Model-Based Control Development for an Advanced Thermal Management System for Automotive Powertrains
A Thesis
Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University
By
Kyle Ian Merical,
Graduate Program in Mechanical Engineering
The Ohio State University
2013
Master’s Examination Committee:
Professor Marcello Canova, Advisor Professor Giorgio Rizzoni, Committee Member Professor Shawn Midlam-Mohler, Committee Member c Copyright by
Kyle Ian Merical
2013 Abstract
Rising fuel prices and tightening vehicle emission regulations have led to a large demand for fuel efficient passenger vehicles. Among several design improvements and technical solutions, advanced Thermal Management Systems (TMS) have been recently developed to more efficiently manage the thermal loads produced by internal combustion engines and thereby reduce fuel consumption.
Advanced TMS include complex networks of coolant, oil and transmission fluid lines, heat exchangers, recuperators, variable speed pumps and fans, as well as active fluid
flow control devices that allows for a greatly improved freedom to manage the heat rejection and thermal management of the engine and transmission components. This control authority can be exploited, for instance, to rapidly warm the powertrain
fluids during vehicle cold-starts, and then maintain them at elevated temperatures.
Increasing the temperatures of the engine oil and transmission fluid decreases their viscosity, ultimately leading to a reduction of the engine and transmission frictional losses, and improved fuel economy.
On the other hand, robust and accurate TMS controllers must be developed in order to take full advantage of the additional degrees of freedom provided by the available actuators and system hardware configuration.
To this extent, this work focuses on developing model-based TMS controls for a pro- totype light-duty automotive powertrain during fully warmed-up vehicle operation.
ii The design of the models and control algorithms is conducted in parallel with the development of a prototype TMS, hence realizing a co-design of the TMS hardware and control system.
In order to achieve this goal, first-principle models are created to characterize the thermal dynamics of the TMS components, and calibrated on specific components’ data. The submodels are then integrated into a complete TMS model predicting the temperature dynamics of the powertrain fluids in response to commands to the available system actuators as well as operating and boundary conditions.
The developed model is then used as a tool for model-based system analysis, optimiza- tion and control design. Specifically, a proof-of-concept control design is conducted to verify the feasibility of the TMS in maintaining the temperatures of the power- train fluids within the recommended range. In particular, a model-based optimization is conducted to define the open-loop actuator positions for various engine operating conditions that maintain the coolant temperature at the desired set-points. The open- loop strategy is then combined with a feedback control loop that combines rule-based and PI controllers to regulate the actuator position based on coolant temperature tracking error, compensating for disturbances and modeling errors.
The prototype TMS controller developed in this work is shown to be effective in re- ducing the fluctuations in the coolant temperatures during the FTP driving cycle, compared to a baseline rule-based controller. Based on the preliminary results ob- tained, indications on the design of a state-space multi-variable feedback controller are made. This will further reduce the coolant temperature tracking error and allow all TMS actuators to work together in unison.
iii This Thesis is dedicated to my parents. They have always been supportive of me in all my endeavors. This Thesis is another addition to the long list of things I could
not have done without them.
iv Acknowledgments
My sincere thanks go to Professor Shawn Midlam-Mohler. Without several long conversations with him, I would probably not have made the decision to pursue my
Master’s Degree at all. His advice in that decision making process ultimately led me down this path, which is undoubtedly a great one for my future career.
I would also like to thank my advisor, Professor Marcello Canova, for inviting me to join this research project, as well as all of the help he has extended to me. I could not have gotten through my work without his support and advice in the model and control development process. Additionally, his guidance in steering the direction of my work helped keep me on track and moving forward.
My heartfelt thanks go to Dr. Fabio Chiara, as well. His vast technical knowledge on building and troubleshooting complex models was truly invaluable to my work.
His attention to detail and willingness to drop everything to help me was also greatly appreciated.
I thank Dr. Lisa Fiorentini for her help with the system analysis and control de- velopment associated with my work. Her extensive knowledge of system dynamics and control design helped shape my work. Also, her optimistic and helpful attitude helped keep me motivated when things got rough.
I would also like to thank my fellow students working on the Chrysler/DoE project at OSU. Their collaborative help troubleshooting models and answering my general
v questions is greatly appreciated. The continued work of Sabarish Gurusubramanian’s efforts to implement the controls developed in this work on the production vehicle are also appreciated. My roommate and colleague, Jeremy Couch, was a great partner to have for this project. His help in my day-to-day struggles with this project as well as class work is greatly appreciated. More importantly, working alongside a friend always helps improve morale during Engineering analysis and Theis writing marathons.
The past efforts of those having already completed their graduate work on this project were not forgotten either. I thank Neeraj Agarwal and Ben Grimm for the work they put into this project to get the full model of the production vehicle working, so that
I could start my work where they left off.
I also thank Chrysler Group LLC for their funding on this project. Additionally, the support and information I received from several Chrysler employees helped to improve the accuracy and significance of my work.
