurements further complicates batch control. In particular, it is common that the quality measurements (relevant to terminal quality targets) are not available during the batch. (Aumi et al. [2011])

Recent work has focused on the problem of directly controlling final quality. This objective was achieved in two steps. First, a data-based model of the process dynamics was fit (using a previously developed modeling technique). Second, a statistical (Partial Least Squares) model was used to predict terminal quality based on output (measurable process variable) trajectories. At any given instance during the process, for a given future input trajectory, the output trajectory was predicted

17 using the dynamics model. Then, using this output prediction, the terminal quality could be predicted using the quality model. Thus, the two models used in conjunction provided a prediction of final product quality at every sampling instance from batch initiation to batch termination.

Having developed these models, they were implemented in a model predictive control scheme to directly control quality. At each sampling instance, a real time optimization problem was solved. The objective of this optimization was to minimize the deviation of the predicted quality (predicted using the models) from the target quality. The decision variables in this problem were the values of the input trajectory at each sampling instance from the current time to batch completion. After solving this minimization at each sampling instance, the first optimal control move was implemented. Then the optimization was repeated with the new measurement for the subsequent sampling time.

The above described control scheme was was implemented in simulations of an industrially relevant batch polymerization reaction (for the production of nylon-6,6). The results showed a significant reduction in variance of the two key quality variables considered (when compared to traditional PI controllers currently used by the industry)(see figure 4.1). (Aumi et al. [2012])

Trajectory tracking 200 Quality-based MPC Desired quality (mol/g)

2 100 NH R

0 0.4 0.6 0.8 1 1.2 1.4 MW 104 ·

Figure 4.1: Comparison of the final qualities obtained from trajectory tracking and quality-based MPC design for 21 new initial conditions.

Research Plan

It is common in batch processes for the recipe to call for an event, at some point in time, part-way through the batch. These include events such as adding ingredients or changing operating conditions. When such changes occur to the process, the underlying dynamics of the system change. One of the directions of proposed research is to focus on a developing control design that explicitly handles such changes in the underlying dynamics of the system. Another direction includes considering processes where accounting for spatial changes/number of particles is important. Finally, the research will also aim at generalizing these ideas to the case of continuous process operation.

Current Status

Current work employs simulations of deterministic process models for testing and validation. To this end a semi-batch emulsion polymerization process has been identified. In this process, three distinct phases exist: aqueous phase, monomer droplets, and micells. One of the key quality parameters of

18 the final product is the particle size distribution. In order to obtain a large particle size distribution, the particular process being considered uses a mid-batch shot of new initiator. This mid-batch event causes a distinct change in both the state of the system and the dynamics of the system. Several literature sources involving emulsion polymerization models have been reviewed. A deterministic model of the process taken from literature has been established (Marinangelo et al. [2011]). This model is currently being implemented and tested using Matlab.

Industrial Collaboration

We are currently seeking collaborative opportunities for this work.

Literature Cited

Aumi, S., Corbett, B., and Mhaskar, P. (2011). Data-based modeling and control of nylon-6,6 batch polymerization. In American Control Conference (ACC), 2011. IEEE.

Aumi, S., Corbett, B., and Mhaskar, P. (2012). Model predictive quality control of batch processes. In American Control Conference (ACC)(Accepted), 2012. IEEE.

Marinangelo, G., Hirota, W., and Giudici, R. (2011). Semi-batch emulsion copolymerization of styrene and butyl acrylate for production of high solids content latexes: Experiments and mathematical model. Chemical Engineering Science,.

Russell, S. A., Robertson, D. G., Lee, J. H., and Ogunnaike, B. A. (1998). Control of product quality for batch nylon-6,6 autoclaves. Chem. Eng. Sci., 53(21), 3685 – 3702.

19 Poster Slides

Batch Processes Batch Processes Batch Processes Control Quality Predictions Control Objective: Reach a desired end point quality by batch termination • Once the model has been developed it can be used to predict the end-point quality . Difficult because quality variables typically not measured during batch of new batches Traditional control difficult because of the unique properties of batch dynamics 1 Initial measurements and online process measurements are unfolded to form a • . Batch dynamics are highly non-linear, time-varying, span a wide range of new row in the same format as the regressor matrix (ie: Z0 X ) operating conditions, lack of equilibrium points. 2 The PLS model is used to predict quality values from that new row   Standard approach is to use controllers to track pre-defined trajectories of The Missing Data Problem • measurable process variables In order to make a quality prediction, a complete trajectory of online measurements . Even with perfect tracking, desired quality might not be reached is needed Inferential Model to predict end-point quality Build multiple models and use a new one for each sampling time in the batch • • . Models fitting is accomplished by first unfolding process measurements, X, in a . Early models may be inaccurate becasue they do not capture effects of the batch wise manner, then adding initial measurements by horizontal concatenation majority of the batch duration Z0 X Use missing data algorithm to fill in missing data • 1 . Assumes that the correlation structure between the collected measurements and   future measurers for the new batch is the same as in the training data . . Time 1 Time K . ··· Batches

B Nonlinear Model Solution 1 ... M1 ... JK Initial measurements Online measurements Fill in missing data with a nonlinear process dynamics model . Unfolded matrix is regressed (using PLS regression) onto the quality matrix to • The resulting model provides a causal, input-output description of quality at yield a model that relates initial measurements and process conditions to quality • any sampling instant during the batch Brandon Corbett Siam Aumi Prashant Mhaskar Nylon-6,6 Batch Quality Control Brandon Corbett Siam Aumi Prashant Mhaskar Nylon-6,6 Batch Quality Control McMaster Advanced Control Consortium (MACC) November 8, 2011 1 / 6 McMaster Advanced Control Consortium (MACC) November 8, 2011 2 / 6 Slide 1 Slide 2

Batch Processes Batch Processes Nylon-6,6 Batch Polymerization Quality Model Development This modeling approach was demonstrated using simulations of a nylon-6,6 batch PLS regression was applied to the database to identify the inferential quality model polymerization reactor Data Pre-Processing: Traditionally in PLS variables are scaled to have unit variance Polymerization reaction carried out in a • • Non-unit variance can be used to increase the influence of given variables jacketed autoclave with a vent Fvent • Weights were assigned based on the importance of each phase in final quality Carboxylic end groups (C) react with • Steam • Vapour Weights of 6, 2, and 4 were applied the the initial conditions, boiling phase, and amine end groups (A) producing a polymer • Liquid chain link (L) and a water molecule (W) Q finishing phase ↑ C + A L + W Condensate Model Structure: 24 principal components were used (based on minimum root mean The reaction takes place in three phases: ↑ Sensors: T , P squared error (RMSE) in predicting quality of the validation set) • heating, boiling, and finishing ↓ Nonlinear 300 Nonlinear Data-driven Data-driven Supervisor

1

Deterministic process used to simulate the process 4 • 200 10 ·

. Highly nonlinear and discontinuous (mol/g) 2 MW . Inputs: Pj , v, measurements: T , V , η NH R 100 . Quality variables: MW , RNH2 (number average mol weight, residual amide conc) 0.5

The deterministic model was simulated 80 times from random initial conditions to 1 5 10 15 20 25 30 1 5 10 15 20 25 30 produce an artificial batch database for subsequent model development Validation Batch Number # Validation Batch Number #

Brandon Corbett Siam Aumi Prashant Mhaskar Nylon-6,6 Batch Quality Control Brandon Corbett Siam Aumi Prashant Mhaskar Nylon-6,6 Batch Quality Control McMaster Advanced Control Consortium (MACC) November 8, 2011 3 / 6 McMaster Advanced Control Consortium (MACC) November 8, 2011 4 / 6 Slide 3 Slide 4

Batch Processes Batch Processes MPC formulation Closed Loop Results

Control Objective: reach a desired endpoint qdes by batch termination The MPC previously described was simulated 21 times from new initial conditions Remarks: MPC formulation Initial guess for the input trajectory • 250 Trajectory tracking was set to the nominal at t = 0 and Quality-based MPC K Desired quality the tail of the previous solution for all 200 min (ˆq qdes )0 Ψ (ˆq qdes ) + ∆u0 (i) Φ∆u (i) u(k) U − − other sampling instances 150 ∈ i=k (mol/g) X 2

The computation time for the first NH 100

s.t. :ˆy (k) = y (t) • R sampling instant was 1.5 seconds L 50 ˆ MPC inputs follow same general yˆ (k) = wl (k) βl x¯ (k) • 0 trend as trajectory tracking but 0.4 0.6 0.8 1 1.2 1.4 = l 1 MW 104 X improve quality · 0 = 0( ) ˆ( + ) 0( + ) ˆ0 ( ) 0 xfuture u k y k 1 u k 1 y K Standard deviations from the desired ··· • Trajectory tracking 1.6 qˆ = xpast xfuture Λ  quality value 1 Quality-based MPC 1.4 (psi) (g/h)

MW RNH 3

2 6

10 1.2 10 notes:   · 0.5 · j v Trajectory 3392 69.69 P 0 1 xpast0 = z(0)0 y 0(0) u0(0) y 0(1) u0(1) y 0(k) which is known Trajectory tracking QBMPC 1240 40.7 Quality-based MPC • 0.8 ··· 0 at the start of the optimization 0 1 2 3 0 1 2 3   Time (h) Time (h)

Brandon Corbett Siam Aumi Prashant Mhaskar Nylon-6,6 Batch Quality Control Brandon Corbett Siam Aumi Prashant Mhaskar Nylon-6,6 Batch Quality Control McMaster Advanced Control Consortium (MACC) November 8, 2011 5 / 6 McMaster Advanced Control Consortium (MACC) November 8, 2011 6 / 6 Slide 5 Slide 6

20 5 Buddhadeva Das

Research title: Offset-free MPC: Design and Application For Vapor Com- pression Cycles Advisor: Dr. P. Mhaskar Date: May 2012 Industrial Collaboration: Johnson Controls, Inc.

Research Goals

Design and implementation of an Offset-free Model Predictive Controller and its application for Vapor Compression Cycles used at the building temperature control.

Background

In a Vapor Compression Cycle (VCC) used in a HVAC system, the refrigerant enters the compressor as a vapor and is compressed to a higher pressure, resulting in increase of the vapor temperature to superheated condition. This superheated vapor then enters a condenser where it is condensed to sub-cooled liquid. The coolant used is the atmospheric air blown by a fan. This then flows into an expansion valve where it forms two phase refrigerant mixture at a less temperature. The refrigerant is passed through an evaporator which absorbs heat from the building air. The building receives the air at a required supply air temperature which is then distributed by air distributors installed in the building. The refrigerant gets heated up and enters the compressor as saturated vapor.

The control objectives in the VCC include the regulation of the refrigerant temperature at evaporator exit and the temperature of the supply air. The building and ambient conditions (i.e. heat loads inside the building and the atmospheric temperature variations) are the key sources of disturbances into the system. The manipulated variables are the compressor RPM and expansion valve opening.

This system is multivariable, has significant interactions and operational constraints. This requires implementation of a model-based controller such as Model Predictive Controller (MPC). The presence of substantial plant-model mismatch, however, exacerbates the off-set observed in the implementation of nominal MPC designs. The resulting offset can impact the tracking performance as well as impact negatively on the energy efficiency of the system.

Offset in both linear and nonlinear MPC arise because of uncertainties in the predictive mechanism used for control. A linear MPC uses linear models derived around an operating point. When this model is used for prediction at another operating point mismatch occurs in the prediction and the controller refuses to move the plant to setpoint because the prediction says that the plant is already at the setpoint. However, situation does not improve by deploying a nonlinear MPC because it too has mismatch in prediction arising from different types of uncertainties in the nonlinear models. In

21 case of VCC which comprises of nonlinear unit operations with a complete recycle, the parametric and structural uncertainties result in a significant offset in the operation of the MPC both linear and nonlinear.

Linear MPC however has an established way of making the MPC offset-free ([Muske and Badgwell, 2002]). As the plant output is observed(measured by sensor) and found to have a discrepancy with the prediction, the difference is used to adjust the next prediction. This is achieved by introducing additional variables named as disturbance variables which is unobserved but is the cause of this discrepancy. Degree of freedom analysis dictates that the number of such variables must be same as the number of observed outputs. As the plant mismatch itself is not expected to vary much in a smaller window of operation, it is logical to assume that the disturbance remains constant between two successive time.

With the above assumptions the state space representation of the linear system is modified by appending the disturbance variables with the state variables and creating an augmented state space structure. The constant disturbance assumption gives rise to the additional equations to determine the state of the augmented variables. The original state equations describing the process now contains the disturbance variables with some constant gains to account for the offset in prediction. This augmented state space system is now ready for an observer mechanism like Luenberger Observer or Kalman Filter to get the total augmented state estimated. This results in the process state variables properly modified to reflect the offsets eliminated.

As the state space representation contains equations for the states and outputs separately, it is possible to introduce the disturbance variables as state variables or output variables or both. However, in any such configuration the associated gains have to be properly chosen. Although the system is shown to be asymptotically stable for any stable observer, it is important to chose them appropriately for proper closed loop performance.

The tuning of the associated steady state gains that can minimize the prediction offset becomes difficult when the size of the system is large. Even as a 2X2 system like VCC it is difficult. There is a need for estimating the gains as they may need to be adjusted at different points of operation. So a tuning guideline needs to be developed which is a primary goal of this research. Good results obtained from the simulations done on a first order reactor system can be extended to the VCC MPC to make it offset-free with good dynamic performance.

The offset-free MPC therefore will contain the prediction mechanism described as above augmented state space system. The prediction will be used in the MPC objective function aimed at minimizing the state from the setpoints and the movements in the plant inputs. Constraints both on the inputs and outputs can be enforced by the optimizer used by the MPC.

Research Plan

22 The research will likely proceed as described in the following.

1. Offset-free MPC design – The search for an offset-free MPC for VCC requires further

investigation on linear and nonlinear MPCs where Tuning Guidelines for Gθ and Gφ will be developed based on an appropriate theory like H and study of eigenvalues. Once good ∞ results are obtained they can be extended to Kalman filter because of their ability to consider noise covariances. This can be further used to develop offset-free mechanism for Robust and Non-Linear MPCs where estimated disturbance variable can be an estimation of uncertainties bound. Output feedback problem can be subsequently taken up.

2. Application to the VCC – The results of the MPC design from the study will subsequently be applied to the nonlinear model of the VCC currently being used in our group. Several issues such as measurement noise, structural mismatch (naturally present when identifying an input-output model for this example) as well as constraints on the rate of change of input variables (such as the expansion valve-to minimize valve wear and tear) will be accounted for and implemented. The overall goal is the build a ‘ready to use’ MPC design that can eventually be ported to test-bed applications.

Current Status– Basic functionality of offset-free design has been simulated and well understood. Basic offset-free mechanism based MPC is also applied to VCC simulation test bed with satisfactory results([Wallace et al., 2012a], [Wallace et al., 2012b]). The tuning method simulations are underway with a good theoretical understanding of the underlying mechanism.

Industrial Collaboration

This project is in collaboration with Johnson Controls Inc, and will benefit substantially from the insight and guidance from the JCI representatives Tim Salsbury and John House.

Literature Cited

Muske, K. R. and Badgwell, T. A. (2002). Disturbance models for offset-free linear model predictive control. Journal of Process Control, 12, 617–632.

Wallace, M., Das, B., and Mhaskar, P. (2012a). Offset-free Model Predictive Control of Vapor Compression Cycle. . Journal of Process Control, final submission.

Wallace, M., Das, B., and Mhaskar, P. (2012b). Offset-free Model Predictive Control of Vapor Compression Cycle. . American Control Conference, presented.