vi Vita
2007 ...... Bellbrook High School
2011 ...... B.S.M.E., The Ohio State University
2011-present ...... Graduate Research Associate, Depart- ment of Mechanical and Aerospace En- gineering, Center for Automotive Re- search, The Ohio State University
Fields of Study
Major Field: Mechanical Engineering
vii Table of Contents
Page
Abstract ...... ii
Dedication ...... iv
Acknowledgments ...... v
Vita ...... vii
List of Tables ...... x
List of Figures ...... xii
1. Introduction ...... 1
1.1 Scope ...... 2 1.2 Document Layout ...... 3
2. State of the Art ...... 5
2.1 Overview of Advancements in Engine and Powertrain Technology . 7 2.2 Current Thermal Mangement System (TMS) Technology ...... 11 2.2.1 Overview of Thermal Management Systems ...... 22 2.3 Thermal Management System Control ...... 25 2.3.1 TMS Control During Rapid Warm-up Phase ...... 26 2.3.2 TMS Control During Fluid Conditioning Phase ...... 34 2.4 TMS Control Design Methodology ...... 44
3. Modeling of a Thermal Management System ...... 45
3.1 Overview of Thermal Management System ...... 45 3.2 Thermal System Modeling Approaches ...... 48
viii 3.2.1 Lumped Parameter Modeling ...... 48 3.2.2 Lumped Thermal Capacitance Method ...... 49 3.2.3 Receivers ...... 49 3.3 Models Previously Developed ...... 50 3.3.1 Engine Thermal Model ...... 51 3.3.2 Slow Response Heat Exchangers ...... 56 3.3.3 Fast Response Heat Exchangers ...... 57 3.3.4 Transmission Thermal Model ...... 59 3.4 Updated Models ...... 61 3.4.1 Coolant Flow Network ...... 62 3.4.2 Electronic Thermostat ...... 66 3.4.3 Radiator Fan ...... 68 3.5 Modeling of Exhaust Gas Recirculation Cooler Thermodynamics . 70 3.5.1 EGRC Model Calibration and Validation ...... 72 3.6 Complete TMS Model Results ...... 79 3.6.1 FTP Engine Operating Range ...... 82 3.6.2 TMS Inputs ...... 84 3.6.3 TMS Outputs ...... 86 3.6.4 TMS Actuator Positions ...... 88 3.6.5 Fuel Consumption ...... 91
4. Thermal Management System Control Development ...... 92
4.1 Control Objectives and Methodology ...... 93 4.2 System Analysis ...... 97 4.3 Baseline TMS Controller ...... 102 4.4 Open-Loop Control Design ...... 108 4.4.1 Open-Loop Controller Performance ...... 117 4.5 Closed-Loop Control Design ...... 123 4.5.1 City Driving Feedback Control ...... 124 4.5.2 Highway Driving Feedback Control ...... 130 4.5.3 Closed Loop Controller Structure ...... 136 4.5.4 Closed-Loop Controller Performance ...... 138
5. Conclusions and Future Work ...... 144
5.1 Conclusions ...... 144 5.2 Future Work ...... 146 5.2.1 Future Control Development Methodology ...... 147
Bibliography ...... 163
ix List of Tables
Table Page
2.1 DOE of TMS Actuator Positions ...... 33
3.1 EGRC Calibration Coefficients ...... 73
4.1 Baseline Coolant Temp. Tracking Error ...... 105
4.2 Baseline Actuator Energy Consumption ...... 107
4.3 DoE Operating Points ...... 110
4.4 Coolant Pump Power Consumption ...... 111
4.5 Radiator Fan Power Consumption ...... 111
4.6 Open-Loop Coolant Temp. Tracking Error ...... 118
4.7 Open-Loop Actuator Energy Consumption ...... 123
4.8 PI Controller Step Response Metrics City Driving ...... 127
4.9 PI Controller Gains for City Driving ...... 130
4.10 PI Controller Step Response Metrics for Highway Driving ...... 132
4.11 PI Controller Gains for Highway Driving ...... 136
4.12 Coolant Temp. Tracking Error ...... 142
4.13 Actuator Energy Consumption ...... 143
x 5.1 EGRC Thermal Model State Variables ...... 152
5.2 EGRC Thermal Model Control Inputs ...... 153
5.3 Equilibrium EGRC Thermal Model Control Inputs ...... 154
5.4 Equilibrium EGRC Thermal Model State Variables ...... 154
5.5 Summary of TMS Model Order Reduction ...... 160
xi List of Figures
Figure Page
1.1 Prototype TMS Architecture ...... 3
2.1 U.S. Liquid Fuel Consumption by Sector, in Millions of Barrels per Day[1] ...... 5
2.2 Primary Energy Use by Fuel [Quadrillion Btu] [2] ...... 6
2.3 Primary Energy Use by Region [Quadrillion Btu] [2] ...... 7
2.4 Characteristics of Light Vehicles Sold in U.S. Between 1980 and 2010 [3] ...... 9
2.5 Market Share of Transmission Gears in Cars Sold in U.S. Between 1980 and 2010 [3] ...... 9
2.6 Energy Audit for EPA Drive Cycle with 2.5L Mid-Size Sedan [4] . . 12
2.7 Viscosity of 0W-40 Engine Oil for Varying Temperature ...... 13
2.8 BorgWarner Hybrid Coolant Pump [5]...... 16
2.9 Coolant Pump Power Consumption During US06 Emission Cycle for BorgWarner Hybrid Coolant Pump (HCP) and mechanical coolant pump (MCP) [5] ...... 17
2.10 Schematic of Exhaust Heat Recover System [6] ...... 18
2.11 Comparison of Performance of Vehicle with EHRS to Baseline [6] . . 19
2.12 Losses Associated with Thermoelectric Device Tested [7] ...... 20
xii 2.13 Flow of Coolant in 2004 Toyota Prius During Cold-Start [8] . . . . . 21
2.14 Simulated Fuel Economy Improvement Using Coolant Resevoir [8] . . 21
2.15 Prototype TMS Configuration ...... 23
2.16 Audi TFSI Coolant Pump with Integrated Rotary Valves [9] . . . . . 27
2.17 Coolant Temp. During NEDC Cycle for Baseline and Advanced TMS Configurations [9] ...... 28
2.18 Coolant Temp. During European Drive Cycle for Baseline and Ad- vanced TMS Configurations [10] ...... 30
2.19 Fuel Consumption of Mercedes A Class During NEDC [10] ...... 31
2.20 TMS Architecture of Vehicle Equipped with Pentastar Engine [11] . . 32
2.21 Pareto Analysis of Pentastar Rapid Warm-up [11] ...... 34
2.22 Simulation Results Using Conventional Thermostat [12] ...... 37
2.23 Simulation Results Using Active TMS and Coolant Temp. Feedback [12]...... 38
2.24 Simulation Results Using Active TMS and Cylinder Head and Wall Temp. Feedback [12] ...... 39
2.25 Schematic of TMS Considered in [13] ...... 41
2.26 Schematic of Experimental Test Set-up [13] ...... 42
2.27 Simulated Control Performance Over Time [13] ...... 43
3.1 Prototype Vehicle TMS Configuration ...... 46
3.2 Mean Value Model of Receiver [14] ...... 49
3.3 Production Vehicle TMS Configuration ...... 52
xiii 3.4 Thermal Masses Included in ETM ...... 53
3.5 Engine Thermal Model Block Diagram ...... 54
3.6 Slow Response Heat Exchanger Block Diagram ...... 56
3.7 Fast Response Heat Exchanger Block Diagram ...... 58
3.8 Transmission Thermal Model Block Diagram ...... 60
3.9 Coolant Flow Network Block Diagram ...... 62
3.10 Normalized Coolant Flow vs. Pressure Rise for Different Pump Speeds 64
3.11 Electrical Analogy Represenation of Coolant Flow Network ...... 65
3.12 Normalized Coolant Flow to All Branches with Varying EGRC CV Position ...... 66
3.13 Thermostat Model Block Diagram ...... 66
3.14 Thermostat Model Steady-State Opening ...... 68
3.15 Thermostat Model Time Constant ...... 68
3.16 Radiator Fan Block Diagram ...... 69
3.17 Normalized Radiator Fan Flow ...... 69
3.18 Shell and Tube EGRC Architecture [15] ...... 70
3.19 EGR Cooler Block Diagram ...... 71
3.20 Experimental Inputs for EGRC Calibration ...... 74
3.21 Experimental and Simulated Coolant Temperature Data for EGRC Calibration ...... 75
3.22 Experimental and Simulated Exhaust Temperature Data for EGRC Calibration ...... 76
xiv 3.23 Experimental Inputs for EGRC Validation ...... 77
3.24 Validation of EGRC Exhaust Outlet Temperature Model ...... 78
3.25 Histogram of Exhaust Temperature Prediction Error ...... 78
3.26 Complete TMS Block Diagram ...... 79
3.27 Vehicle Energy Simulator Hierarchy ...... 81
3.28 Vehicle Velocity During FTP ...... 82
3.29 Engine Speed During FTP ...... 83
3.30 Throttle Opening During FTP ...... 83
3.31 FMEP Calculation ...... 84
3.32 Friction Mean Effective Pressure During FTP ...... 85
3.33 Transmission Efficiency During FTP ...... 86
3.34 Engine and Transmission Fluid Temperatures During FTP ...... 87
3.35 EGR Temperature During FTP ...... 88
3.36 Thermostat Opening During FTP ...... 89
3.37 Coolant Pump Speed During FTP ...... 90
3.38 Radiator Fan Speed During FTP ...... 90
3.39 Fuel Consumption During FTP ...... 91
4.1 Effects of Fluid Temperature Oscillations [16] ...... 93
4.2 Maximum EGR Temperature at EGRC Outlet ...... 95
4.3 Heat Rejected to Coolant from Engine ...... 98
4.4 Heat Rejected to Coolant from Engine with FTP Operating Points . 99
xv 4.5 Heat Rejected to Radiator With Mechanical Thermostat Actuation . 100
4.6 Heat Rejected to Radiator With Electric Thermostat Actuation . . . 100
4.7 Engine Coolant Temperature With Baseline TMS Controller . . . . . 104
4.8 EGR Temperature With Baseline TMS Controller ...... 104
4.9 Thermostat Opening With Baseline TMS Controller ...... 106
4.10 Coolant Pump Speed With Baseline TMS Controller ...... 106
4.11 Radiator Fan Speed With Baseline TMS Controller ...... 107
4.12 Open-Loop Thermostat Actuation (1=electrical, 0=mechanical) . . . 109
4.13 Open-Loop Coolant Pump Speed ...... 113
4.14 Open-Loop Radiator Fan Speed ...... 114
4.15 Block Diagram of Open-Loop Radiator Fan Controller ...... 116
4.16 Block Diagram of Open-Loop Coolant Pump Controller ...... 117
4.17 Open-Loop Coolant Temperature During Simulated FTP ...... 118
4.18 Open-Loop EGR Temperature During Simulated FTP ...... 119
4.19 Open-Loop Coolant Pump Speed During Simulated FTP ...... 120
4.20 Open-Loop Radiator Fan Speed During Simulated FTP ...... 121
4.21 Open-Loop Thermostat Opening During Simulated FTP ...... 121
4.22 Open-Loop Thermostat Operating Mode During Simulated FTP . . . 122
4.23 Open-Loop Coolant Pump Operating Mode During Simulated FTP . 122
4.24 Step Input of Throttle at 1200 RPM ...... 125
xvi 4.25 Step Response of Coolant Temperature at 1200 RPM ...... 126
4.26 Coolant Pump Speed During Step Response at 1200 RPM ...... 127
4.27 Radiator Fan Speed During Step Response at 1200 RPM ...... 128
4.28 Thermostat Opening During Step Response at 1200 RPM ...... 128
4.29 Control Effort During Step Response at 1200 RPM ...... 129
4.30 Step Input of Throttle at 2800 RPM ...... 131
4.31 Step Response of Coolant Temperature at 2800 RPM ...... 132
4.32 Coolant Pump Speed During Step Response at 2800 RPM ...... 133
4.33 Radiator Fan Speed During Step Response at 2800 RPM ...... 134
4.34 Thermostat Opening During Step Response at 2800 RPM ...... 134
4.35 Control Effort During Step Response at 2800 RPM ...... 135
4.36 Block Diagram of Closed-Loop Radiator Fan Controller ...... 136
4.37 Block Diagram of Closed-Loop Coolant Pump Controller ...... 137
4.38 Closed-Loop Coolant Temperature During Simulated FTP ...... 139
4.39 Closed-Loop EGR Temperature During Simulated FTP ...... 139
4.40 Closed-Loop Coolant Pump Speed During Simulated FTP ...... 140
4.41 Closed-Loop Radiator Fan Speed During Simulated FTP ...... 140
4.42 Closed-Loop Thermostat Opening During Simulated FTP ...... 141
4.43 Closed-Loop Thermostat Operating Mode During Simulated FTP . . 141
4.44 Closed-Loop Coolant Pump Operating Mode During Simulated FTP 142
5.1 TMS Controller Design Methodology [16] ...... 148
xvii 5.2 Block Diagram of Linearized EGRC Model ...... 155
5.3 Block Diagram of Reduced Order and Linearized EGRC Model . . . . 157
5.4 Inlet Exhaust Temperature Step Input ...... 158
5.5 Step Response of EGRC Thermal Model ...... 159
5.6 Linearization Point Selection ...... 161
xviii Chapter 1: Introduction
Effort has been made to increase the efficiency of the internal combustion engine ever since its invention in 1860 [17]. However, the global energy crisis along with strict emission laws for passenger vehicles has caused interest in improving the efficiency of the internal combustion engine to peak in recent years. Many new powertrain technologies have succeeded in improving engine efficiency. In so doing, they have improved the performance of passenger vehicles, as well as reduced their fuel consump- tion. However, despite new powertrain technologies, such as variable valve timing and direct fuel injection, the Thermal Management Systems (TMS) of most passen- ger vehicles has remained relatively unchanged. The TMS is tasked with maintaining suitable temperatures for the engine itself, as well as all engine and transmission flu- ids. Since the hardware of the TMS is often not actively controlled and is sized to cool the vehicle’s powertrain during harsh conditions such as high-load trailer towing, it overcools the powertrain during normal operation. This wastes energy by allowing engine oil temperatures to fall, thus increasing friction, as well as allowing the TMS actuators to consume more energy as they overcool the engine.