23 Poster Slides

Introduction Offset Offset in linear MPC When a non-linear plant uses a linear model to calculate future moves • Offset-free Model Predictive Control: for the MPC, it results in an offset due to plant model mismatch. Design and Application to Vapor Compression Cycle A single-input, single-output system: by Buddhadeva Das, Supervisor: Dr Prashant Mhaskar • . x˙ = f (x) + G(x)u which starts at x = 0, u = 0, x˙ = 0 ss ss . Consider a step change u that takes the plant to a new steady state xnl ss ss ss ss ss . At steady state x˙nl = 0 = f (xnl ) + G(xnl )u which determines xnl Current research focus is to provide the best offset-free MPC for Vapor • Compression Cycle(VCC) used in HVAC systems Let us do the same for the linearized version of the plant: • VCC system has a compressor, a condenser, an expansion valve and an . x˙ = ax + bu which starts at x = 0, u = 0, x˙ = 0 • ss ss evaporator connected sequentially by pipes and a refrigerant flows . Consider a step change u that takes the plant to a new steady state xl ss ss ss ss buss through them in a complete recycle . At steady state x˙nl = 0 = axl + bu which determines as xl = − a MPC aims at the regulation of the refrigerant temperature at evaporator • exit and the temperature of the supply air with heat loads inside the In general x ss = x ss , meaning a linear plant will show offset on closed • nl 6 l building and the atmospheric temperature variations as disturbances loop linear MPC VCC system is highly nonlinear, multivariable and has significant • interactions and operational constraints One approach is to use linear MPC with offset-free mechanism which is • Both linear and nonlinear MPC, applied to VCC, show offset because of explained with a simulated CSTR as an example • uncertainties in the predictive mechanism used for control Buddhadeva Das (McMaster) Offset-free MPC 2 / 7 Buddhadeva Das (McMaster) Offset-free MPC 3 / 7 Slide 1 Slide 2

CSTR Disturbance Model Example: a nominal MPC on CSTR showing offset Augmented State Space using Disturbance Model Open-loop step test of CSTR with corresponding MPC Consider a basic linear time-invariant, discrete system: • • xk+1 = Axk + Buk and yk = Cxk Assume disturbances in internal states θ and outputs φ • k k xk+1 = Axk + Buk + Gθθk , and yk = Cxk + Gφφk Assuming constant disturbances, we have θ = θ and φ = φ • k+1 k k+1 k Augmented Disturbance model: •

xk AGθ 0 B — x˜ = θ , A˜ = 0 I 0 , B˜ = 0 , C˜ = C 0 G (1)  k      φ In the open-loop test, blue line is the actual non-linear plant response φ 0 0 I 0 • k   and the green is the approximate linear model response and they are       ˜ ˜ This is the internal model principle representation x˜k+1 = Ax˜k + Bu˜k directionally same but there is a mismatch • ˜ and yk = Cx˜k In the nominal MPC, the blue line is the output variable and the green is • Since the disturbance states are unobserved we can use a predictor • the setpoint to it and there is an offset mechanism like Luenberger Observer or Kalman Filter Using Luenberger Observer, x˜ˆ = A˜x˜ˆ + Bu˜ + L(y C˜x˜ˆ ) • k+1 k k − k The filter L, should be stable, and require the knowledge of G and G • θ φ Since these gain matrices are unknown, they become tuning parameters • Buddhadeva Das (McMaster) Offset-free MPC 4 / 7 Buddhadeva Das (McMaster) Offset-free MPC 5 / 7 Slide 3 Slide 4

CSTR VCC offset-free Offset-free MPC on CSTR Offset-free results for VCC A Luenberger observer is suitably tuned with corresponding MPC The similar approach was taken for the VCC system with appropriately tuned • Luenberger Observer. This shows offset elimination.

— The actual plant and the Luenberger estimator output match on • openloop step test Future Directions A Closed-loop MPC is run with the red line is the setpoint. Offset is 1. Tuning of Gθ based on the study of eigenvalues and H • ∞ eliminated here 2. Extend the above study to Kalman Filter alternative 3. Estimated disturbance variable can be an estimation of uncertainties bound required for nonlinear bounded control 4. Combine other NLMPC methods with the current offset-free 5. Study the output feedback problem 6. Suggest and Implement the best offset-free MPC mechanism for VCC Buddhadeva Das (McMaster) Offset-free MPC 6 / 7 Buddhadeva Das (McMaster) Offset-free MPC 7 / 7 Slide 5 Slide 6

24 6 Miao Du ‡

Research title: Fault Diagnosis and Fault-Tolerant Control of Chemical Pro- cess Systems Advisor: Dr. P. Mhaskar Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

This research aims at developing a fault diagnosis and fault-tolerant control framework to handle equipment abnormalities in chemical process systems. One goal of this work is to identify faulty actuators or sensors in a process control system. In particular, we explore how to utilize the information embodied in a process model to identify the faulty equipment. The other goal of this work is to handle severe actuator faults that preclude the possibility of continued operation at the normal operating point. For this problem, we investigate how to utilize the remaining control action to achieve stable operation during the period of fault rectification. Specifically, we address several issues for the practical implementation of the “safe-parking” approach. The results of this work are expected to help people enhance profitability and safety of chemical process operations.

Background

The last few decades have witnessed significant improvement in efficiency and profitability of chemical process operations due to the advances in automatic control techniques. The increased level of automation, however, also makes process control systems susceptible to equipment abnormalities, such as failures in actuators (e.g., valves and pumps) or sensors (e.g., thermocouples and flow meters). If not properly handled, they can significantly jeopardize the profit of chemical process operations and even lead to safety hazards to facilities and personnel, as well as damages to the environment. These considerations strongly motivate the development of fault detection, fault diagnosis, and fault-tolerant control techniques to deal with various faults in a chemical plant.

There exist several challenges on fault diagnosis and fault-tolerant control of chemical processes. The objective of fault diagnosis is to identify the faulty equipment and the characteristics of the fault, such as the size. Most existing results are passive in the sense that the process data are obtained under the control law designed for normal operation. Therefore, faults may not be isolated if the closed-loop structure does not allow isolation of faults under normal operation (i.e., the process operates under the normal control law). Second, there exist limited results on isolation of sensor faults with an explicit consideration of nonlinear dynamics compared to those for actuator faults. How to utilize the information embodied in a process model to isolate sensor faults is an

‡This student will be graduating in the near future and is available for employment interviews.

25 interesting problem of practical importance. After a fault is isolated, corrective control action should be taken to reduce the effect of faults. Most existing results have studied the problem of preserving normal operation by assuming sufficient residual control action or the availability of a backup control configuration. In practice, however, there exist numerous situations where faults preclude the possibility of continued operation at the normal operating point regardless of the control law used. For example, the failed actuator reverts to a fail-safe position (e.g., complete open or shut). To address this problem, our research group proposed a “safe-parking” approach to handle severe actuator faults. The key idea is to operate the process at an appropriate temporary operating point (a safe-park point) that can enable stable operation during the period of fault rectification and resumption of normal operation after the fault is repaired.

Research Plan

The research will proceed as described in the following.

1. Active fault isolation of nonlinear process systems – In this work, we consider the problem of designing an active fault isolation scheme for nonlinear process systems subject to actuator faults and disturbances (Du and Mhaskar [2012a]). The key idea of the proposed method is to drive the process state to a region which allows isolation of faults not otherwise achievable under normal operation by utilizing control action. To this end, dedicated residuals are generated as fault indicators with an explicit consideration of plant-model mismatch. A fault is isolated when the corresponding residual breaches its threshold. These residuals, however, may not be sensitive to all the faults under normal operation. To make the residuals sufficiently sensitive, a switching rule is designed to drive the process state, upon fault detection, to move towards a different operating point that, for any given fault, results in the reduction of the effect of other potential faults on the evolution of the same process variable.

2. Isolation and handling of sensor faults in nonlinear process systems – This work addresses the problem of sensor fault isolation and fault-tolerant control for nonlinear process systems subject to input constraints (Du and Mhaskar [2012b]). The key idea of the proposed method is to exploit model-based sensor redundancy through state observer design. To this end, a state observer (specifically a high-gain observer) is designed to recover the process state from measured outputs for a generalized class of nonlinear systems. The enhanced applicability of the observer design is then utilized to build a bank of state observers, each of which is driven by a subset of the measured outputs. A residual is generated for each observer, which is sensitive to faults in the corresponding sensors. The faulty sensor is identified when all the residuals breach their thresholds except for the one generated without using the erroneous measurements. Upon fault isolation, the state estimate generated using measurements from the healthy sensors is used by the controller to continue normal operation.

3. Safe-parking of chemical process systems – This work considers several issues on the

26 practical implementation of the “safe-parking” approach. (1) We address the effect of changes in process dynamics on the “safe-parking” design (Du and Mhaskar [2011]). For instance, a chemical reactor often operates in multiple modes, which correspond to different inlet conditions and product quality specifications, by following a production schedule. For a fixed production schedule, it is proposed to operate the process at successive safe-park points as it transits to successive modes. (2) We also consider the case where a failed actuator seizes at an arbitrary position (Du et al. [2012]). For this case, safe-park point candidates are designed for a number of actuator positions. The output of the failed actuator is estimated on-line. This information is then used to choose a safe-park point. (3) In addition to an isolated unit, the “safe-parking” approach is studied in the context of a networked plant (Du et al. [2011]). The objective is to confine the effect of faults and prevent it from propagating through the network. To this end, an algorithm is proposed to identify the units that can absorb the effect of faults in networked processes with parallel and recycle streams.

Current Status

The effectiveness of the active fault isolation scheme has been demonstrated through application to a solution copolymerization process of methyl methacrylate and vinyl acetate.

Industrial Collaboration Sought

We look forward to an industrial chemical process for fault diagnosis and fault-tolerant control designs.

Literature Cited

Du, M., Gandhi, R., and Mhaskar, P. (2011). An integrated fault detection and isolation and safe-parking framework for networked process systems. Industrial and Engineering Chemistry Research, 50, 5667–5679.

Du, M. and Mhaskar, P. (2011). A safe-parking and safe-switching framework for fault-tolerant control of switched nonlinear systems. International Journal of Control, 84, 9–23.

Du, M. and Mhaskar, P. (2012a). Active fault isolation of nonlinear systems. In Proceedings of the American Control Conference, Montr´eal,Canada, in press.

Du, M. and Mhaskar, P. (2012b). Isolation and handling of sensor faults in nonlinear systems. In Proceedings of the American Control Conference, Montr´eal,Canada, in press.

Du, M., Nease, J., and Mhaskar, P. (2012). An integrated fault diagnosis and safe-parking framework for fault-tolerant control of nonlinear systems. International Journal of Robust and Nonlinear Control, 22, 105–122.

27 Poster Slides

2012 MACC Meeting and Workshop Background(

Process control systems subject to equipment abnormalities Fault Diagnosis and Fault-Tolerant Control of ⊲ Efficiency and profitability improved over last few decades Model predictive control (MPC) widely implemented since 1960s Chemical Process Systems ⋄ ⊲ Faults ubiquitously present in a chemical plant

Disturbances Actuator (e.g., valves and ⋄ pumps) faults u˜ xsp u y Controller Plant Sensor (e.g., thermocouples and ⋄ flow meters) faults y˜ uɶ yɶ pɶ Process equipment (e.g., reactors xˆ ⋄ Observer and separators) faults p˜

A fault is an unpermitted deviation of input, output, or parameter of the system ⋄ from the usual conditions Miao Du (Ph.D. Candidate) ⊲ Economic losses, safety hazards, and damages to the environment Supervisor: Dr. Prashant Mhaskar McMaster Advanced Control Consortium U.S. petrochemical industry loses an estimated $20 billion per year1 ⋄ May 15, 2012 1Nimmo, Chem. Eng. Prog., 1995 2 Slide 1 Slide 2

Active fault isolation of nonlinear processes2( Isolation and handling of sensor faults in nonlinear processes3(

Key idea i ⊲ Switching rule Key idea x˜ (tk ): State prediction based on a previous ⋄ estimate ⊲ To drive the process state to a region ux (t), 0 t < tdetection ⊲ To utilize the information embodied in a u(t) = ≤ where residuals become sufficiently ( u (t), t t process model, as well as plant data, to ⊲ Fault isolation logic x˜ ≥ detection sensitive to faults x˜: a fault isolation point (a. a feasible identify a faulty sensor ri (k) > δi (a threshold) implies a fault in the ⋄ ⋄ corresponding two sensors operating point; b. di (˜x) = [0, ..., dij (˜x), State observer Fault isolation mechanism ..., 0]) A fault in y is isolated if r (k) > δ for all ⋄ j i i As the state approachesx ˜, the effect of other i 1, 2, 3 j ⊲ Recovers the process state ∈ { }\{ } ⊲ Consider a fault θj , such as a bias ⋄ faults reduces ⊲ Use measurements from healthy sensors ⊲ Isolation possible before a process is far ˙ x˙i = fi (x) + gi (x)u + wi (x, t) + dij (x)θj (t) ζˆ = Aζˆ + Bφ (ˆx, u(t )) + H(y Cζˆ) 0 k − to continue normal operation q away from the normal operating region ˆ + d (x)θ (t) other faults ζ(tk ) = T (ˆx(tk ), u(tk )) CSTR: three process variables measured ik k ← CSTR: faults in flow rates of two inlet streams k=1,k=j X6 0.05 2 0.5 0.5 0.5 ζ = T (x, u): coordinate transformation r1 > δ1 r2 > δ2 r3 < δ3 ⋄ ⊲ Compute bounds on xi in a moving 1 2 3

Establishes closed-loop stability under an r r r 2 1 ˜ ˜ r horizon fashion r 1 ⋄ appropriate controller Not sensitive enough x x 0 0 0 i i to the fault 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 0 0 Fault isolation and handling x˜i,u 0 1 2 3 4 0 1 2 3 4 Time (min) Time (min) Time (min) Time (min) Time (min) x˜i,l x˜i,u a. A fault in CA is isolated x˜i,l a. Normal operation ⊲ A bank of observers (e.g., three outputs) 1 340 330 0.05 2 1 T 1 Measurements Fault isolated Observer 1: y = [y2, y3] xˆ → Continuation of 320 tk T tk time tk T tk time (K) 2 T 2 0.5 330 normal operation (K) c − − R 2 (mol/L) 1 Observer 2: y = [y , y ] xˆ

1 3 T T ˜ ˜ r r 1 → A 310 Degraded control

a. No fault in θ b. A fault in θ declared C True values j j 3 T 3 performance Observer 3: y = [y1, y2] xˆ 0 320 300 → 0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10 Dedicated residuals equivalently defined 0 0 Time (min) Time (min) Time (min) ⋄ 0 1 2 3 4 0 1 2 3 4 Time (min) Time (min) i i Residuals may not be sensitive enough to faults ⊲ Residuals ri (k) = x˜ (tk ) xˆ (tk ) b. State profiles in the presence and absence of fault-handling ⋄ under normal operation b. Active fault isolation −

2Du and Mhaskar, ACC, 2012, in press 3 3Du and Mhaskar, ACC, 2012, in press 4 Slide 3 Slide 4

Safe-parking of chemical process systems( Conclusions and future work(

Key idea ⊲ Actuator frozen at an arbitrary position5 ⊲ Conclusions ⊲ To operate the process at an appropriate Active fault isolation scheme temporary operating point (a safe-park Position 1 FDI ⋄ . point) that enables stable operation . Enables isolation of faults not otherwise achievable under normal operation . Estimate of the failed ⋄ Position i actuator position Safe-parking of an isolated unit . Sensor fault isolation and handling . ⋄ . ⊲ Schematic of safe-parking operation Exploits model-based sensor redundancy for fault isolation Position m Stability conditions ⋄ x Safe-parking of chemical process systems Integrated fault diagnosis and safe-parking ⋄ HH Safe-parking of networked processes6 Changes in process dynamics, an actuator stuck at an arbitrary position, and xsafe-park ⋄ x the network structure of a chemical plant normal ⊲ Objective: to confine the effect of faults LL ⊲ Future work t Recycle stream tfault trepair Stream 2 a. The fault does not a. Safe-parking b. No safe-parking Handling limited measurements for active fault isolation Stream 1 affect the final product ⋄ Reactor-2 4 Stream 3 Not all the process variables are measured, such as concentrations ⊲ Changes in process dynamics b. Each unit operates at a ⋄ Reactor-1 safe-parking point Number average molecular Separator Explicit consideration of plant-model mismatch for sensor fault isolation 4 weight (kg/kmol) Grade transition of an Reactor-3 ⋄ x 10 ⋄ 3.5 MMA polymerization Robustness to disturbances is of great importance Repair process ⊲ Algorithm for safe-parking design ⋄ 3 Successive safe−parking Identify the units that can absorb the effect of ⊲ Relevant industrial collaboration sought ⋄ Fault Transition Operate the plant at faults ⋄ successive safe-park 2.5 Generate safe-park points for the subsystem We look forward to an industrial chemical process for fault diagnosis and 0 2 4 6 8 10 points ⋄ ⋄ Time (hr) comprising these units fault-tolerant control designs

4Du and Mhaskar, IJC, 2011; 5Du et al., IJRNC, 2012; 6Du et al., I&ECR, 2011 5 Miao Du McMaster University 6 | Slide 5 Slide 6

28 7 Yasser Ghobara

Research title: Modeling, Optimization and Control of Industrial Electric Arc Furnace Operation Advisor: Dr. C.L.E. Swartz Date: May 2012 Industrial Collaboration: Arcelormittal Contrecoeur and McMaster Steel Research Centre

Research Goals

The main aim of this research is to develop a mathematical model and computational strategy for use as an on-line optimization-based decision support tool for EAF operation. A dynamic model of the EAF process is developed and then it is used within an optimization framework to determine the optimal input trajectories. The implementation of the model-based optimization is envisaged to bring significant savings through reduced consumption of electric power, natural gas, oxygen, carbon and fluxes such as limestone and dolomite. This work is an extension of an earlier study by MacRosty [2005].