1 1.1 Scope
A typical modern TMS usually consists of only a radiator, engine oil cooler, and transmission oil cooler. The coolant, engine oil, and transmission oil pumps are all mechanical pumps which are coupled to the engine crankshaft with a fixed gear ratio. A passive thermostatic valve controls flow to the radiator, based on coolant temperature. An additional thermostatic valve controls the flow of transmission oil to the transmission oil cooler, as a function of transmission oil temperature. An electric radiator fan can be used to increase air flow to the radiator, however, this actuator is typically controlled with only crude rule-based on/off control.
In an effort to improve vehicle fuel economy through optimized thermal management,
Chrysler Group LLC has propsed the advanced TMS architecture shown in Figure
2.15. This prototype TMS is part of a large project funded by Chrysler Group LLC and the United States Department of Energy (DOE), to improve fuel economy through advanced powertrain technologies. To that measure, the prototype TMS employs additional heat exchangers and actuators to increase the available control authority of the TMS on engine and transmission fluid temperatures. This allows the engine oil and transmission oil to be warmed more quickly following a cold-start of the engine, thus decreasing frictional losse and fuel consumption. After the inital “rapid warm- up” phase, the TMS must maintain the temperature of all fluids at elevated target temperatures, to reduce frictional losses during fully warmed-up vehicle operation.
This work focuses on developing model-based TMS controls for fully warmed-up ve- hicle operation. The rapid development schedule of the prototype powertrain and accompanying TMS necessitate that TMS controls be developed before the prototype powertrain is fitted to a test vehicle. This requires a very high fidelity TMS model, in
2 Figure 1.1: Prototype TMS Architecture
order to develop a TMS controller without any experimental calibration. To this mea- sure, OSU has developed a Vehicle Energy Simulator (VES) in Matlab/Simulink for the production vehicle. This model consists of physics-based models for the thermal, mechanical, and electrical systems on the vehicle. The model is capable of predict- ing vehicle fuel consumption for both steady-state and transient vehicle operation and was rigorously calibrated and validated using experimental data readily available for the production vehicle. The VES was updated with the new parameters for the prototype powertrain and is used as a tool for developing TMS control strategies.
1.2 Document Layout
This Thesis contains four chapters in addition to the Introduction. A brief outline of each chapter is given in the following list:
3 • Chapter 2: A review of new and developing technologies in the areas of pow-
ertrains and TMSs is presented. Control strategies currently used on advanced
TMSs of both research and production vehicles are also explained.
• Chapter 3: The physics-based models which comprise the TMS model are re-
viewed. The models inherited from previous work at OSU as well as the model
recalibration procedure used are explained. Simulation data gathered from the
updated VES is presented.
• Chapter 4: Both open-loop and closed-loop control techniques developed for the
fully warmed-up TMS are detailed. Simulation data is presented to validate the
performance of these controllers.
• Chapter 5: A summary of the conclusions drawn from the work presented in
this Thesis is given. Future work in TMS control development is presented.
4 Chapter 2: State of the Art
Improving the fuel economy of passenger cars is extremely important to resolving the worldwide energy crisis. Figure 2.1 shows that the transportation sector consumes the majority of liquid fuels in the U.S. Although the forecasted liquid fuel consumption of other sectors is stable, the consumption of the transportation sector is expected to grow from approximately 50 million barrels per day to nearly 70 billion barrels per day during the next two decades [1].
Figure 2.1: U.S. Liquid Fuel Consumption by Sector, in Millions of Barrels per Day [1]
5 Figure 2.2 shows that the use of petroleum and other liquid fuels in the U.S. is ex- pected to decline over the next two decades, as the use of biofuels and other renewable fuels increases. However, many of these biofuels will be consumed by the transporta- tion sector, in additon to petroleum and other liquid fuels. All hydrocarbon fuels produce the green house gas carbon dioxide and pollutants when burned, and thus contribute to global warming and pollute the environment. It is also shown in Figure
2.3 that although energy consumption in OECD regions such as the U.S. is expected to grow only slightly in the next decades, developing Non-OECD countries in Asia are expected to double their current energy use. As countries such as China continue to industrialize and grow, their energy consumption rises sharply.
Figure 2.2: Primary Energy Use by Fuel [Quadrillion Btu] [2]
The projected rise in energy consumption in the U.S. and other parts of the world is compounding the current energy crisis. As more fuels are burned, fuel becomes
6 Figure 2.3: Primary Energy Use by Region [Quadrillion Btu] [2]
more scarce and expensive. Burning hydrocarbon fuels also pollutes the environ- ment. Since the transportation sector consumes a large portion of energy in the U.S. and elsewhere, it makes sense to improve the efficiency of vehicles in order to de- crease overall fuel consumption. Great strides have been made in the past decades to decrease automotive fuel consumption, as higher fuel prices motivate investing in ex- tensive research to develop fuel saving technologies. The following sections summarize some of the key advancements in automotive powertrain technology.
2.1 Overview of Advancements in Engine and Powertrain Technology
Automotive manufacturers have made many recent advances in automotive technol-
ogy in order to adhere to strict government enforced limits on fuel consumption and
emission production. As shown by Figure 2.4, sales-weighted data on new light ve-
hicles sold in the U.S. show a 110% increase in engine power output, 34% decrease
7 in 0 - 60 mph times, as well as a 17.2% improvement in fuel economy between 1980 and 2010 [3]. This increase in vehicle performance as well as fuel economy is due to the adoption and optimization of several powertrain technologies. For instance, variable valve timing and camshaft phasing have been used to increase the volumetric efficiency of engines [18]. Better fuel delivery systems and engine control software has allowed engines to run higher compression ratios and more spark advance, thereby increasing thermal efficiency [19]. Increasingly, larger engines are abandoned in favor of smaller, turbocharged and intercooled engines. It has been shown that a spark ignition (SI) engine can be downsized by 40% and turbocharged, to maintain the power of the original engine, and yield a 20% improvement in fuel economy [20]. A properly designed turbocharged engine also produces greater torque at low engine speeds, which allows the engine to operate at a lower engine speed for a given torque demand. The downsizing and downspeeding of this new generation of turbocharged engines yields significant fuel economy improvements [21]. Direct in-cylinder injec- tion of turbocharged gasoline engines can help cool the fuel-air charge and yield even further performance gains [21]. Many engines also utilize cylinder deactivation, re- ducing the number of cylinders firing at part load, as well as stop-start technology, preventing fuel consumption during engine idling [22, 23].
Figure 2.5 shows that the number of gears in transmission of passenger vehicles has also been increasing in the past three decades [3]. The extensive use of light weight materials in vehicle construction contributes to the greater fuel economy of current production vehicles, as well [24]. Hybridization as well as complete electrification of vehicle powertrains also yields large gains in fuel economy [25].
8 Figure 2.4: Characteristics of Light Vehicles Sold in U.S. Between 1980 and 2010 [3]
Figure 2.5: Market Share of Transmission Gears in Cars Sold in U.S. Between 1980 and 2010 [3]
In light of the pressing needs to reduce fuel consumption in transportation and carbon dioxide emissions, the U.S. Department of Energy has launched a number of initia- tives to improve the energy efficiency of automotive powertrains [26]. To that measure, the U.S. Department of Energy (DOE) has awarded $14.5 million to Chrysler Group
9 LLC for researching more fuel efficient powertrains for its line-up of light-duty vehicles
[26]. As a recipient of this grant, the Advanced Technology Powertrains for Light-
Duty (ATP-LD) Vehicles Program at Chrysler has the objective of demonstrating an increase in fuel economy of a Chrysler Town & Country vehicle by 25 % over a stan- dard FTP drive cycle, using only conventional powertrain improvements (no weight or drag reduction or hybridization) [27]. To accomplish this, Chrysler is investing an additional $15.5 million in the program and developing a more efficient powertrain which uses an inline four cylinder engine with twin sequential turbochargers and a nine speed automatic transmission. The engine also utilizes a high compression ratio, along with exhaust gas recirculation (EGR), for knock control [27]. Gasoline is deliv- ered via direct fuel injection and E85 is delivered by port fuel injection, for high-load knock control.
The researchers at the Center for Automotive Research of The Ohio State University are assisting in the ATP-LD Project by developing controls for an advanced Thermal
Management System (TMS), as well as Ancillary Load Reduction (ALR) strategies.
Ancillary load reduction is used to harvest excess energy from the vehicle’s crankshaft during deceleration, in order to power the alternator and air conditioning system.
This Thesis focuses on the advanced TMS, which uses heat exchangers and fluid
flow control devices to control the thermal loads produced by the engine, to reduce fuel consumption. This is accomplished by utilizing a TMS control strategy that maintains the engine oil and transmission oil at higher temperatures, thereby reducing frictional losses. This control strategy also minimizes the energy consumption of the components included in the TMS, such as the radiator fan.
10 2.2 Current Thermal Mangement System (TMS) Technology
While the engine and transmission have been subject of considerable design changes and optimization in the past years, the TMS of most production vehicles is still relatively simple [28]. Further demand for more fuel efficient vehicles has led to more manufacturers investigating ”smart” TMS technologies. This is because nearly one third of all fuel energy a typical ICE consumes is wasted as heat sent to the engine coolant [4]. Approximately that same amount is wasted in the form of exhaust heat energy, with less than one third being utilized by the crankshaft to propel the vehicle, as shown in Figure 2.6. These losses are already minimized by current powertrain technology, therefore the goal of a smart TMS is to attempt to recover some of these thermal losses.
Oil viscosity decreases exponentially with increasing temperature, as shown in Figure
2.7. High viscosity oil takes more energy to pump and does not lubricate moving parts as well, resulting in high frictional losses. Due to this, the primary goal of a smart
TMS during an engine “cold-start” scenario is to warm the engine and transmission oil as quickly as possible. Rapid warm-up of engine and tranmission oil following a cold-start reduces frictional losses and therefore fuel consumption and emissions.
Fuel consumption is further reduced because of rapid warm-up of intake ports of the engine, leading to less fuel puddling during cold-start [8]. On liquid-cooled engines, rapid warm-up is achieved by first warming up the engine coolant, and then using heat exchangers to transfer the heat in the coolant to the engine and transmission oil. The engine coolant is rapidly warmed by reducing the coolant flow through the engine, via a variable speed pump, or by recovering additional heat from the exhaust. Exhaust heat can be recovered with exhaust to coolant heat exchangers, such as the EGR
11 Figure 2.6: Energy Audit for EPA Drive Cycle with 2.5L Mid-Size Sedan [4]
cooler commonly used for diesel applications. Insulated coolant storage vessels can also store hot coolant from previous vehicle operation, to be used for rapid warm-up during future use.
Following rapid warm-up, the TMS must maintain the temperatures and flow rates of each engine fluid at the desired levels. This is done by regulating engine oil and transmission oil temperature with oil to coolant or oil to air heat exchangers. The coolant temperature is regulated by sending coolant flow to the radiator, using an electronic thermostat and variable flow coolant pump. Variable speed electric fans provide precise control of radiator air flow, regardless of vehicle speed. Engine fluids are maintained at higher than normal temperatures using the advanced TMS, to
12 12
10
8
6
4 Oil Viscosity [kg/(m−s)]
2
0 −40 −20 0 20 40 60 80 100 120 140 160 Oil Temperature [ oC]
Figure 2.7: Viscosity of 0W-40 Engine Oil for Varying Temperature
reduce engine and transmission friction losses. However, special care is exercised to not exceed the thermal performance of the coolant or engine components, else engine damage occurs. Additionally, maintaining the coolant, and therefore the cylinder wall, at elevated temperature heats the air/fuel charge inside the combustion chamber and increases the chance of knock. Knock sensed by the ECU causes it to reduce spark advance from MBT timing, therefore reducing fuel economy. Continued engine knock events damage the engine. For these reasons, engine coolant temperature is often regulated at 10◦C to 15◦C lower during high-load engine operation [29]. Care is
13 also excercised to avoid large variance in fluid temperature, as this can cause large spikes in control effort of the TMS controller. This wastes energy by energizing actuators too often and also causes unexpected controller instability. Many current
TMS technologies are discussed below.
Electric Radiator Fans
Radiator fans are the most commonly electrified actuator in the TMS on production vehicles. Older model vehicles are equipped with radiator fans mechanically driven by a belt connected to the crankshaft. To reduce uncessary paracitic losses of this configuration, manufacturers started to introduce electric fans with on/off control, based on coolant temperature [30]. Current TMS designs employ electric fans with completely variable speed control. The evolution of the radiator fan shows the key benefits behind electrifying TMS actuators. Electrified TMS actuators are controlled independently of all other vehicle systems and are used only when needed, reducing energy consumption.