Background

Electric arc furnaces (EAFs) are widely used in steel industry to produce molten steel from scrap metal. This is a high energy intensive batch process and possesses a high degree of complexity. Constructing a model which considers the melting process, chemical reaction and energy additions would generate different motivating research opportunities. This includes optimization and control of the EAF operation, targeted design for desired product grade and increasing process sustainability through minimizing energy wastage and maintaining the composition of the off-gas components within appropriate ranges.

EAFs involve relatively low levels of automation and rely heavily on operator involvement. As with most industrial processes, operator experience is invaluable for the operation of the process. However, this experience can be limited due to the multivariate interactions and subtle relationships that are easily overlooked. Detailed process knowledge, in the form of a model, makes it possible to take advantage of more complex relationships such as finding the optimal balance of the energy contributions from chemical reactions and electrical power. Several models have been developed and reported in literature (Bekker et al. [1999] and Matson and Ramirez [1999]) based on mass and energy conservation laws, fundamental thermodynamic and kinetic relationships and empirical equations.

The EAF is modeled by MacRosty [2005] as a multi-zone system which comprises Gas, Solid, Slag and Molten Metal zones. Exchanges between zone interfaces are considered through the material and energy balances. Chemical equilibrium is assumed within the slag and gas zones through minimizing

29 the Gibbs energy and therefore, atoms tracking balance was considered. Slag foaming is considered and the foam height is calculated through the duration of the batch. The calibration of this model is very challenging due to the lack of measurements. Therefore, parameter estimation plays a key role in the validation process of the model, in which the model results are calibrated against the plant data. The most sensitive parameters were identified and estimated. The model was then incorporated in a mathematical optimization framework to determine the nominally optimal input profiles for the furnace based on an economic objective function subject to prevailing constraints.

Research Plan

The model developed by MacRosty [2005] utilized a dynamic first principles model. This model comprised 85 differential states and 1050 algebraic variables. The base case model was developed in collaboration with Arcelormittal Dofasco (Industrial Partner) and therefore, the model needs to be re-calibrated according to the new industrial partner (Arcelormittal Contrecoeur West). The model was coded in gPROMS (General Process Modelling System).

• Phase I (In progress): The short term phase of this research focuses on parameter estima- bility and identifiability. This involves re-estimating the parameters to a reasonably high degree of accuracy and carrying out sensitivity analysis with respect to both the parameters and inputs to the plant. This represents one of the crucial challenges due to the lack of measurements which is a characteristic of those systems. The maximum likelihood function was used to estimate the parameters and through defining the variance model, the whole function is reduced to a weighted least squares problem. This is considered as an optimization problem with the parameters treated as the decision variables. Most of those parameters are correlated and therefore, sensitivity analysis is essential to reduce the decision variables within the optimization problem to only the significant ones. The main objective of this phase is to obtain a robust model.

• Phase II (In progress): The dynamic simulation of the model takes few CPU seconds while the optimization takes significantly longer. The duration of each batch is approximately an hour; therefore, model reduction strategies would be essential to enable real-time application of the model. Two strategies could be applied; one is to reduce the physical process through simplified models and the other is to use surrogate modeling techniques. Model reduction through simplifying the physics and kinetics of the process is in progress. The base model considered radiation within the furnace and approximated the physical shape of each surface to calculate the net radiative transfer from each surface to the other. In literature, it has not been established, how the scrap structure changes as it melts within the furnace and as a result several assumptions are required to develop the radiation model. Therefore, removing the radiation model and approximating the amount of radiation lost to the walls and the roof of the furnace through an estimated parameter could simplify the model significantly. The radiative transfer between the other surfaces (Scrap, Arc and Bath) could be compensated

30 through the heat transfer coefficients for the convective heat transfer between those surfaces. On the other hand, surrogate models could be a response surface model or a data driven model using partial least squares (PLS) techniques. The challenge in this case is to choose an accurate approximate representation of the complex model, since the process is time-varying and nonlinear. In PLS model development, both the plant measurements and the simulated results could be used to have better accuracy. The reduced model and the complex model could be implemented online and offline respectively.

Current Status

At this point in time, the radiation model was removed, additional parameters were included and the model simulated successfully. The next stage in progress is to calibrate the model using plant data through estimating the parameters using gEST in gPROMS.

Optimization scenarios will be generated to demonstrate the capability of the mathematical model in performing ”what-if” scenarios and also identifying opportunities for process improvement and cost reduction.

Industrial Collaboration

ArcelorMittal Contrecoeur will be contributing to the project by providing process data and technical expertise. The project is run in collaboration with McMaster Steel Research Center.

Literature Cited

Bekker, J. G., Craig, I. K., and Pistorius, P. C. (1999). Modeling and simulation of an electric arc furnace process. ISIJ (Iron Steel Institution Japan) International, 39, 23–32.

MacRosty, R. (2005). Modeling, Optimization and control of an Electric Arc Furnace. PhD thesis, Department of Chemical Engineering, McMaster University.

MacRosty, R. D. M. and Swartz, C. L. E. (2007). Dynamic optimization of electric arc furnace operation. AIChE Journal, 53(3), 640 – 653.

Matson, S. and Ramirez, W. F. (1999). Optimal operation of an electric arc furnace. In 57th Electric Furnace Conference Proceedings. Pittsburgh, Pennsylvania., pp. 719–728.

31 Poster Slides

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32 8 Jaffer H. Ghouse

Research title: Integrated Coal Gasification and Natural Gas Steam Reform- ing Advisor: Dr. T.A. Adams II Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

Conventional entrained flow gasifiers, such as that of GE-Texaco, employ a radiant syngas cooler (RSC) to cool the hot syngas produced from gasification of coal. Conventionally, the hot coal-derived syngas is used to generate high pressure steam within the tubes in the RSC. This project will investigate a new design concept in which the available heat from the hot coal-derived syngas is used to drive the endothermic reaction of catalytic natural gas steam reforming inside the tubes in an energy-efficient manner. The proposed system produces hydrogen-rich syngas from natural gas and when blended with coal-derived syngas, it significantly improves the molar H2/CO ratio required for the downstream production of liquid fuels such as methanol and Fischer-Tropsch liquids. Thus, this novel configuration will improve the overall efficiency of a polygeneration plant. The objective of this project is to study (i) the feasibility of the proposed configuration; (ii) the best design which will offer the required cooling to the gasifier and achieve optimal conversion of natural gas. To this end, we will, a) Develop a multi-scale, dynamic, heterogeneous two-dimensional model of the RSC based on first principles modelling b) Perform simulation studies for various dynamic behaviours to design a preliminary control structure for the proposed system

Background

Industrial scale gasification has been in practice for many years but is gaining more significance owing to fluctuating oil prices and the demand for technologies which use fossil fuels in a more sustainable way. Gasification is an integral part of Integrated Gasification Combined Cycle plants (producing power) and synthetic fuels plants (producing liquid fuels). Gasifier types can be broadly classified into (i) fixed bed; (ii) fluidized bed; and (iii) entrained flow gasifiers. Among these, the widely preferred and commercialized are entrained flow gasifiers (the GE-Texaco design is used in this project in this project) (Phillips [2004]), (Ordorica-Garcia et al. [2006]). These gasifiers employ two types of coolers, radiant and quench, to cool the hot coal-derived syngas. The current state of the art RSC cools the hot coal-derived syngas by generating high pressure steam (up to 550◦ C) in the process (Figure8.1a). This configuration, though effective, does not take full advantage of the available exergy due to very high-temperatures.

33 Figure 8.1: (a) Conventional RSC generating steam, (b) proposed new RSC configuration integrating natural gas steam reforming and gasification

Recent interests in polygeneration plants producing multiple products such as hydrogen, electricity, gasoline, methanol, have shown the significance of gasification units for converting solid based carbon sources to more valuable products (Adams II and Barton [2009]). The Fischer-Tropsch (FT) process which converts synthesis gas, produced from solid based fuels such as coal/biomass, to liquid fuels forms an integral part of a polygeneration plant. The method of syngas generation, which is the feed to the FT synthesis, significantly affects its efficiency and profitability. Coal-derived syngas has a low H2/CO molar ratio of 0.7-1.1 and thereby needs to be upgraded to meet the H2/CO molar ratios of approximately 2 to be used as a feed to FT synthesis. Various configurations to meet this requirement have been explored by Adams et al and have shown that combining natural gas steam reforming with coal gasification as shown in Figure8.1b is often the most energy efficient and profitable strategy (Adams II and Barton [2009]).

The objective of this work is to explore the feasibility and implementation considerations of the proposed configuration by constructing a rigorous differential mass, energy and momentum balance model of the radiant cooling section. While the proposed concept has been shown to be very favourable at the systems level, this work now takes a closer look at the details of the fluid flows, compositions, temperatures and reactions occurring at the macro and micro scales.

Research Plan

1. Model Development – A multi-scale, dynamic, heterogeneous, two-dimensional model of the RSC based on mass, energy and momentum balances will be developed. The RSC model will involve the coupling of individual models for shell refractory, shell-side hot coal-derived

34 syngas, tube wall, tube-side process gas phase and tube-side catalyst phase. The resulting system of non-linear partial differential algebraic equations will be solved in the gPROMS software package, an equation oriented process modeling environment, by discretizing the variables in time and space.

2. Model Validation –Validating the model for the proposed RSC will be a challenge owing to the new design and lack of any related literature data for this specific unit. To circumvent this complexity, we propose to validate the model as two separate models, first the model for the shell-side hot coal-derived syngas, and second the model representing catalytic natural gas steam reforming in the tubes. Both of these models can be validated individually using available literature data, which will be sufficient to demonstrate the validity of the RSC model as a whole.

3. Design – The dynamic model will be used to simulate various operating conditions and study complex dynamic behaviours during start-up and shut-down. The result will aid in (i) designing the control structure for the new system; (ii) developing a preliminary design of the new RSC. The preliminary design can then be implemented and optimised in commercial Computational Fluid Dynamics (CFD) software such as Ansys CFX to improve the heat transfer efficiency from the hot coal derived syngas to natural gas stream within the tubes. The optimized design resulting from the CFD studies will then be used in a cost analysis of a new process which uses the novel RSC.

Current Status

The multi-scale, dynamic, heterogeneous, two-dimensional model of the RSC has been developed that accounts for mass, energy and momentum balances. The system of non-linear partial differential and algebraic equations is being implemented and solved using the equation oriented process modeling environment in the gPROMS software package.

Literature Cited

Adams II, T. A. and Barton, P. I. (2009). A dynamic two-dimensional heterogeneous model for water gas shift reactors. International Journal of Hydrogen Energy, 34(21), 8877–8891.

Ordorica-Garcia, G., Douglas, P., Croiset, E., and Zheng, L. (2006). Technoeconomic evaluation of IGCC power plants for CO2 avoidance. Energy Conversion and Management, 47(15-16), 2250–2259.

Phillips, J. (2004). Different Types of Gasifiers and Their Integration with Gas Turbines 1.2.1-1 Introduction. , 67–77.

35 Poster Slides

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36 9 Nor Farida Harun

Research title: Flexible Polygeneration Systems with Gas Turbine Solid Ox- ide Fuel Cell Hybrids Advisor: Dr. T.A. Adams II Date: May 2012 Industrial Collaboration: National Energy Technology Laboratory (NETL), U.S. Department of Energy, Morgantown, West Virginia, U.S.

Research Goals

The aim of this research is to move toward the development of flexible polygeneration systems with solid oxide fuel cells (SOFCs) which would be able to transition between various steady states and product portfolios depending on market prices and demand. In this study, the research primarily focuses on the investigation of the flexible polygeneration system’s performance using SOFC/gas turbine (GT) hybrid system for dynamic load demand (that is, changing the power output throughout the day according to the current demand). In order to quantify the performance of these flexible systems, dynamic simulations and experiments will be used to determine the trajectory of the process variables during transients using the hardware-based SOFC/GT hybrid installed at National Energy Technology Laboratory, U.S. Department of Energy, Morgantown, West Virginia. This information will be used in a techno-economic analysis to determine system efficiencies, fuel consumption, environmental impact and profitability.

Background

Polygeneration systems are systems which co-produce electricity and chemical products such as diesel, methanol, and gasoline. Flexible polygeneration systems would be able to transition between various steady states and product portfolios depending on market prices and demand; for example, more electricity is produced in the daytime and less is produced at night according to demand, or methanol is produced when methanol sale prices are high. Thus flexible polygeneration plants can have significant profitability advantages since the products can be changed dynamically to match market conditions for maximum revenue generation (Chen et al. [2011]). Furthermore, polygeneration plants using SOFCs can take advantage of the added environmental benefits, such as high energy efficiency and zero CO2 emissions at low costs (Adams and Barton [2011]).

While SOFCs are a promising technology, they have not yet commercially reached their full potential in terms of complete usage of the fuel and cell lifetime. However, it is possible to integrate SOFCs with a gas combustion turbine (GT) a mature technology which combusts fuels at elevated temperatures and pressures to produce electricity (J. [2006]). This SOFC/GT hybrid system can overcome many of the challenges associated with the current state-of-the-art SOFC and provide highly efficient power generation. In the electricity generation portion of the polygeneration facility,

37 a hybrid SOFC/gas turbine (GT) power generation system is proposed as the best near-term way to produce power with high energy efficiency and reduced environmental impact (McLarty et al. [2012]). The SOFC/GT hybrid system could be used for both base-load power generation as well as load-following power generation. Motivated by the above considerations, this study will quantify how dynamic use of SOFC/GT hybrid system will affect the fuel-to-electricity efficiency, total plant thermal efficiency, the profitability and the system operational flexibility (that is, the upper and lower bounds on the production capacities of each of the products).

Research Plan

In this study, flexible polygeneration system’s performance using SOFC/gas turbine (GT) hybrid system for dynamic load demand will be investigated. To do this, the transient characteristics of the proposed polygeneration system will be investigated by performing experiments with a hardware based pilot plant which includes gas turbines, compressors, pumps, valves, and heat exchangers. Other parts of the polygeneration system which cannot be constructed in the lab due to safety or cost reasons, such as the SOFCs, coal gasifier, and methanol reactors, are simulated using dynamic models which are directly integrated with the hardware and run simulations in real-time. The experiments will be performed at HyPer, the hardware-based simulation facility installed at National Energy Technology Laboratory, U.S. Department of Energy, Morgantown, West Virginia. The experimental results using this system will be used to determine the performance of the system, technical and operational limitations, economics, efficiencies, and other critical information that can be used toward the full-scale implementation of the cycle.

Current Status

To provide a fundamental insight into the dynamic operation of polygeneration system with SOFCs, steady-state Aspen Plus models for this system have been developed. The existing Aspen Plus model from Adams and Barton [2010] was utilized as the base case for polygeneration model, and then modifications were made to simulate six new system configurations according to two design decisions illustrated in Figure9.1.

All of these systems use coal and natural gas in some combination as the fuel and produce electricity, diesel, gasoline, and methanol as products. At this stage, the goal was to investigate how changes brought on the six different plant configurations considered, as well as changes in the product portfolio (percentage of electricity vs. fuels produced) affect the total thermal efficiency of the polygeneration system and the CO2 emissions. Industrial Collaboration

A portion of this research will be conducted in collaboration with the National Energy Technology Laboratory (NETL), U.S. Department of Energy, Morgantown, West Virginia. The hardware-based simulation facility installed at the NETL, called the Hybrid Performance (HyPer) project, will be

38 Figure 9.1: Simplified superstructure of polygeneration system for six system configurations used to investigate the performance of a dynamic polygeneration system with solid oxide fuel cells.

Literature Cited

Adams, T. and Barton, P. (2010). High-efficiency Power Production from Coal with Carbon Capture. AIChE Journal, 56(12), 3120–3126.

Adams, T. and Barton, P. (2011). Combining coal gasification, natural gas reforming, and solid oxide fuel cells for efficient polygeneration with CO2 capture and sequestration. Fuel Processing Technology. Fuel Processing Technology, 92, 2105–2115.

Chen, Y., Adams, T., and Barton, P. (2011). Optimal Design and Operation of Flexible Energy Polygeneration Systems. Industrial and Engineering Chemistry Research, 50, 4533–4566.

J., B. (2006). Hybrid Gas Turbine Fuel Cell Systems, in The Gas Turbine Handbook. DOE/NETL edition.

McLarty, D., Kuniba, Y., Brouwer, J., and Samuelsen, S. (2012). Experimental and Theoretical Evidence for Control Requirements in Solid Oxide Fuel Cell Gas Turbine Hybrid Systems. Journal of Power Sources, 209, 195–203.

39 Poster Slides

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40 10 Mohammad Zamry Jamaludin

Research title: Integration of Dynamic Real-time Optimization and Model Predictive Control Advisor: Dr. C.L.E. Swartz Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

This project aims to improve plant economics during transient operations using dynamic optimization. There are two main objectives in this project. The first objective is to systematically integrate dynamic real-time optimization (D-RTO) and model predictive control (MPC) for calculation and implementation of economically optimal set point trajectories of manipulated and controlled variables for process plants under transient operations. The second one is to design and implement the two-layer framework of integrated D-RTO and MPC for processes under extreme operations that includes plant startup, shutdown and partial shutdown.

Background

The current global economic environment requires more agile plant operation in order to optimize cost, profit and productivity under flexible operating conditions with respect to market demands. This requires judicious decisions by the economic optimizing control strategy, which is distributed within the so-called plant decision hierarchy. Such strategy drives process plants to be responsive to any changes in operational well as economic variables in order to seek and remain at the highest profit margin.

Currently in practice, plant economics are translated into plant operating conditions, or set points, using steady-state real-time optimization (SS-RTO). For multivariable-constrained control problems, these set points are passed to the model predictive control (MPC) for tracking purposes. Communi- cation between SS-RTO and MPC layers in the conventional plant decision hierarchy is limited with respect to the achievable plant flexibility and economic performance, especially when considering processes under transient operations. One major drawback is due to model inconsistencies between the two layers (Backx et al. [2000]). SS-RTO uses a steady-state nonlinear process model in its algorithm whereas MPC uses a dynamic linear process model. This approach leads to a limitation that the optimal set points calculated in the SS-RTO layer may be unreachable when viewed from the dynamic MPC layer. Another drawback in the use of steady-steady model in the SS-RTO layer is the delay in computing new plant set points because the SS-RTO calculation can only be executed when the process is already stabilized at a steady-state (Backx et al. [2000]; Engell [2007]). SS-RTO also experiences performance loss during a plant transient period due to changes in internal or

41 external disturbances (Zhang and Forbes [2000]). In this case, the plant economic optimum has shifted, but the controllers still try to enforce the previously computed optimal set points. Taking into consideration processes under transient operations, SS-RTO is also unable to seek and maintain the plant economic optimum because it contains no information on process dynamics (Chong and Swartz [2011]).

Limitations in SS-RTO can be improved by replacing the steady-state first-principles process model typically used in the SS-RTO layer with a dynamic first-principles process model, and thus transforming the SS-RTO to dynamic real-time optimization (D-RTO). The idea is that dynamic optimization has the ability to provide the plant with economically optimal set point trajectories, instead of steady-state set points, which are more responsive to process and economic fluctuations.

Research Plan

Five main research topics have been identified for investigation in this project, described in the following.

1. Problem formulation and solution strategies – The two-layer framework of integrated D-RTO and MPC is formulated as a DAE dynamic optimization problem. This topic includes investigation on the appropriate modelling approach for each layer because D-RTO responds to closed-loop MPC dynamics whereas MPC responds to open-loop plant dynamics. In addition, the effects of closed loop dynamics in the MPC layer on economics in the D-RTO layer will also be investigated.

2. Integration of multi-tiered D-RTO and MPC – The idea of multi-tiered D-RTO is to address multiple objectives optimization based on priority, such as maximization of plant profit as the first priority and maximization of product quality as the second priority. In this topic, computational delay issues in dynamic optimization will also be addressed using appropriate techniques.

3. Dynamic optimization under uncertainty – Uncertainties in the economic optimizing control loop may come from process disturbances, measurements, models and economics. Robustness of the two-layer framework will be investigated against these uncertainties to ensure that the optimal solution will still be feasible at some level of probability. The focus of the third topic is to study robust optimization of the two-layer framework against uncertainties.

4. Translation of SS-RTO design considerations to D-RTO – SS-RTO design considera- tions will be taken into account in the design and implementation of D-RTO, and this includes data reconciliation, model updating and results analysis.

5. Processes under extreme operations – The ultimate objective of this project lies in the fifth research topic, which is to implement the two-layer framework for processes under extreme

42 operations, and this includes plant startup, shut down and partial shutdown. The idea of plant partial shutdown operation is to keep the process running in the event of failure in certain plant equipment.

Current Status

Recent work is on the design and implementation of the two-layer framework using a test problem of an exothermic reaction carried out in a constant volume continuous stirred-tank reactor (CSTR). The reactor dynamics consist of seven state equations. In this particular case study, the objective function in D-RTO layer is to maximize reactor profit in terms of the cost of raw materials and the price of products while the objective function in MPC layer is to minimize offset from controller set points. Among simulation cases that have been performed are fluctuations in process disturbances and changes in the raw material prices. The computational delay issue is not considered in this study and thus it is assumed that the optimal solution is obtained instantaneously. General simulations results show that the two-layer framework is able to drive and retain the plant economics at the highest possible value. It is also observed that the D-RTO updates the plant set points as quickly as possible whenever changes in process or economic variables occur in the system. A performance comparison study between of different economic optimizing control methods is in progress. Performance of the two-layer framework of integrated D-RTO and MPC is compared with the one-layer framework of economics MPC.

Literature Cited

Backx, T., Bosgra, O., and Marquardt, W. (2000). Integration of model predictive control and optimization of processes. In International Federation of Automatic Control (IFAC) Symposium: Advanced Control of Chemical Processes (ADCHEM 2000), Pisa, Italy.

Chong, Z. and Swartz, C. (2011). Discontinuous modeling formulations for the optimal control of partial shutdowns. In 18th International Federation of Automatic Control (IFAC 2011) World Congress, Vol. 18, pp. 3659–3664, Milan, Italy.

Engell, S. (2007). Feedback control for optimal process operation. Journal of Process Control, 17(3), 203–219.

Zhang, Y. and Forbes, F. (2000). Extended design cost: a performance criterion for real-time optimization systems. Computers & Chemical Engineering, 24(8), 1829–1841.

43 Poster Slides

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44 11 Yaser Khojasteh Salkuyeh

Research title: Sustainable Power Generation and Liquid Fuel Production from Coal-Based Processes Advisor: Dr. T.A. Adams II Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

The goal of this project is to improve the economic and environmental efficiency of coal gasification plants by using a series of process improvements and alternative methods. The main steps can be summarized as: 1) Instead of using pure-coal feeds, use a mixture of coal, natural gas, biomass, crude oil, and/or nuclear energy. 2) Reduce the energy consumption of carbon capture by using new methodsand innovative processes. 3) Utilize the polygeneration concept to produce liquid fuel by-products and take advantage of process snyergies. 4) Improve the efficiency of the power generation section to reduce the electricity generation cost. 5) Determine the optimum operating conditions for each individual section Yi et al. [2012] and the polygeneration system as a whole by considering all possible alternative technologies, which includes the selection of the optimal feeds, products, and processes. In addition, uncertainty in the sale prices of the products will also be considered. The optimization of the polygeneration system is a large scale mixed-integer nonlinear problem which can be solved by using decomposition methods and other established algorithms.

Background

The rising crude oil price and current greenhouse gases emission challenges are motivating new efforts to find alternative processes for the generation of fuel and power with improved energy and environmental efficiencies. Coal-based processes are still of interest because around 40% of all power world-wide is supplied by coal, especially via coal-fired power plants. However, although coal is a cheap energy resource, it has a large environmental impact because of the high rate of air pollution

(particularly CO2 emissions) generated by combustion. Current emissions-reducing technologies for coal such as carbon-capture and gasification processes are very expensive, thus incentivizing the use of other technologies such as new combined fuel systems like natural gas/coal, or novel gasification approaches like chemical looping gasification and also optimizing the design and operation of the polygeneration systems.

Research Plan

1. New Carbon Capture System – To have an efficient and environmentally friendly coal- based technology, some improvements to current carbon capture processes are necessary. By

45 using a chemical looping process(cyclic metal oxidization/reduction), it is possible to convert

synthesis gas to hydrogen, power, or liquid fuel with nearly 100% CO2 capture Li [2009].

2. Liquid Fuel Production Section – The main products of a polygeneration system, in addition to power, can be methanol, DME, diesel and gasoline. Furthermore, synthesis gas can be used for hydro-processing which upgrades heavy crude oil or heavy fractions in downstream refinery plants. Using shale oil as an untapped fossil fuel resource in the gasification model

to produce power and liquid products in a zero CO2 emission process is another idea in polygeneration system Wang et al. [2012]. A new model for a coupled pyrolysis-gasification system integrated with a new coal/natural gas gasification process is presented in Fig. 11.1. Another approach is to incorporate nuclear energy since nuclear-based electricity can be

produced with zero CO2 emissions. Heat produced by nuclear energy can be integrated with a coal-to-liquid plant to supply some of the required heat.

Figure 11.1: Using shale oil as a new feedstock for power/fuel production

3. Power Section – Increasing the efficiency of combined cycles (for power generation with gas turbines) improves the performance of the whole plant. However, using higher temperature gas (which usually increases the efficiency of turbines) requires cooling of turbine blades to reduce the thermal stress. In addition, for a specific blade cooling technology, when the inlet temperature is raised beyond a certain value, the cooling penalties are such that cycle efficiency falls. It means because power generation is tightly integrated with the process, the optimum operating conditions of the polygeneration plant is not necessarily at the optimum operating conditions of the gas turbine (Fig. 11.2). Therefore, proper thermal management of the turbine blades are essential to maximizing the polygeneration plant efficiency. Possible cooling techniques which use air or steam as the coolant are: 1. Closed loop cooling; 2. Open loop with: a. internal convention; b. film cooling; c. transpiration. In this part of the project, accurate models will be developed for the gas turbines and their cooling systems to increase the efficiency of power generation by determining the optimum coolant rate and conditions.

46 4. CO2 Sequestration – One strategy for CO2 storage preparation is the condensation approach,

in which CO2 is condensed at supercritical pressures. Alternatively, hydrate-based separation

processes based on hydrate crystallization of CO2 in reactors to produce solidified carbon dioxide above the freezing point of carbon dioxide is under development.

Figure 11.2: Power/process schematic: 1- coolant air; 2- coolant steam in; 3- coolant steam exit

Current Status

Step 1.Combined GTL-CTL-NTL. For this part, the goal was to determine if the integration of nuclear heat into a polygeneration system would result in a higher efficiency and higher net present value. In addition, other strategies which use natural gas in more efficient ways have been investigated. The results indicate that it is better to incorporate natural gas and/or nuclear heat when the price of natural gas is below 6 $/MMBtu. A manuscript detailing this step is in preparation.

Step 2. Chemical Looping. A new combined Fe/Ni/Ca chemical looping system was investigated to produce power/DME fuel with zero emissions. Iron-based chemical looping is used to generate H2 blended with coal-derived syngas to increase the H2/CO ratio. The maximum thermal efficiency of this combined chemical looping plant with around 40% of output as electricity is 56.6% (HHV), which is an improvement over the 50-54% for the processes in Step 1. So, in addition to its capability to produce fuel/power it has higher efficiency. A manuscript detailing this step is in preparation.

Literature Cited

Li, F. (2009). Syngas Chemical Looping Gasification Process: Oxygen Carrier Particle Selection and Performance. EnergyandFuels, 23, 4182–4189.

Wang, S., Jiang, X., Han, X., and Tong, J. (2012). Investigation of Chinese oil shale resources comprehensive utilization performance. Energy, , 1–9.

Yi, Q., Feng, J., and Li, W. Y. (2012). Optimization and efficiency analysis of polygeneration system with coke-oven gas and coal gasified gas by Aspen Plus. Fuel, 96, 131–140.

47 Poster Slides

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48 12 Richard Mastragostino ‡

Research title: Optimization-based Formulations for Design and Control of Process Supply Chains Advisor: Dr. C.L.E. Swartz Date: May 2012 Industrial Collaboration: NSERC Strategic Network on Value Chain Optimization

Research Goals

A supply chain is a network of facilities that performs the functions of raw material procurement, raw material transformation into intermediate and finished products and distribution of end products to customers. In a chemical process supply chain, like in the petrochemical or pharmaceutical industry, manufacturing is a major component [Grossmann, 2012]. Supply chain optimization (SCO) and supply chain management (SCM) involves the coordinated optimization of business processes, including strategic network design, purchasing, production, transportation and distribution in order to bring greater net value to the customer, at minimum overall cost. Key drivers toward an increased focus on SCO in the chemical industry include, increasingly global markets, reducing costs/inventories, improving responsiveness (agility), and mitigating against uncertainty. Our research is concerned with two key open issues in SCO, namely (i) an effective decision-support tool for SCM of hybrid process supply chains under uncertainty, and (ii) a formulation for quantitatively assessing dynamic performance considerations during supply chain design.

Background

Processes operate in continually changing (volatile) environments, and are required to operate satisfactorily under sustained, and short-term changes. The term “process operability” reflects the ability of a process to perform satisfactorily under conditions away from the nominal operating point, where two significant concepts in operability assessment are process flexibility and dynamic resiliency. The design of a process plant can have a significant impact on its dynamic resiliency, motivating the development of optimization-based formulations for addressing dynamic considerations during the design stage [Sakizlis et al., 2004]. We have extended this methodology to consider dynamic performance during process supply chain design. Analogous to a process, a supply chain is required to operate satisfactorily under continually changing market conditions. Agility is regarded as a key characteristic of a dynamically resilient supply chain [Fisher, 1997; Christopher, 2000], and reflects the ability of a complex system to quickly adjust operations to respond to volatility in the environment. Synonymous with agility is “quick response”, which enables supply chains to rapidly meet customer demands for shorter lead times. Optimization-based formulations have been proposed for supply chain design with consideration of economic and “responsiveness” criteria [You

‡This student will be graduating in the near future and is available for employment interviews.