Electronic Thermostat
The thermostat in a conventional TMS is a passive element which includes a valve held shut by a solid wax at room temperature. This wax melts as the engine coolant reaches operating temperature, and the thermostat opens. On cold-start, the thermostat closes coolant flow to the radiator, and forces it to continue to circulate through the engine. As the coolant heats up, the valve opens and allows coolant flow to the radiator. However, an electrically actuated thermostatic valve or a heated wax thermostat provides additional control of coolant flow [31]. An active thermostat is used to follow a changing coolant reference temperature (e.g. lower reference temp. at high-load engine operation) as well as reducing thermal shocks associated with
14 poor coolant flow control. Active thermostats are also used to avoid heat soak after the engine is turned off, by keeping the coolant flow between the radiator and engine open. This allows for coolant to continue to flow through the radiator, to be cooled by electric radiator fans. The coolant flows after engine shut-off either by means of the thermo-syphon effect, or actuation of an electric coolant pump. This allows for a more gentle cool down, and avoids localized boiling [31].
Electric Coolant Pump
The engine coolant pump is typically linked to the crankshaft via a belt or chain.
This causes the coolant pump to rotate with the engine crankshaft at some given pulley or gear ratio. This eliminates all possibility of actively controlling coolant
flow rate with the coolant pump. Variable speed electric coolant pumps are in use today on advanced TMSs. These pumps operate independent of engine speed, and are controlled based on engine cooling needs. This is accomplished either by using a completely electric coolant pump or a dual-mode coolant pump. The dual-mode coolant pump includes a clutch that enables it to operate in mechanical mode, where it is driven from a pulley coupled to the engine crankshaft, or in electrical mode [5].
The dual-mode pump produced by BorgWarner Inc., and used on the prototype pow- ertrain developed by Chrysler LLC, is shown in Figure 2.8. This pump is advantagous over a completely electrical pump because the high coolant flow requirements of the engine at full-load (e.g. towing a trailer) necessitate a very large electric motor. This large motor presents packaging issues and requires an upgraded electrical system. By coupling a small 200W electric motor with a mechanical drive, electrical mode is used when reduced or no coolant flow is desired, as well as for cooling after the engine is turned off. The mechanical mode is engaged when additional coolant flow is needed.
15 Figure 2.9 shows that this control strategy consumes much less energy during normal operation than a standard mechanical coolant pump. This power savings of 0.27 kW during the US06 cycle translates into a 0.7% reduction in fuel consumption [5].
Figure 2.8: BorgWarner Hybrid Coolant Pump [5].
16 Figure 2.9: Coolant Pump Power Consumption During US06 Emission Cycle for BorgWarner Hybrid Coolant Pump (HCP) and mechanical coolant pump (MCP) [5]
Exhaust Waste Heat Recovery
The increase in ICE efficiency achieved over the past decades has led to less heat being rejected to the cylinder walls and coolant [6]. This trend slows the warm- up of the engine on cold-start. To improve this warm-up time and decrease fuel consumption, it is desirable to recover waste heat from the exhaust using an exhaust gas-to-coolant heat exchanger. Figure 2.10 shows the exhaust heat recovery system
(EHRS) investigated in [6]. The heat recovered by the coolant is transferred to the engine oil, using a liquid-to-liquid heat exchangers (not pictured). This improves engine warm-up time and decreases frictional losses.
Experiments using a direct injection diesel engine are carried out to investigate the benefits of using the EHRS. The engine cooling system is at −7◦C at the begining of the test and the engine is warmed up for 1600 seconds during two ECE drive cycles.
17 Figure 2.10: Schematic of Exhaust Heat Recover System [6]
Figure 2.11 depicts the results of the tests and shows that the addition of the EHRS improved cabin heater performance and fuel economy.
Thermoelectric devices recover otherwise wasted energy from the vehicle exhaust system. The Peltier effect shows that if a temperature gradient is established across the junction between two different semiconductors, an electric current is generated.
This is exploited by placing a heat exchanger outfitted with thermoelectric devices in the exhaust of a vehicle to generate electricity, thereby reducing the paracitic torque consumed by the alternator.
The authors of [7] conduct experiments using a 2.0L midsize vehicle with a exhaust gas to coolant heat exchanger with about 800 semiconducter junctions. Tests for several drive cycles show less than 0.5% improvement in fuel economy for each cycle.
Figure 2.12 shows the various inefficiencies associated with harvesting energy from the exhaust using the thermoelectric device. It is shown that due to the poor performance of the device, only 22 W of power was harvested from the exhaust, out of the 4000 W
18 Figure 2.11: Comparison of Performance of Vehicle with EHRS to Baseline [6]
available. Significant advances in efficiency, weight and cost need to be made before
thermoelectric devices are used to harvest energy on production automobiles.
Heat Storage Tank
Insulated coolant storage tanks store coolant heated from one vehicle use, and use the
hot coolant to quickly warm the engine during its next use. Toyota Motors utilizes
a vacuum insulated coolant resevoir that will keep 3 liters of coolant at 70◦C for
24 hours of soaking, and at 50◦C after 3 days of soaking [8]. This small volume of
19 Figure 2.12: Losses Associated with Thermoelectric Device Tested [7]
coolant allows for pre-heating of the intake ports of the engine before engine start, reducing fuel puddling in the intake manifold. Figure 2.13 shows how this system operates on the 2004 Toyota Prius, utilizing an electric water pump and electronic valves to control coolant flow before the engine is turned on [8]. The system reduces wall wetting reduces fuel consumption as well as emissions. The hot coolant storage tank also reduces fuel consumption on cold-start due to more rapid warm-up of the engine fluids. Figure 2.14 shows that for short trips, as much as an 8% fuel economy can be attained using the coolant resevoir.
Grille Shutters
20 Figure 2.13: Flow of Coolant in 2004 Toyota Prius During Cold-Start [8]
Figure 2.14: Simulated Fuel Economy Improvement Using Coolant Resevoir [8]
21 Grille shutters are active aerodynamic devices which are actuated to either close or open flow through the grille of a vehicle. Closing the grille shutters during engine warm-up blocks the flow of ambient air to the engine. This decreases aerodynamic drag and engine warm-up time, thereby reducing fuel consumption [32]. These effects are more pronounced at colder ambient conditions. This is because rapid warm- up is more important in colder conditions, due to the nonlinear nature of the oil temperature vs. viscosity curve shown in Figure 2.7. Colder air is also more dense, increasing the aerodynamic drag on the vehicle. Drag reduction effects are more significant due to higher initial levels of drag.
2.2.1 Overview of Thermal Management Systems
The overall goal of the TMS is to use heat exchangers and electrified actuators with a robust control strategy, to recover waste heat produced by the engine. This reduces engine frictionional losses and also minimizes actuator energy consumption, which boosts vehicle fuel economy. Friction is reduced during cold-start scenarios by quickly warming up the coolant by reducing coolant flow through the engine or recovering heat from the exhaust gas. The warmed coolant is used to quickly heat the engine and transmission oil, via liquid to liquid heat exchangers. Warming of the engine fluids reduces friction in moving parts of the engine, and reducing the coolant flow through the engine reduces the power consumed by the coolant pump. When the engine is fully warmed-up, the electric cooling fans and thermostat work with the coolant pump to maintain a stable, elevated, coolant temperature. The coolant is used to maintain the other fluids at elevated temperatures and reduce frictional losses. Special care is taken to not exceed the thermal performance of any materials or the coolant.