49 and Grossmann, 2008]. A key application area for this work is the forest products industry (FPI), where a possible strategy to improve the struggling business model entails the shift from high-volume commodity products, toward low-volume, high-value speciality products. The increased capital cost to upgrade facilities is adequately justified by the ability to manufacture with flexibility. This new paradigm implies a core transformation from physically efficient (lean) to market-responsive (agile) supply chains.

On the operational side, a decision-support tool for SCM is beneficial for exploiting supply chain agility. Model predictive control (MPC) is a promising solution for the effective control of process supply chains [e.g., Perea-L´opez et al., 2003; Li and Marlin, 2009]. Furthermore, uncertainty is a relevant issue in SCM, and if not addressed can contribute to poor decision-making. Multi-stage stochastic programming approaches have been proposed for the treatment of uncertainty in design, planning, and scheduling problems.

Research Plan

Design of Dynamically Resilient Process Supply Chains for Forest Industry Trans- formations The key feature of this work is to propose an optimization-based methodology to quantitatively assess the dynamic resiliency of a supply chain. This study will comprise of three key phases. First, a supply chain model which describes the dynamic behaviour of a multi-echelon supply chain consisting of suppliers, multi-product manufacturing sites, and distribution centers is formulated. Second, a methodology is developed for dynamic resiliency analysis of a supply chain. Dynamic resiliency is expressed in terms of a responsiveness criterion, dependent on manufacturing and transportation delays, and inventory management. The proposed methodology is incorporated within a two-stage stochastic, mixed-integer-linear-programming (MILP) framework, which captures demand uncertainty. Lastly, the effect of design on dynamic performance will be explored through manufacturing and supply chain case studies, with relevance to the FPI.

Robust Decision Making for Hybrid Process Supply Chain Systems via Model Pre- dictive Control The decision-support tool proposed in this work captures uncertainty in model parameters and demand by stochastic programming, accommodates hybrid process systems with decisions governed by logical conditions/rulsets, and addresses multiple supply chain performance metrics, within an integrated optimization framework. The tool is applied for the SCM of a multi-echelon, multi-product supply chain system. Furthermore, a key feature of this work is to reduce the conservativeness of “open loop” decision making under uncertainty by approximating the future closed loop prediction of uncertainty propagation with two-stage stochastic programming.

50 Current Status

At this point, a methodology has been proposed to quantitatively asses the dynamic resiliency of a supply chain. An introductory case study has been completed which explores how the supply chain network structure, and plant configuration affect dynamic resiliency in the presence of demand uncertainty. Additionally, a Pareto analysis has been conducted to investigate the trade-off between economic and responsiveness criteria. Further work will enhance the methodology by considering other relevant supply chain performance metrics.

Concerning the decision-making tool, a robust framework for SCM has been developed which addresses uncertainty in demand and model parameters explicitly at the execution of the model predictive controller. Through simulation, the robust formulation is shown to substantially reduce the occurrence of back orders, as compared to a nominal MPC formulation, by maintaining a sufficient level of safety stock. Currently, this work has been applied to a linear supply chain system, dedicated to the production and distribution of a single intermediate and final product. Future work plans to investigate the closed loop behaviour of a large scale system, reflecting a supply chain with complex branching, interacting multi-product plants, and decision making that occurs at different intervals.

Literature Cited

Christopher, M. (2000). The agile supply chain - competing in volatile markets. Industrial Marketing Management, 29, 37–44.

Fisher, M. (1997). What is the right supply chain for your product? Harvard Business Review, 75, 105–116.

Grossmann, I. (2012). Advances in mathematical programming models for enterprise-wide optimization. In Proceedings of Foundations of Computer-Aided Process Operations/Chemical Process Control.

Li, X. and Marlin, T. (2009). Robust supply chain performance via model predictive control. Comput. Chem. Eng., 33, 2134–2143.

Perea-Lopez,´ E., Ydstie, B., and Grossmann, I. (2003). A model predictive control strategy for supply chain optimization. Comput. Chem. Eng., 27, 1201–1218.

Sakizlis, V., Perkins, J., and Pistikopoulos, E. (2004). Recent advances in optimization-based simultaneous process and control design. Computers & Chemical Engineering, 28, 2069–2086.

You, F. and Grossmann, I. (2008). Design of responsive supply chains under demand uncertainty. Computers & Chemical Engineering, 32, 3090–3111.

51 Poster Slides

Introduction Design of Dynamically Resilient (Agile) Process Supply Chains

A supply chain is a network of facilities, including suppliers, manufacturing sites, Design of a process plant can have a significant impact on dynamic performance • • distribution centers, and retailers . Motivates the development of optimization-based formulations for addressing dynamic . A key goal is temporal and spatial integration of decision-making performance (resiliency) considerations during process design[ Sakizlis et al., 2004] Our work extends this methodology for addressing dynamic considerations during supply • chain design Agility is regarded a key attribute of a dynamically resilient supply chain [Christopher, 2000] • . “Quick response” enables supply chains to rapidly meet customer demands for shorter lead times Key application area is the forest products industry (FPI) • . Shift from high-volume commodity products, to low-volume, high-value specialty product to improve struggling business model

Distribution Integrated Forest Biorefinery (IFBR) Supplier Manufacturing Site Market Forests Center

Biomass P&P Products, Supply Chain Optimization (SCO) involves the coordinated optimization of business processes, Biofuels, Biochemicals, including strategic network design, purchasing, production, transportation and distribution in order Biomaterials, Energy to bring greater net value to the customer at minimum overall cost

Key drivers for SCO: Our research addresses two key open issues: Chips . Increasingly global markets . Development of an optimization-based . Reducing costs/inventories framework for assessing dynamic performance considerations during supply chain design . New paradigm implies a core transformation from physically efficient (lean) to market-responsive . Improving responsiveness (agile) supply chains . An effective decision-support tool for control . Collaborative project with NSERC Strategic Network on Value Chain Optimization . Mitigating against uncertainty (SCO) of hybrid process supply chains

R. Mastragostino McMaster University May 2012 2 / 7 R. Mastragostino McMaster University May 2012 3 / 7 Slide 1 Slide 2

Research Objectives & Methodology Current Results & Future Work

106 · Configuration 1 Configuration 2 Configuration 1 800 800 Phases of Current Research RM at IFBR A RM at IFBR A 1.2 Configuration 2

1 Development of dynamic model which describes process supply chain system 600 600

2 Development of optimization-based methodology for analyzing dynamic resiliency 1 400 400 3 Explore the effect of design on dynamic resiliency through case studies

Cost ($) 200 200

0.8 Inventory Setpoint

Dynamic supply chain model reflects a discrete-time, mixed-integer-liner-programming (MILP) 0 0 • 0 2 4 6 0 2 4 6 formulation 0.6

Dynamic resiliency expressed in terms of a “responsiveness” criterion 0 2 4 6 800 P A at IFBR A 800 IP at IFBR A • P B at IFBR A P A at IFBR A Lead Time (day) P B at IFBR A Key idea: lead time for the supply chain system 600 600 • Figure above - Pareto frontier between economic to respond to a step change in demand • Delivery and responsiveness criteria 400 400 Demand . Demand uncertainty Configuration 2 is more agile than Configuration 1 200 200 . • Inventory Setpoint Inventory setpoint is a design variable to Cost is higher for configuration 1 at equivalent level • hedge against uncertainty (inventory of responsiveness 0 0 quantity @ t=0) 0 2 4 6 0 2 4 6 Plots right - Decreasing trend in inventory setpoint . Assume manufacturing facility is idle at • 1,500 1,500 as responsiveness decreases (push to pull system) P A at RDC A P A at RDC A instance of step change P A at RDC C P A at RDC C Lead Time Time (day) P B at RDC B P B at RDC B . Formulation considers delivery, P B at RDC C P B at RDC C Future work 1,000 1,000 Horizon Length manufacturing and transportation delays in supply chain Enhancement of framework (other appropriate  metrics?) 500 500

Addressing supply chain design decisions (e.g. Inventory Setpoint Proposed methodology incorporated within a bi-criterion, two-stage stochastic framework  • network design, process selection/design) 0 0 Introductory case study completed, which explores dynamic resiliency of two distinct manufacturing Explore more complex case studies in relations to 0 2 4 6 0 2 4 6 •  configurations developments in FPI Lead Time (day) Lead Time (day)

R. Mastragostino McMaster University May 2012 4 / 7 R. Mastragostino McMaster University May 2012 5 / 7 Slide 3 Slide 4

Robust Decision Making via Model Predictive Control (MPC) Current Results & Future Work

A decision-support tool can be beneficial for exploiting supply chain agility • MPC is a promising solution for controlling supply chains [e.g., Perea-López et al., 2003; Li 100 100 •

400 R O I and Marlin, 2009] 50 50 . Consideration of interactions, delays, and hybrid continuous-discrete nature of supply chain 0 0 . Explicit consideration of uncertainty through a robust MPC approach 10 20 30 40 10 20 30 Finite number of scenarios for capturing uncertainty in demand and process yield 200 80 100  60 I I Back Orders (Unit)

. I Multi-objective optimization for simultaneously considering customer service and economic (1) ( ) 40 P 2 50 performance 20

S Supplier 0 0 0 10 20 30 40 10 20 30 PS Plant Site 0.8 1 1.2 1.4 I I I 150 Rt PIt It PFt Ft RS Raw Material Operating Cost ($) 4 ISt Bt 10 Storage · 100 100

IPM Intermediate Product F F

Figure above - Pareto frontier between I

F P RS IPM IPS FPM WH Ft Manufacturing S DS D • 50 Ft IPS Intermediate Product customer service and economic 50 PS Storage performance 0 0 FPM Final Product 10 20 30 40 10 20 30 Ot Operating at point denoted by (1) is Manufacturing • superior to (2) - comparable customer 60 WH Warehouse 60 DS Distribution Site service is achieved at significantly lower 40 F cost S 40 I F

Plots right - Closed loop results with 20 20 . State variables x [Inventory - I, Back orders - Robust MPC formulation • robust MPC framework 0 0 B] in red Safety stock is held to hedge against 10 20 30 40 10 20 30 . n 1 • Control variables u [Procurement - O, − T T uncertainty min E [ ] := ρs Cx xt+1,s + Cu ut 100 Production - P, Transportation - FF ] in blue s t=0 40 ut Z

. Disturbances d [Demand - D ] in green Future work F F B 50 D . s - scenario index xt+1,s = A1xt,s + B1s ut + Gdt,s t = 1 ... n 1 20 P P ∀ − Explore closed loop behaviour of more .ρ s - probability  A1∗xt+1,s + B1∗ ut + G∗dt,s + c 0 t = 1 ... n 1 complex supply chains 0 0 s ≤ ∀ − 10 20 30 40 10 20 30 . n - prediction horizon Address decision making occurring at x =x ˜  Time (day) Time (day) . Cx , Cu - Cost vectors 1,s different time intervals

R. Mastragostino McMaster University May 2012 6 / 7 R. Mastragostino McMaster University May 2012 7 / 7 Slide 5 Slide 6

52 13 Jake Nease

Research title: Integration of Solid-Oxide Fuel Cells and Compressed Air Energy Storage for Peaking Power with Zero Carbon Emis- sions Advisor: Dr. T.A. Adams II Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

In recent years, renewable sources of electricity have become a prevalent topic of discussion and research worldwide. There have been many efforts to utilize renewable energy sources such as solar, wind, hydro-electric and bio-fuels, but these methods are decades away from being able to meet the continuously growing demand for electricity. Since many of these aforementioned low-carbon energy sources are not yet cost-feasible for use as a major power source, electricity producers aim to maximize the efficiencies of current power generation technologies, while at the same time capturing and thereby controlling CO2 emissions.

The goal of this research is to investigate the potential of integrating a Solid-Oxide Fuel Cell (SOFC) power generation system with underground Compressed Air Energy Storage (CAES) to provide peaking power with cost-effective CO2 capture. This study will investigate the economic, environmental, and political feasibility of the integrated SOFC/CAES plant. It is also desired to examine the operational capabilities of the proposed system for different storage spaces, demand patterns, and fuel sources. It is anticipated that the SOFC/CAES system will provide peaking power with no emissions at a lower cost than any currently comparable system.

Background

An SOFC utilizes a carbonaceous fuel gas (synthesis gas, for example) and an oxidant (typically air) to efficiently produce electrical power through an electrochemical reaction across a solid oxide barrier, as depicted in the appended slides. There are several advantages to using SOFCs for power production: the anode exhaust is mainly H2O and CO2, which are easy to separate; and the cathode exhaust is mostly N2 at high temperatures and pressures (900◦C and 10 bar), which can be used for additional power generation or heat recovery and vented without posing an environmental risk. Several studies have been conducted to show that SOFC systems are capable of generating power at high efficiencies with no CO2 emissions (see Adams and Barton [2010a], for example). However, one significant disadvantage of SOFC systems is that there are currently potentially cost-prohibitive operability challenges associated with their dynamic operation. As such, most studies regard SOFC systems as a base-load power provider that is unable to follow the typical peaking profile of power demands. Therefore, an SOFC system is not suitable for use in a scenario when demand must be

53 met at all times, unless the system is designed to always produce the maximum expected demand, which is wasteful. A possible solution to this problem is to integrate an SOFC system with CAES.

CAES has been the subject of significant research and implementation in recent years, especially with its application for levelling intermittent wind sources. CAES operates on the principal that, during periods of excess generation capacity, air can be extracted from the atmosphere, compressed, and stored as potential elastic energy in a large above- or below-ground void that may be man-made or naturally existent. During periods of higher demand, the stored air is released from the storage space, pre-heated and expanded through low- and high-pressure turbines before being vented to the atmosphere. The turbine is connected to a generator that supplies power back to the grid. A simple schematic of a CAES system is shown in the appended slides. CAES is a well-proven technology; Raju and Khaitan [2012] report that a fully functional 110 MW plant owned by the Alabama Electric Corporation has been operating in McIntosh, Alabama since 1991, and a 290 MW plant owned by E.N. Kraftwerke has been in service in Huntorf, Germany since 1978. The dynamics of a CAES system are limited only by those of the compressors and turbines, which make it an excellent candidate for power load-following applications.

Since the cathode exhaust from the SOFC is already at a high temperature and pressure, it lends itself to the use of CAES to provide peaking capabilities to the combined power generation system. Moreover, the electricity required for compression during the cavern charging phase can be drawn from the power produced by the SOFC, causing the net output of the plant to be below (in the case of cavern charging) or above (in the case of cavern discharging) the baseline production of the SOFC and therefore allowing for the combined system to dynamically follow demand profiles.

Research Plan

1. Modeling of the Integrated CAES/SOFC Plant Fuelled by Natural Gas A steady-state Aspen Plus simulation of a natural gas-fuelled SOFC plant has been obtained from Adams and Barton [2010b]. The addition of CAES turbomachinery and appurtenances is to be added to the existing flowsheet. The plant will then be simulated under a variety of charging and discharging operating scenarios to investigate the impact of the CAES plant on the combined system’s power production capabilities. Information about stream variables, compression ratios and whether or not the CAES is charging/discharging will be used to build a data-based model that can be used in dynamic load-following simulations.

2. Dynamic Model of CAES Storage Cavern Once the combined SOFC/CAES system has been modeled, a model of a potential underground storage facility is to be developed. The model will be required to perform mass balances and pressure calculations using a non-ideal equation of state during simulation scenarios in which the combined plant will be required to follow a simulated demand profile as closely as possible.

54 3. Load-Following Simulations to Assess SOFC/CAES Performance Publicly available Canadian market demand information will be scaled to the relative size of the SOFC/CAES system and used for a variety of simulations in which the plant will attempt to match demand at each simulated time interval. Simulations will be performed over periods of days, weeks and years and various metrics (such as % load followed) will be used to investigate the efficacy of the combined system.

4. Techno-Economic Analysis of SOFC/CAES System After the SOFC/CAES system has been conceptually designed, a full techno-economic analysis will be performed to determine its required capital investment and resulting levelized cost of electricity. A series of case studies under various emission-incentive programs (such as carbon taxes) will then be performed to examine the economic tractability of the proposed system in a future sustainability-oriented setting.

5. Modeling of the Integrated CAES/SOFC Plant Fuelled by Pulverized Coal A steady-state Aspen Plus simulation of a coal-fuelled SOFC plant has been obtained from Adams and Barton [2010a]. The steps of objectives (1) to (4) will then be repeated for a coal-based SOFC/CAES system. SOFC plants are anticipated to utilize coal in future applications, thereby necessitating the same analysis as above with coal as the fuel source.

Current Status

Modeling of the integrated SOFC/CAES system using natural gas has been completed in Aspen Plus. Furthermore, a storage cavern model has been developed and several promising simulations have been performed. The next steps in this project will be to calculate the expected capital investment of the SOFC/CAES plant and examine its economic feasibility through a variety of emission incentive scenarios.

Literature Cited

Adams, T. and Barton, P. (2010a). High-efficiency power production from coal with carbon capture. AIChE Journal, 56, 3120–3136.

Adams, T. and Barton, P. (2010b). High-efficiency power production from natural gas with carbon capture. Journal of Power Sources, 195, 1971–1983.

Raju, M. and Khaitan, S. (2012). Modeling and simulation of compressed air storage in caverns: A case study of the Huntorf plant. Applied Energy, 89, 474–481.

55 Poster Slides

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56 14 Alicia Pascall

Research title: Semicontinuous biomass to dimethyl ether production Advisor: Dr. T.A. Adams II Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

The objective of this research is to develop a dynamic model and control system for the semicontinuous separation of dimethyl ether (DME) from synthesis by-products. The integrated model will then be used to assess its profitability and commercial suitability for production of DME from biomass.

Background

DME has great potential as a clean fuel as it can be used as a fuel additive, substitute for diesel and liquefied petroleum gas or fuel source for power generation due to lower NOx, SOx and particulate emissions. This clean fuel when produced from biomass is of considerable interest as it presents both a solution to mitigating climate change and reducing dependence on fossil fuels. However, the process by which DME is produced from biomass must be economical in order to achieve widespread commercialization. Since biomass feedstock has a low energy density and is distributed in nature, large-scale production facilities require collection over a larger area increasing transportation costs (Wright and Brown [2007]). While increasing the size of production facilities leads to lower production costs due to economy of scale benefits, the large transportation costs cause the optimum size of biomass facilities to be some intermediate scale (Wright et al. [2008]).

Technological advancements in the synthesis process, such as direct synthesis of DME utilising a dual catalyst, have enabled DME production to be more economically favourable compared to the conventional two-step process with methanol as an intermediate. The single step synthesis of DME allows for higher conversion efficiency. However, its downstream separation is more complex and costly as compared to the two-step process (Peng et al. [1999]). Integrating the direct synthesis step with a separation process that reduces the number of distillation columns would have an impact on the overall economics of a biomass-to-DME facility.

Semicontinuous separation systems allow for the combination of multiple separation steps using a single distillation column integrated with one or more middle vessels based on a forced cyclic technique in which no steady state exists. Semicontinuous separation has been shown to reduce lifecycle costs making it economically preferable to traditional continuous and batch processes at intermediate production rates(Adams and Seider [2006], Adams and Seider [2008], Adams and Seider [2009]). Given the economic challenges which exist with biomass facilities this work focuses on the development of a dynamic model and control system for the semicontinuous separation system. The

57 model will then be used to assess the profitability and commercial suitability of integrating the semicontinuous process within the biomass-to-DME facility (Figure 1).

Figure 1: Simplified process flow diagram for biomass to DME production

Research Plan

1. Semicontinuous, continuous and batch separation modelling – The first phase of this project involves the development of the continuous model for the separation section. This forms the baseline for determining the design configuration of the semicontinuous system. The semicontinuous ternary separation system modelled in this research transitions through three modes during one cycle with distillate and bottoms products removed continuously and the intermediate product concentrating in the middle vessel.

2. Development of semicontinuous system control scheme – An essential part of the semicontinuous system operation lies in the control structure which drives the forced cyclic behaviour. The control system ensures that purity specifications are met and flooding and weeping conditions inside the distillation column are avoided despite mode transitions and feed composition changes. Control strategies for the model developed will be analyzed to achieve these operational and specification objectives.

3. Optimization (Semicontinuous, Continuous and Batch systems) – The separation systems will be optimized to reduce total annualized cost. In the semicontinuous case as the control scheme drives the behaviour of the process as such design and operation decision (controller parameters) must be made together. These two sets of variables will form decision variables in the optimization problem formulation solved using “black-box” optimization.

4. Lifecycle Analysis and Techno-economic Assessment of Biomass-to-DME produc- tion – Techno-economic and life-cycle analyses will then be conducted for the final designs. These results can later be incorporated into an optimization framework for determining the optimal biomass-to-DME plant size.

Current Status

58 1. Continuous Model and Optimization – A model for the continuous process has been developed in Aspen Plus based on data from previous research on a biomass-to-DME process. The base case production rate has been optimized for design (number of stages, feed tray location) and operating variables (reflux and reboil ratios).

2. Semicontinuous separation dynamic model and control system – The semicontinuous model has been implemented in Aspen Dynamics and a PI control system designed to achieve target product specification while avoiding column flooding. Early conceptual results have been published (Adams and Pascall [2012]).

3. Semicontinuous separation system Optimization – Currently, a Particle Swarm opti- mization algorithm has been developed and integrated with Aspen Dynamics to automatically select the key design and control parameters (such as controller gains, flow rates, etc.) which minimizes the total lifetime costs of the process.

Literature Cited

Adams, T. A. and Pascall, A. (2012). Semicontinuous Thermal Separation Systems. Chemical Engineering and Technology,.

Adams, T. A. and Seider, W. D. (2006). Semicontinuous Distillation with Chemical Reaction in a Middle Vessel. Industrial & Engineering Chemistry Research, 45(16), 5548–5560.

Adams, T. A. and Seider, W. D. (2008). Semicontinuous Distillation for Ethyl Lactate Production. AIChE Journal, 54(10), 2539–2552.

Adams, T. A. and Seider, W. D. (2009). Semicontinuous reactive extraction and reactive distillation. Chemical Engineering Research and Design, 87(3), 245–262.

Peng, X. D., Wang, A. W., Toseland, B. A., and Tijm, P. J. A. (1999). Single-Step Syngas-to-Dimethyl Ether Processes for Optimal Productivity, Minimal Emissions, and Natural Gas-Derived Syngas. Industrial & Engineering Chemistry Research, 38(11), 4381–4388.

Wright, M. and Brown, R. C. (2007). Establishing the optimal sizes of different kinds of biorefineries. Biofuels, Bioproducts and Biorefining, 1(3), 191–200.

Wright, M., Brown, R. C., and Boateng, A. A. (2008). Distributed processing of biomass to bio-oil for subsequent production of Fischer-Tropsch liquids. Biofuels, Bioproducts and Biorefining, 2(3), 229–238.

59 Poster Slides

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60 15 Shailesh Patel

Research title: Integrated Planning and Scheduling for Supply Chain Opti- mization Advisor: Dr. C.L.E. Swartz Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals

The primary objective of our research is to develop a framework to create an optimal schedule of production activities to maximize the economic performance in presence of uncertainties.

The optimal manufacturing activities are scheduled by solving production planning and scheduling problems in a hierarchical framework. However, the schedule derived using a hierarchical structure often becomes sub-optimal or unrealizable due to various issues such as model inconsistency and uncertainties. To address this issue, we are working on integration of the planning and scheduling problem.

Background

Production planning (here referred to as planning) and scheduling are closely linked activities with a common objective of optimal allocation of available resources to perform a collection of tasks to manufacture one or several products. The optimal production schedule is derived in a typical hierarchical control structure where the planning problem is solved first to generate production targets and then these targets are passed to the scheduling level.

Typical planning problems cover activities over a few weeks to months and are concerned about generation of production and inventory targets for each production facility, allocation of resources within the production facility, and transportation quantities from facilities to distribution centers. On the other hand, the scheduling level determines operational decisions, such as tasks to equipment assignment and production sequences with the time horizon of a few days to weeks. Since both levels consider activities on a different time range, it demands the use of different time scale models. However, it introduces model inconsistency and hence the production targets derived at the planning level generally result in sub-optimal or infeasible scheduling activities. For example, the planning level does not include the effects of daily inventory levels, machine set up time, production sequences and thus tends to generate an optimistic estimate as compared to the scheduling model. Therefore, the coordination between these two levels should be achieved to maximize the system performance (van den Heever and Grossmann [2003]; Sung and Maravelias [2007]; Li and Ierapetritou [2010]; Kopanos et al. [2011]). The coordination activity requires integration of these decisions over wide time scales, from long term (tactical) to short term (operational), which may not be

61 easy to handle. Since both levels are trying to optimize the system with one goal, many trade-offs exist between decisions made at each level. Therefore, these decisions should be computed in an integrated framework, which considers the impact of decisions derived at each level on all other stages. Naturally, the involvement of different time scale activities makes this exercise complex.

Another important aspect is the validity of the optimal decisions derived from the optimization problem. The quality of the optimal decisions is highly dependent on the accuracy of the input information and the system representation. Modeling of planning and scheduling activities is a complicated task as it is not straightforward to decide what details need to be included. An accurate description of a supply chain system generally requires a large and complex model to be built and therefore it is common practice to include only relevant information to keep the model simple. However, such practices eventually introduce plant-model mismatch. Further, calculating the exact value of model parameters, like processing time, process yield, prices, machine reliability, is not a trivial procedure and there is a high chance of having inaccurate measurement/calculation of these parameters. Moreover, demand is the most important input parameter for supply chain optimization and accurate prediction of demand is a very difficult task. In other words, the supply chain system is constantly impacted by unmeasured disturbance in the form of demand variations. In order to ensure the optimality of the scheduling decisions, it is therefore critically important to consider these uncertainties in the optimization problem (Verderame and Floudas [2010]; Wu and Ierapetritou [2007]).

Research Plan

We identified two main threads that could possibly lead to an efficient integrated framework.

1. In the first phase of the research, the framework to coordinate the planning and scheduling activities will be developed. The idea is to use a hybrid modeling approach which combines planning and scheduling activities in one optimization problem. In hybrid modeling, the early time periods are modeled with scheduling model while the later time period are modeled with planning model. The argument is that the level of uncertainty is low for early time periods, hence scheduling detailed production activities make sense. High uncertainty for later periods does not suggest making detailed decisions as they need to be updated, once accurate information becomes available, thus a planning model (abstract information) would be appropriate for those time periods. The model integration will help to reduce the infeasibility issue and generate optimal scheduling activities by assessing its long term impact through a long planning horizon.

2. In the second phase of the research, the uncertainty information will be included in the hybrid model and the resulting optimization problem will be solved using a robust optimization method. The inclusion of uncertainty information in the integrated problem will generate the decisions that remain valid over a wide range of operation conditions and thus it can increase

62 the chance of getting a feasible (realizable) schedule which will increase the economic efficiency of the system. It should be noted that the computational complexity of the integrated problem is relatively high due to presence of large number of integer variables and complex constraints resulting from including detailed operational information. The inclusion of uncertainty will further increase the computational complexity. Attention will be given on reducing the computational complexity by alternate formulations of the integrated problem.

Current Status

Currently, we are working on the hybrid model development to represent the planning and scheduling activities by a discrete time mixed integer dynamic model.

Literature Cited

Kopanos, G. M., Puigjaner, L., and Maravelias, C. T. (2011). Production planning and scheduling of parallel continuous processes with product families. Industrial & Engineering Chemistry Research, 50(3), 1369–1378.

Li, Z. and Ierapetritou, M. G. (2010). Rolling horizon based planning and scheduling integration with production capacity consideration. Chemical Engineering Science, 65(22), 5887–5900.

Sung, C. and Maravelias, C. T. (2007). An attainable region approach for production planning of multiproduct processes. AIChE Journal, 53(5), 1298–1315. van den Heever, S. A. and Grossmann, I. E. (2003). A strategy for the integration of production planning and reactive scheduling in the optimization of a hydrogen supply network. Computers & Chemical Engineering, 27(12), 1813–1839.

Verderame, P. M. and Floudas, C. A. (2010). Integration of operational planning and medium-term scheduling for large-scale industrial batch plants under demand and processing time uncertainty. Industrial & Engineering Chemistry Research, 49(10), 4948–4965.

Wu, D. and Ierapetritou, M. (2007). Hierarchical approach for production planning and scheduling under uncertainty. Chemical Engineering and Processing: Process Intensification, 46(11), 1129–1140.

63 Poster Slides

Supply Chain Optimization Research Objectives and Literature Review

Supply chain/Scheduling Objectives Supply Chain Planning Strategic Decisions 1. What is the optimal production (Structure of supply chain system) Hierarchical Approach Months or years • target? . Solve the planning problem. Pass 2. What is the optimal inventory level Products Aggregate the planning decisions to the to be produced production target (safety stocks)? scheduling problem. . Solve the scheduling problem to 3. What are the optimal transportation meet these targets quantities? Long term Production Planning Production Capacity demand forecast Tactical Decisions System representation 4. Which resources/euipment should be Weeks or Months Shortcomings • Suppliers Plants Warehouses DCs Customers used for production and when? . No interaction between levels Production target Shipment Inventory level Rate . Planning decisions (targets) may Raw material order Demand lead to infeasible scheduling problem Integrated modeling approaches Solution approaches Scheduling Production time • • Short term Machine set up time . demand forecast Operational Decisions Production sequencing Possible Reason . Monolithic scheduling models (Maravelias and Decomposition methods Days or Weeks • rules Sung 2009) - Temporal decomposition : Time scales . Model inconsistency (Heever and Grossmann 2003) Revised Revised Production Tasks . Approximate scheduling models (Heever and Production Level Inventory Level Sequences Assignment - Different time scale models Grossmann 2003) - Spatial decomposition : Network - Inaccurate abstractions . Offline surrogate models (Li and Ierapetritou geometry (Terrazas-Moreno and Grossmann 2010) 2011) Plant - Heuristic : Process knowledge (Li and Production Facility Uncertainty handling • Ierapetritou 2010) . Combination of a robust optimization and a . Full space methods probabilistic optimization method (Verderame - Bender’s decomposition (Benders 1962) and Floudas 2010) - Lagrangian relaxation (Li and Ierapetritou Need of Integrated Framework . Three stage multi-stage stochastic 2010) programming (Wu and Ierapetritou 2007) Shailesh Patel Planning and Scheduling MACC Meeting 2012 1 / 6 Shailesh Patel Planning and Scheduling MACC Meeting 2012 2 / 6 Slide 1 Slide 2

Production Planning Scheduling

Production planning is concerned about generation of production and inventory targets for each • Scheduling is mainly concerned about optimal resource allocation and production sequencing production facility, allocation of resources within the production facility, and transportation quantities • from facilities to distribution centers Typically runs over few days to weeks • Typically runs over few weeks to months • Continuous variables General scheduling model Cp Production cost General planning model B Batch size c c Con consumption min Cpt = F Wi,s,t + Var Bi,s,t min Cstp + Cbotp + Cptp p i s t s s tp s S Product inventory subject to: subject to: R Received amount P P P P
Pr Production amount Inventory balance Ij,t = Ij,t + Pj,t Dj,t j, tp Allocation Constraints W 1 s, ts p p 1 p − p ∀ i t =t pt +1 i,s,ts0 ≤ ∀ − s0 s − is Binary variables Back-order balance BOj,tp = BOj,t + Demj,tp Dj,tp j, tp p 1 − ∀ Sequencing Constraints Wi,s,t + W 1 s, f , f 0, ts − i s i t =t cl pt i0,s,ts0 ≤ ∀ W Task - Equipment P P 0 s0 s − ff − is Pl y P Pu y j, t 0 j · j,tp ≤ j,tp ≤ j · j,tp ∀ p assignment Sj,t = Sj,t 1 + Prj,i,s,t pt Ps s − P Pi s s − is Cst = hj Ij,t tp Mass Balance j, ts p j · p ∀ ∀ Parameters Conj,i,s,t + Rj,t Dj,t c − i s P Ps s − s F Fixed cost Cbotp = qj BOj,tp tp c P j · ∀ V l W B V u W j, s, t Var Variable cost j,s · i,s,ts ≤ i,s,ts ≤ j,s · i,s,ts ∀ s Capacity constraints P P C Storage capacity Continuous variables Binary variables l u . Objective function : minimization of total cost C S , C j, ts V Production capacity P sj ≤ j ts ≤ sj ∀ Cp Production cost y Product - Facility (production cost + Storage cost + Back order Cs Storage cost assignment cost) of system Pr = P j j,i,s,ts ptis j,tp Indices Target Setting ts i s − ∀ Cbo Back order cost . Design variables : Production amount, products i Task Parameters S = I j I Inventory to be produced in each time period, Inventory Pj,ts =tPp Pj,tp ∀ j Material P Production amount h Holding cost level s Equipment q back order cost BO Back-order quantity . The presence of binary variables yields a mixed ts Scheduling time D Delivery rate integer model instant Indices Dem Actual demand . It includes only aggregated process dynamics of . Objective function : minimization of production cost j Product the production system . The production and inventory targets derived at planning level are treated as targets tp Planning time instant Shailesh Patel Planning and Scheduling MACC Meeting 2012 3 / 6 Shailesh Patel Planning and Scheduling MACC Meeting 2012 4 / 6 Slide 3 Slide 4