22 Figure 2.15: Prototype TMS Configuration
The aim of Chrysler Group LLC for the DOE Advanced Technology Powertrains for Light-Duty (ATP-LD) Vehicles Program is to improve the fuel economy of the
Chrysler Town and Country platform by developing a more efficient powertrain. An advanced TMS is used to reduce frictional losses in the powertrain by rapidly warm- ing all engine fluids following a cold start and then maintaining them at elevated temperatures. The TMS architecture adopted in the advanced powertrain system proposed by Chrysler is shown in Figure 2.15. This system consists of the following heat exchangers.
• Radiator - coolant to air heat exchanger
23 • EGR Cooler (EGRC) - exhaust gas to coolant heat exchanger
• Engine Oil Cooler (EOC) - coolant to engine oil heat exchanger
• Transmission Oil Heater (TOH) - coolant to transmission fluid heat exchanger
• Transmission Oil Cooler (TOC) - transmission oil to air heat exchanger
• Cabin Heater Core (CHC) - coolant to cabin air heat exchanger
The following actuators are used to control the TMS:
• Dual-mode coolant pump - operates in electrical mode or mechanical mode to
circulate coolant through coolant flow network
• Electric thermostat - electrically heated thermostat for active control
• EGRC coolant valve - electronically actuated to control or block coolant to
EGRC
• Three way valve - electronic valve that varies position to split coolant flow
between the CHC and branch with EOC and TOH
• TOH coolant valve - electronic valve that controls coolant flow to TOH
• Radiator fans - PWM controlled electric radiator fans
The work in this Thesis aims to find a model-based control strategy for the prototype
TMS in fully warmed-up conditions. This is done by creating an accurate model of the entire system. This model is then used to create accurate open-loop and closed-loop control to maintain the desired coolant temperature at the engine outlet. The EGRC coolant valve is used to ensure that the temperature of exhaust gas exiting the EGRC
24 is acceptable for the engine. The dual-mode coolant pump switches between modes to provide the coolant flow necessary for each branch of the coolant flow network, in a way that minimizes power consumption. The electronic thermostat controls the coolant flow to the radiator. The three-way valve determine coolant flow through the CHC and TOH. All valves are also used to indirectly control flow to all branches of the coolant flow network. This is because the coolant flow network is a control volume, and if flow through one branch decreases, flow through one or more other branches must increase.
2.3 Thermal Management System Control
Current thermal management systems are more complex than ever before, and now require more advanced control techniques to achieve satisfactory performance. As the number of actuators, and thus degree of complexity of the modern TMS increases, it becomes increasingly difficult to control the system such that all of the actuators work together harmoniously. TMS control strategies are divided into two phases.
The rapid warm-up phase occurs after cold-start of the engine and seeks to warm the engine up as quickly as possible. Actuator activity is minimal in this phase because most actuators are energized in order to cool the engine or fluids, which is not desirable during rapid warm-up. Following engine warm-up, the fluid conditioning phase begins. The objective of this phase is to control all of the material and fluid temperatures within acceptable ranges, despite any disturbances. Several control techniques are studied, ranging from utilizing look-up tables with PID feedback for each actuator command to developing a nonlinear model-based multi-variable control.
A brief explanation of each control strategy is given below:
25 2.3.1 TMS Control During Rapid Warm-up Phase
Figure 2.16 shows the coolant pump used by Audi in the 1.8L TFSI engine and doc- umented in [9]. This pump is mechanically driven, but houses electronically actuated rotary valves that control coolant flow to the engine, engine oil cooler, and transmis- sion oil heater. A separate electric coolant pump is also included for providing flow to the cabin heater core. Rapid warm-up of all fluids is controlled by the following sequence of events:
1. Rotary valve 2, as shown in Figure 2.16, initially closes all coolant flow to the
engine during cold-start.
2. After a specific coolant temperature is reached, rotary valve 2 is actuated and
allows a very small flow of coolant go through the engine.
3. Rotary valve 1 rotates and allows flow of coolant to the engine oil cooler.
4. A switching valve opens coolant flow to the transmission oil heater.
5. At a coolant temperature of 107◦C rotary valve 2 allows coolant to begin flowing
to the radiator.
A switching valve allows the electric pump for the cabin heater core circuit to circulate coolant through the heater core when the coolant in the engine is moving slowly or not at all. In this mode, coolant is only circulated between the cylinder head (with integrated exhaust manifold) and the heater core. This increases cabin comfort during the rapid warm-up phase.
Audi’s advanced TMS and control strategy warms the engine up significantly faster than the previous engine that uses a conventional TMS. Figure 2.17 shows that with
26 Figure 2.16: Audi TFSI Coolant Pump with Integrated Rotary Valves [9]
the advanced TMS, the coolant reaches 60◦C a full 60 seconds earlier than the base- line vehicle. This time difference of 60 seconds translates to a coolant temperature difference between the two architectures of approximately 10◦C at any given time, which is maintained for the rest of the drive cycle. Results for differences in warm-up of the other fluids or fuel consumption during the experiments were not shown in [9].
27 Figure 2.17: Coolant Temp. During NEDC Cycle for Baseline and Advanced TMS Configurations [9]
Valeo Engine Cooling utilizes an active TMS consisting of a 200 W electric coolant pump, electronically controlled thermostat (14 W butterfly valve) and electronic radi- ator fan in a study shown in [10]. The following sequence controls the rapid warm-up of the engine:
1. Following a cold-start, the electronic thermostat is closed and the cooling fan
is off. The coolant pump spins to produce a constant coolant flow of 170 lph.
2. When the coolant exiting the engine reaches 110◦C, the pump is used to regulate
the temperature difference between the coolant entering and exiting the engine
to 10◦C.
28 3. The electronic thermostat is opened and used along with the pump to regulate
coolant temp. at 110◦C.
4. The fan is turned on to begin PI temperature regulation when the valve is fully
opened and the coolant temp. exceeds 110◦C.
A second TMS control strategy is used which utilizes the same strategy as above save for utilizing a ”no-flow” strategy for the coolant pump during step 1. The electric coolant pump is activated after 400 seconds of engine operation, for safety reasons.