Uncertainty & Disturbances Integrated Planning and Scheduling

Demand uncertainty Hybrid Model : Integration of planning and scheduling model • • . Demand is the most critical input for supply chain optimization Supply Chain Optimization Planning Model . Accurate prediction of customer is a difficult Uncertainty Production Planning task + Tactical Decisions Demand Forecast Weeks or Months (Long term) Scheduling Scheduling Planning ... Planning Model uncertainties Model Model Model Model • . Invalidate the underlying process model Scheduling Model n=1 2 3 . . . Ns which is used to optimize the system. Uncertainty Scheduling t=1 2 3 Np + Operational Decisions Demand Forecast Days or Weeks (Short term) Uncertainty handling Integrated problem considers both type of uncertainties in the • Optimal decisions derived by solving deterministic optimization problem will not remain optimization problem optimal in the changed demand situation Plant The uncertainty will be handled in the proposed approach by, Production Facility • . Two-stage stochastic optimization . Robust optimization Classification Uncertainty consideration Model uncertainties : Process yield Hybrid model combines the planning and scheduling model in one optimization problem • 1. Stochastic optimization • Process uncertainties : Transportation It provides a better compromise between the computational complexity and the modeling accuracy • • time . Two-stage stochastic optimization . Lower level of uncertainties makes sense to schedule detailed production activities for early time periods Input uncertainties : Demand, prices Probabilistic optimization • • Discrete uncertainties : Equipment 2. Robust optimization : worst case optimization • availability Optimal production schedule with long term impact assessment through a long planning horizon

Shailesh Patel Planning and Scheduling MACC Meeting 2012 5 / 6 Shailesh Patel Planning and Scheduling MACC Meeting 2012 6 / 6 Slide 5 Slide 6

64 16 Mudassir M. Rashid

Research title: Fault Detection and Root-cause Diagnosis in Chemical Pro- cesses Advisor: Dr. J. Yu Date: May 2012 Industrial Collaboration: Praxair, Inc.

Research Goals

Effective monitoring and diagnosis of chemical processes is important in process systems engineering as it is essential to ensure the stable operation of chemical plants, maintain product quality at desired grades, optimize production economics, and improve plant safety, energy efficiency, and environmental sustainability.

The goal of this research is to develop an efficient fault detection and diagnosis framework for monitoring nonlinear and non-Gaussian processes. The early fault detection and root-cause diagnosis of process faults can allow for corrective actions to be taken immediately in order to prevent serious incidents and mitigate the deterioration of product quality.

Background

Multivariate statistical process monitoring (MSPM) techniques such as principal component analysis (PCA) and partial least squares (PLS) have been widely used in process monitoring. The conventional MSPM methods project the highly correlated and noisy data onto a lower dimensional subspace that best characterizes the variations of the process variables. The lower dimensional subspace is defined by a number of orthogonal latent vectors that capture the feature information from the process variables. An inherent assumption in the derivation of the confidence limits for the monitoring statistics is that the process data come from a single operating mode and thus obey a multivariate Gaussian distribution approximately. Therefore, non-Gaussian processes may not be effectively monitored using the conventional MSPM methods. Moreover, regular PCA and PLS models assume that the observations at a time are statistically independent from previous observations and thus ignore the time-varying process dynamics.

Research Plan

The proposed research is being conducted as follows:

1. Fault Detection – A number of novel fault detection techniques have been developed for monitoring dynamic, nonlinear, and non-Gaussian chemical processes with multiple operating modes or phases.

65 2. Fault Diagnosis – A new framework to identify the faulty variables and diagnose the root causes of process faults is to be developed using probabilistic inference and artificial intelligence algorithms along with the integration of process knowledge.

Current Status

1. A hidden Markov model (HMM) based adaptive independent component analysis (ICA) approach has been developed for monitoring complex chemical processes (Rashid and Yu [2012b]). The advantages of HMM to account for system dynamics and uncertainty are combined with the merit of ICA for handling non-Gaussianity. The integrated HMM-ICA approach is proposed to characterize the process uncertainties and random transitions of various operating conditions in chemical plants. The comparison of the HMM-ICA method with regular ICA in Table 16.1 shows that the HMM-ICA approach performs better with a higher fault detection rate and lower false alarm rate.

2. ICA is integrated with multidimensional mutual information (MMI) to measure the statistical independency between two independent component (IC) subspaces, which represents the subspace dissimilarity (Rashid and Yu [2012a]). The proposed approach does not require any assumptions regarding the relationships among measurement variables and can deal with the process data following an arbitrary probability density distribution. In contrast to the angle based dissimilarity factor, the new multidimensional mutual information based dissimilarity takes into account the higher-order statistics and thus can well capture the non-Gaussian features of process data. Fig. 1 shows the comparison of fault detection results for PCA, PCA dissimilarity, ICA, angle based ICA dissimilarity and MMI based ICA dissimilarity methods. It is readily seen that the proposed method outperforms the other methods with superior fault detection.

Table 16.1: Results of ICA and HMM-ICA Monitoring Methods for Tennessee Eastman Chemical Process

Monitoring Method Fault Detection Rate (%) False Alarm Rate (%) ICA 25.88 12.59 HMM-ICA 95.69 6.43

Industrial Collaboration

Praxair, Inc. has provided the ability to use the diagnostic framework developed with a commercial industrial plant in order to evaluate the efficacy of the proposed approaches. Their experience and information has been invaluable and will help us to form a realistic and beneficial study. The enthusiasm and support provided by Praxair is greatly appreciated.

66 Figure 1: Fault Detection Results for Multidimensional Mutual Information Based ICA Dissimilarity

Literature Cited

Rashid, M. M. and Yu, J. (2012a). A New Dissimilarity Method Integrating Multidimensional Mutual Information and Independent Component Analysis for Non-Gaussian Dynamic Process Monitoring. Chemom. Intell. Lab. Syst., DOI: 10.1016/j.chemolab.2012.04.008, Accepted, In Press.

Rashid, M. M. and Yu, J. (2012b). Hidden Markov Model Based Adaptive Independent Component Analysis Approach for Complex Chemical Process Monitoring and Fault Detection. Ind. Eng. Chem. Res., 51, 5506–5514.

67 Poster Slides

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68 17 Ali M. Sahlodin ‡

Research title: Toward Efficient Global Optimization of Dynamic Processes Advisor: Dr. B. Chachuat, Dr. P. Mhaskar Date: May 2012 Industrial Collaboration: Relevant industrial interaction sought

Research Goals Dynamic optimization is the technology capable of optimizing transient process performance under constraints. Conventional dynamic optimization methods can only guarantee finding a local solution. On the other hand, deterministic global optimization for dynamic systems is still at an early stage of development, and can barely tackle industrial problems. The objective of this research is to advance the current state-of-the-art in global dynamic optimization (GDO) that can address such practical applications.

Background Many industrial processes are either transient in nature or have major transient courses during a normal operation. Typical examples in chemical engineering include batch and semi-batch processes, systems operating at a cyclic steady state (e.g. pressure swing adsorption), and start-ups/shutdowns of units or plants. Dynamic optimization is the technology that can address the optimization of the above-mentioned transient systems. It has also a wide application in model calibration from time-series data, where sampling and fitting of time-series data is a common way of estimating a subset of the model parameters.

Despite its importance, seldom has dynamic optimization been used in industry so far. This can be attributed to the high level of expertise needed to solve these problems both reliably and efficiently. Conventional optimization tools can only guarantee finding locally optimal (and possibly suboptimal) solutions. However, dynamic processes may exhibit many suboptimal operating points due to their complexity. Failure to locate a global optimum can not only lead to large economic losses, but it can also have dramatic consequences in terms of safety and environmental impact. This greatly motivates the development of methods that can guarantee finding the best possible operating point, namely GDO methods.

The general objective of this research project is to develop efficient GDO methods. Two classes of approaches are currently available for global optimization, namely stochastic and deterministic methods (Neumaier [2004]). Stochastic methods are typically based on sampling the decision variable space to increase the likelihood of finding the globally optimal solution. Consequently, stochastic methods require infinite runtime to perform a complete search and guarantee finding a global optimum; this is an impractical requirement. Rather, the focus of this research is on

‡This student will be graduating in the near future and is available for employment interviews.

69 deterministic approaches, where a theoretical guarantee of finding a global optimum in a finite time (at an arbitrary finite precision) can be established. Most deterministic methods rely on a spatial branch-and-bound (SBB) procedure (Neumaier [2004]). The idea behind SBB is to construct lower and upper bounds on the global solution, and shrink these bounds successively by branching on the decision variable space until the bounds enclose the global solution within some tolerance.

While there has been good progress in applying SBB to steady-state optimization problems, its application to dynamic optimization is still in a state of infancy. The main difficulty is that dynamic models are comprised of differential equations, for which no explicit solutions are available in general. This prevents the application of conventional bounding and relaxation techniques to dynamic models. This research aims to address this bottleneck by focusing on the development of efficient techniques to bound and relax the solution of complex dynamic systems. Of particular interest are techniques that compute convex/concave bounds, which generally offer a faster convergence than simple interval bounds. In turn, such techniques can be incorporated into SBB algorithms, thereby giving the ability to solve bigger dynamic optimization problems to global optimality.

Research Plan This research has been conducted in the following stages.

1. Development of a new state-relaxation algorithm– In the first stage, a novel procedure for constructing convex/concave bounds (i.e. relaxations) of state variables has been developed (Sahlodin and Chachuat [2011b]). The algorithm builds upon interval methods for validated solution of ordinary differential equations (ODEs) (Nedialkov et al. [1999]) in combination with McCormick’s relaxation technique (McCormick [1976]).

2. Extension of relaxation algorithm to Taylor models –Classical interval analysis is known to suffer from excessive overestimation for nonlinear complex expressions. Such overestimation affects the (tightness) quality of the computed state bounds. On the other hand, Taylor model methods (Berz [1997]) have the ability to mitigate such overestimation to a great extent. The second stage of the research has involved incorporating Taylor models for improved bounding quality. This has been done in two variants. In the first variant, the state-relaxation algorithm developed in Stage 1 has been extended to a Taylor model method for validated solution of ODEs. In the second variant, the Taylor model ODE method is not extended, but only McCormick relaxation of final-time Taylor models is considered. The resulting convex/concave state bounds are guaranteed to be no weaker than their underlying interval bounds obtained via Taylor models (Sahlodin and Chachuat [2011a]), and they have been found to outperform other state-relaxation techniques as the parameter domain shrinks.

3. Algorithm enhancement by incorporation of polyhedral relaxations. Direct use of the nonlinear relaxations developed in Stage 2 for SBB would be inefficient due to the high computational demand and robustness issues of nonlinear programming (NLP) solvers. A

70 workaround would be linearization of the relaxations. Although simple, this method can lead to loose bounds. Rather, this stage considered polyhedral relaxations (Smith and Pantelides [1999]) of Taylor models in order to construct linear, yet relatively tight bounds for the dynamic optimization problem.

4. GDO with proposed relaxation algorithm– The proposed relaxation algorithm has been embedded into a SBB procedure for global optimization of dynamic processes. The efficiency of the resulting GDO algorithm has been tested on a variety of benchmark problems, and compared with existing GDO algorithms.

Current Status All the above-mentioned stages have been accomplished. The results from this research are being disseminated through journal publications and/or conference proceedings. Also, areas of potential improvements are being identified as suggestions for future work.

Literature Cited

Berz, M. (1997). From taylor series to taylor models. In Nonlinear Problems in Accelerator Physics, pp. 1–27. American Institute of Physics CP405.

McCormick, G. P. (1976). Computability of global solutions to factorable nonconvex programs: Part I – Convex underestimating problems. Math Program, 10, 147–175.

Nedialkov, N. S., Jackson, K. R., and Gorliss, G. F. (1999). Validated solutions of initial value problems for ordinary differential equations. Applied Math and Comput, 105, 21–68.

Neumaier, A. (2004). Complete search in continuous global optimization and constraint satisfaction. Acta Numer, 13, 271–369.

Sahlodin, A. and Chachuat, B. (2011a). Convex/concave relaxations of parametric ODEs using Taylor models. Comput. Chem. Eng., 35(5), 844–857.

Sahlodin, A. and Chachuat, B. (2011b). Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs. Appl Numer Math, 61(7), 803–820.

Smith, E. and Pantelides, C. (1999). A symbolic reformulation/spatial branch-and-bound algorithm for the global optimisation of nonconvex MINLPs. Comput. Chem. Eng., 23(45), 457 – 478.

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72 18 Matt Wallace

Research title: Offset-free Model Predictive Control of a Vapor Compres- sion Cycle Advisor: Dr. P. Mhaskar Date: May 2012 Industrial Collaboration: Johnson Controls, Inc.

Research Goals

A comfortable indoor environment in buildings is provided by mechanical and electrical systems classified as heating, ventilating and air-conditioning (HVAC) systems. A significant portion of the energy usage in buildings goes towards the operation of these HVAC systems. Increased environmental and cost concerns have placed greater emphasis on the energy efficiency of these systems, which through either better building design, retrofitting existing equipment/material and/or improving upon the existing HVAC control design can result in significant energy and cost savings. This work focuses on the latter option, where the following hierarchical approach was/is taken in solving this problem. Initially, this consisted of improving the local cooling device control using classical designs, which provided a performance baseline to use as we continue to progress towards the successful design and implementation of predictive control designs on the specific cooling device. Once improved local control is achieved, the focus of this work will shift towards designing/implementing an integrated control framework which will account for the start- up/shutdown of the cooling devices, while ensuring the cooling device is operated in a cost and energy efficient manner during all states of operation.

Background

In the recent past there have been a significant number of simulation and experimental-based studies on the modeling and control of cooling systems including refrigeration systems for food preservation, roof top cooling units, and chillers. This work focuses on a vapor compression cycle (VCC), a commonly used cooling mechanism in HVAC systems, for which models (validated using experimental data) covering various regimes of operations have been developed.

A VCC refers to a type of thermodynamic machinery that transfers heat using a compressible fluid referred to as the refrigerant. The most common realization of a VCC consists of four components: a compressor, condenser, expansion valve, and an evaporator. In a VCC unit, the refrigerant enters the compressor as a superheated vapor and is compressed to a higher pressure, resulting in the superheated vapor. From the compressor, the superheated refrigerant vapor enters a condenser (typically placed outdoors), condensing to a sub-cooled liquid at the condenser exit as a fan blows the ambient air over the condenser. The high pressure sub-cooled liquid then flows into an expansion valve which decreases the pressure and temperature of the refrigerant, causing a liquid-vapor

73 mixture to form. Then, the two-phase refrigerant mixture enters an evaporator that is exposed to the environment to be cooled. The environment temperature is above the temperature of the refrigerant, resulting in the evaporation and subsequent heating of the refrigerant to a superheated vapor at the evaporator exit. The cooling medium (air or water), in turn, is cooled and available to be distributed for cooling. The superheated vapor from the evaporator exit then flows back into the compressor, completing the cycle.

The control objectives are typically defined in terms of degrees of superheat in the refrigerant at the evaporator exit (Ts,e) and the air temperature (or the temperature of the cooling medium) at the o evaporator exit (the supply air temperature, T a,e). Ensuring that superheated refrigerant exits the evaporator is of utmost importance in preventing physical damage in the VCC, as liquid refrigerant can damage the mechanical components within the compressor. At the same time, maximization of the two-phase region within the evaporator maximizes the energy efficiency of the cycle resulting in a tradeoff between optimality and safety. For our VCC model, manipulated variables include the compressor speed and the expansion valve opening.

When using single-input-single-output (SISO) control approaches (classical PI/PID or various versions of it), the performance of the system is limited by the inherent nonlinearity and multivariable nature of the system. One control approach better suited to handle such system characterisitics is that of model predictive control (MPC), which recently has become more common within HVAC system control.

Research Plan

One of the challenges in the implementation of linear MPC on VCC units is the significant plant- model mismatch due to structural, functional, and parametric uncertainties. One approach to handle these is to assume additional constant process or measurement disturbance ‘states’ and to estimate them using a state estimation technique resulting in offset-free MPC designs (Muske and Badgwell [2002]). A key issue in the implementation of these designs however, is the tuning of the state estimator and the MPC to enable tight (offset-free) control while allowing the MPC to satisfy the performance (and energy efficiency) criteria. With these objectives as well as a practical implementation in mind, we have developed the following research plan.

One of the key steps is to design an offset-free (OF) MPC, comprising of a Luenberger observer (to estimate the assumed constant ‘disturbance’) coupled with a standard MPC formulation, followed by implementation on a first-principle model of a VCC linked to a building simulator. Next, tuning guidelines are to be developed that enable the ‘decoupling’ of the Luenberger and MPC design parameters. Once a systematic tuning approach has been developed, the closed performance of this control design will be compared with that of conventional approaches under simulation conditions that closely resemble those which a practical cooling unit is exposed to. Specifically, this will include a combination of measurement noise (contributed by sensor noise) and subjecting the cooling unit

74 to realistic disturbances in both internal and ambient air conditions. Testing the controller against a realistic model and on test bed applications are within the scope of the research.

Current Status

Currently, all tasks in the research plan have been completed, including achieving superior closed- loop performance with the OF MPC design for a majority of the different conditions for which the control designs were subjected to. These closed-loop results have been summarized in the following table.

Table 18.1: Closed-loop Performance Comparison

T o ISE ( s·oC2) Cumulative Energy (kJ) System Conditions a,e PI MPC PI MPC Standalone VCC 804 226 2.27 x 104 2.17 x 104 s.t. Measurement Noise 5753 2489 2.27 x 104 2.16 x 104 s.t. Realistic Disturbances 6499 6112 2.27 x 105 9.10 x 104 s.t. Real. Dist. + Meas. Noise 5296 5890 9.52 x 105 5.21 x 104

However, due to limitations in our current VCC model, specifically it’s lack of validity in certain operating regions in addition to it’s low cooling capacity, we plan on re-implementing this plan on a different HVAC system model, with the purpose of designing and testing on a more practically- relevant cooling system. To date, we’re in the process of obtaining a heat pump model (to take the place of the VCC model) validated over a wider range of operating conditions and with a considerably larger cooling capacity (∼ 3 times larger). For further detail into the control design and the subsequent closed-loop results from the implemented research plan, the reader is referred to slides 3-6 located on the last page of this research summary.

Industrial Collaboration

Feedback from researchers at Johnson Control Inc. (JCI) has been invaluable in designing a control approach that is well understood from a theoretical perspective while still remaining practically- relevant. Their partnership with TLK Thermo, has enabled us to obtain an HVAC system model of more practical-relevance in terms of both validation range as well as in terms of cooling/heating capacity. Another significant advantage in collaborating with JCI, is their ability to provide us with a practical medium, in the form of a JCI heat pump, to eventually test out our control design(s) on.

Literature Cited

Muske, K. and Badgwell, T. (2002). Disturbance Modeling for Offset-free Linear Model Predictive Control. Journal of Process Control, 12, 617–632.

75 Poster Slides

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76 19 Ian Washington

Research title: Large-Scale Dynamic Optimization for Design & Operation of Chemical Processes Advisor: Dr. C.L.E. Swartz Date: May 2012 Industrial Collaboration: Praxair, Inc.

Research Goals

Recent advances in modeling, simulation and optimization technology have promoted numerous applications of large-scale plant-wide dynamic simulation and optimization studies. One particular application where this technology has had significant benefit is in improving dynamic performance of cryogenic air separation processes (see, Cao et al. [2011]). The first goal of this on-going research is the assessment of current dynamic optimization techniques for the design and operation of air separation plants with the objective of assessing the numerical performance of the applied algorithms. A second goal, and major contribution of the project, is the development and implementation of a dynamic optimization algorithm applicable to large-scale DAEs. In particular, the multiple-shooting algorithm has shown promising results for large-scale process systems (see, Leineweber et al. [2003]). Our ultimate goal is to utilize this technique within a multi-scenario based formulation for handling uncertainty within integrated design and control problems. A key implementation aspect to be explored is the use of parallel computing for reducing the computation time particularly within the multi-scenario optimization approach.

Background

Cryogenic air separation is a widely used technology for producing high purity gases and liquids of nitrogen, oxygen and argon for a variety of applications, but is a highly energy intensive process. Given ever increasing electricity/energy prices, to be competitive, the utility providers must ensure customers of consistent operating costs and as such must design the plant to operate in a versatile and agile manner capable of meeting required customer demands while minimizing overall energy expenditures. A key technology to achieving such “optimal” designs is model-based optimization techniques that utilize plant-wide dynamic models. The application of dynamic optimization to determine optimal designs and operating policies for realistic plant models requires efficient numerical algorithms tuned to handle a high computational load. There are three established practical classes of algorithms for large-scale dynamic optimization, namely sequential, simultaneous and multiple- shooting methods. Sequential methods solve an embedded dynamic model at each optimization iteration, simultaneous methods fully discretize the model and then solve the optimization and model simultaneously, and multiple-shooting is a hybrid of the former two methods.

77 The application of dynamic optimization technologies to air separation plants has only been performed in a few select past studies. Kroner et al. [2001] use the sequential approach for parameter estimation of discontinuous high-index DAE models. Schenk et al. [2002] identify economic and operability benefits by considering both design and control in a unified framework, whereby a mixed-integer sequential approach is used. Cao et al. [2011] have again used the sequential approach for identifying design characteristics that limit plant agility during dynamic changes in production demand and electricity prices. Given the size of the process models of interest (500 – 3000 DAEs), the sequential approach is a natural first choice since the resulting optimization problem is relatively small (< 100 decision variables). However, advances in nonlinear programming (NLP) solvers over the last 10 years has enabled very large NLPs (thousands to millions of decision variables) to be solved very quickly, which has enabled both simultaneous and multiple-shooting methods to be used efficiently on large-scale DAEs.

Research Plan

Currently we are investigating all three of the noted dynamic optimization techniques in a comparative manner in order to gage each methods performance for solving large-scale dynamic optimization problems. On-going work includes the development of our own dynamic optimization tool that utilizes the multiple-shooting technique and second the development of a multi-scenario dynamic optimization algorithm suitable for the optimal design of dynamic systems under uncertainty. The research is planned to proceed as follows,

1. Model Development and Simulation – This phase serves as a preliminary phase in order to build several scalable first-principles models to be used for optimization algorithm testing and application. Our models of interest are distillation-based and in particular the column portion of an air separation plant.

2. Current Optimization Algorithm Assessment – The next phase serves to evaluate currently available dynamic optimization tools utilizing our particular process model. Tools currently being used are a sequential algorithm called DAEOC (developed by B. Chachuat), a tool called MLDO (developed by Z. Chong) that enables the simultaneous approach through translating an equation based description of the process model and optimization problem to AMPL, and a multiple-shooting algorithm called MUSCOD-II (developed by H.G. Bock at IWR Heidelberg).

3. Optimization Algorithm Development and Application – The next major phase in- volves algorithm development where first a multiple-shooting technique will be implemented that makes use of available tools for DAE (e.g., IDAS) and NLP (e.g., SNOPT, IPOPT) solution. Furthermore, since multiple-shooting lends itself nicely to parallelization we will implement the algorithm to offer the option of parallel computing. Second, extensions will be made to develop an algorithm to efficiently handle multi-scenario formulations. Aspects to be explored

78 include: parallelization of DAE solution (possibly at multiple levels within the algorithm), and decomposition techniques. Throughout this phase a number of air separation applications will be developed that will be geared towards demonstrating integrated design and control on large-scale systems.

Current Status

Several rigorous distillation models have been constructed and applied for set-point transitions using open-loop optimal control. Currently we are working with a nitrogen air separation model and assessing the numerical solution performance of the above noted dynamic optimization techniques. Several design-based application case studies are being developed to demonstrate each optimization technique on a series of industrially relevant problems. Completed results for this comparative study are anticipated shortly and will be presented at this years CSChE conference. Initial work has also commenced on our own implementation of the multiple-shooting algorithm and we are currently fleshing out the software framework and solver interface. The development of this algorithm and extensions to solve multi-scenario formulations compose the major tasks of this project and as such are long-term project goals.

Industrial Collaboration

We will continue our collaboration with Praxair Inc. to extend previous air separation modeling and optimization work. Their expertise and close communication has been invaluable and will help us going forward on this project.

Literature Cited

Cao, Y., Swartz, C., and Baldea, M. (2011). Design for dynamic performance: Application to an air separation plant. In American Control Conference, San Francisco, USA.

Kroner, A., Kronseder, T., Engl, G., and von Stryk, O. (2001). Dynamic optimization for air separation plants. In Gani, R. and Jorgensen, S. (Eds.), ESCAPE–11, Vol. 9, pp. 433–438. Elsevier.

Leineweber, D., Schafer, A., Bock, H., and Schloder, J. (2003). An efficient mulitple shooting based reduced SQP strategy for large-scale dynamic process optimization. Parts 1 and 2. Computers and Chemical Engineering, 27(2), 157–174.

Schenk, M., Sakizlis, V., Perkins, J., and Pistikopoulos, E. (2002). Optimization-based methodologies for integrating design and control in cryogenic plants. In Grievink, J. and van Schijndel, J. (Eds.), ESCAPE–12, Vol. 10, pp. 331–336. Elsevier.

79 Poster Slides

Dynamic Optimization for Integrated Design & Control Research Objectives & Planned Project Work

. Large-scale design and control: large models and optimization problems 1 Optimization solution assessment using sequential, multiple-shooting, and simultaneous approaches . Objective: simultaneously determine economically optimal design and control performance (e.g., equip. size, set-points, controller parameters, ref. trajectories) 2 Initial assessment using a simplified air separation unit (ASU) model . Realistic solutions require: inclusion of uncertainty within exogenous forces (e.g., electricity prices, product demand) and internally within the model (parameters) 3 Dynamic optimization algorithm development (multiple-shooting code) . development using C

IRC ω0 AIR . distributed parallel u(t)

Ta(t) implementation using MPI ω1 ω2

COM ωn 1 . DAE solvers: IDAS (open-source) − E(t) Drain x(t) ξ0,j+1 . NLP solvers: IPOPT (open-source) ξ0,1 Time of Day ξ0,0 ξ0,j LN2 WORHP (free for acad.)

PHX t0 t1 t2 t3 tf ··· EXP . AD tool: ADIC (free for acad.) HPC D(t) 4 Multi-scenario algorithm development incorporating multiple-shooting algorithm Waste . The DAEs for each scenario can be trivially solved in parallel; however, a Time of Day GN2 more crucial aspect for investigation is how to efficiently decompose the NLP

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Dynamic Optimization Formulation w/ Uncertainty Multi-Scenario Approach to Handle Uncertainty

. Expected value over all possible parameter realizations θ . Determine d (common for all scenarios) for all θ θ(i) ns ∈ { }i=1

J (i) (i) (i) (i) (i) min := Eθ Γ Φ(t, x(t), z(t), u(t), v(t), θ, d) d = design parameters min J := Φdes(d) + wi Φi tf , x (tf ), z (tf ), u (tf ), v (tf ), d, θ d,u(t) ∈ { } i S d,u(i)(t) i S ∈ · u(t) = open-loop controls ∀ ∈ st: fd (t, x˙(t), x(t), z(t), u(t), v(t), θ, d) = 0 st: DAE model, ConstraintsP , Bounds i S = 1,..., n
x(t) = differential states ∀ ∈ { s } fa (t, x(t), z(t), u(t), v(t), θ, d) = 0 h (t, x(t), z(t), u(t), v(t), θ, d) = 0 z(t) = algebraic states g (t, x(t), z(t), u(t), v(t), θ, d) 0 v(t) = disturbances Optimal Plant Design ≤ Model 1 L U L U • Optimal s.s. set-points d [d , d ], u(t) [u , u ] θ = uncertain parameters ∈ ∈ Model 2 L U • Distillation sizing Γ = θ θ [θ , θ ] wi + Model 3 = { | ∈ } . • Heat-exchanger areas . . Optimal Operating Policies C D Remarks: E Model ns • State trajectories • θ considered time-invariant parameters where v(t) := f (t, θ) w := probability of realization i • Open-loop inputs • Could consider closed-loop formulations where u(t) are not direct opt. decisions CE := electricity price • d include equipment sizes, operating points, controller tuning parameters D := product demand

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Dynamic Optimization Solution Techniques Open-loop Set-Point Transition Example

GN2 1 2 7 stage ASU distillation column ( 80 DAEs) IRC Waste 1 Sequential Method (aka. CVP, single-shooting) , Shooting-based Methods ≈ 2 Multiple-Shooting Method • Controlled variables: y(t) := (Tbot, Ttop)> rdraw Obj./Constr. Obj./Constr. 3 Simultaneous Method (aka. full transcription) • Manipulated variables: u(t) := rdraw Gradients at t at t [t , t + ] LN2 i i ∈ j j 1

tf 2 2 2 ω ∂x(t) ∂x(t) min J := y(t) ysp + u(t) u¯ dt + ∆uk 0 ∂p , ∂ξ x(t) Q R S u(t) NLP Solver 0 u(t),u¯ t0 k − k k − k k k ω(k) Ω Fl HPC ω1 ω2 ωn 1 − ∈ ξ(k) Ξ st: DAER model 0 ∈ t t P u(τ) u¯ = 0 where τ (t0 + M, tf ] Fv U(t, ω) − ∈ L U LC DAE Solver u(t) [u , u ], u¯ ∈ ∈ T 1 t [tj , tj+1] j t ∈ ∀ Drain 0.3 x(t) 2 3 draw 0.25 method #var J #iter #feval CPU (sec) Simultaneous Method r 0.2 sequential † 21 56.54 19 58 816 Discretize NLP Solver 89.55 3 (k) (k) OCFE t [t0, tf ] ω Ω, ξ Ξ top 89.5 simultaneous ‡ 6761 56.54 421 508 724 τ0 τ1 τ2 τ0 τ0 ∈ ∈ ∈ ··· T 89.45 † using DAEOC which uses DASPK and SNOPT; . ( ) := U( , ω) ‡ using DAEOC with IPOPT and DAEPACK for AD; controls parameterized over n stages (elements) u t t 91.2 bot

. states determined by DAE solver or OCFE via NLP solver T 91.1 • currently using MUSCOD-II multiple-shooting code 91 on a smaller test problem; preliminary solution 0 200 400 . level of discretization increases from sequential (minimal) to simultaneous (full) times are quite fast Time (sec)

Ian Washington | Chris Swartz Large-Scale Dynamic Optimization for ChE Processes 5 Ian Washington | Chris Swartz Large-Scale Dynamic Optimization for ChE Processes 6 Slide 5 Slide 6

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