Figure 2.18 shows a comparison of coolant temperature during a European drive cycle for a Renault Megane equipped with varying TMSs and control strategies. This vehicle uses a 1.4L, 75 hp, engine and was tested with the baseline TMS, a TMS with mechanical coolant pump but 110◦C coolant set point, and the full active TMS which utilized the second control strategy (no coolant pump flow on initial start-up). The time elapsed before the coolant reached 100◦C was cut in half with the full advanced
TMS, and fuel consumption was reduced by about 2%.
Each of the two previously mentioned control strategies was tested on a Mercedes
A Class equipped with a 1.6L, 102 hp, engine on the MVEG drive cycle. Figure
2.19 shows that both TMS control strategies acheive approximately 2% better fuel economy than the baseline vehicle during the MVEG cycle. The second control strategy is slightly more fuel efficient. However, both TMS control strategies were reported to produce much more NOx emissions than the baseline case. This is almost undoubtedly due to the coolant pump remaining dormant or supplying very little
flow for the first several hundred seconds of each drive cycle. Despite the efforts of the authors, high in-cylinder temperatures almost certainly arose, potentially causing knock as well. The associated high heat and pressure causes higher NOx production.
29 Figure 2.18: Coolant Temp. During European Drive Cycle for Baseline and Advanced TMS Configurations [10]
Additionally, modern engines will not tolerate zero coolant flow for several hundred seconds, as exhaust valve bridges and other critical areas are endangered. The poor thermal management of the in-cylinder temperatures when using the TMS control stratigies outlined in [10] warrant the development of a less aggressive rapid warm- up strategy (i.e. decrease time of minimum/no coolant flow at begining of rapid warm-up).
Previous work on the ATP-LD Program was done to optimize the rapid warm-up of the Chrysler Town & Country van equipped with the 3.6L ”Pentastar” engine, as detailed in [11] and [14]. The TMS shown in Figure 2.20 was used for the rapid
30 Figure 2.19: Fuel Consumption of Mercedes A Class During NEDC [10]
warm-up. In this system, the exhaust gas flowing through the EGRC is used to heat the coolant during rapid warm-up.
31 Figure 2.20: TMS Architecture of Vehicle Equipped with Pentastar Engine [11]
Simulations are carried out using previously developed models in [11] to decide if it is best to use the heat in the coolant to warm-up the transmission oil or engine oil
first. The full factorial Design of Experiments (DOE) shown in Table 2.1 is carried out by varying the position of the EGRC coolant valve and three way valve (3WV) between simulations. Each simulation respresents a FTP drive cycle which began with all fluids at the ambient temperaure of 25◦C. The EGR Bypass Valve is kept closed during all simulations, to maximize the heat transfer from the exhaust to the coolant. It is determined that smaller openings of the EGRC coolant valve coincide with faster coolant warm-up. Small openings of the 3WV send more flow to the CHC, thereby heating the transmission oil more slowly. Large openings of the 3WV show large improvements in transmission oil warm-up time, with only small increases in coolant and engine oil warm-up times.
32 Table 2.1: DOE of TMS Actuator Positions
Scenario 0 1 2 3 4 5 6 7 EBPV position 1 0 0 0 0 0 0 0 3WV position 0 1 0.75 0.5 0.25 0 1 0.75 EGRCC position 0 1 1 1 1 1 0.7 0.7 Scenario 8 9 10 11 12 13 14 15 EBPV position 0 0 0 0 0 0 0 0 3WV position 0.5 0.25 0 1 0.75 0.5 0.25 0 EGRCC position 0.7 0.7 0.7 0.2 0.2 0.2 0.2 0.2
tfluid WTRfluid,s = (2.1) tfluid,s Equation 2.1 was used to compare the best time for warming up a particular fluid to the time achieved for that same fluid in a particular scenario. Since the minimized value is in the numerator, the larger the value of WTRfluid,s, the better that scenario is for warming that fluid. Figure 2.21 is of particular interest and shows that a very distinct trade-off exists between rapid warm-up of the engine oil vs. rapid warm-up of the transmission oil. Scenario 15 shows that the faster engine oil warm-up time causes a 1/0.6=1.67 times larger transmission fluid warm-up time. However, scenario
11 shows that the faster transmission oil warm-up time only causes the engine oil to take 1/0.97=1.03 times longer to warm-up. The large improvements in transmission
fluid warm-up time compared to the accompanying small increase in engine oil warm- up time shown in scenarios 11, 12, and 13 prove that the 3WV should opened as much as possible during rapid warm-up, to give priorty to rapid warm-up of the transmission fluid. However, it should be noted that heating demands from vehicle
33 occupants cannot be ignored and may warrant moving the 3WV from the optimal position that sends all flow to the TOH.
Figure 2.21: Pareto Analysis of Pentastar Rapid Warm-up [11]
2.3.2 TMS Control During Fluid Conditioning Phase
Feed-Forward Coupled with PID Feedback
34 This technique utilizes pre-determined functions or look-up tables to establish an actuator command for a given control objective and engine operating point. An in- teraction term is also used to determine the initial actuator command, which accounts for the current activity of all actuators in the system. This couples the actuator be- havior and ensures that they act in unison. Disturbances are corrected for using PID feedback to augment the final actuator command.
In a study conducted at Clemson University, the conventional TMS of a vehicle is replaced by a servo-actuated thermostatic valve and an electric coolant pump [12].
Both actuators are modeled using first order dynamics for electrical current energizing the device and second order dynamics for the angular position of the motor shaft.
Lumped parameter models for first order temperature dynamics are constructed for the thermal system.
An independent function f(.) and coupled function f0(.), are used to command ac- tuator position based on coolant temperature, engine speed, manifold pressure, and current actuator positions, as shown in Equation 2.2.
˜ uht , uωp = f(Tcool, N, MAP ) + f0(ht, ω˜p) (2.2)
The targeted coolant temperature is defined by a look-up table, based on engine operation, as shown in Equation 2.3.
Tsp = f(N, MAP ) (2.3)
The coolant set point temperature is used to determine the commanded thermostat position, as shown in Equation 2.4 and error between commanded and actual valve
35 position is used to enforce PI control on the valve’s servo-motor voltage. βht represents the thermostat displacement per temperature gain.
¯ htd = f(Tcool,Tsp, βht ) (2.4)
The coolant pump speed is commanded by the summation of a set point that is a function of engine operation, and a temperature correction factor, based on coolant
temperature, coolant temperature set point, and βωp , the pump speed per temperature gain. This relationship is shown in Equation 2.5.
ωpd = f(N, MAP ) + f(Tcool,Tsp, βωp ) (2.5)
An additional control architecture is proposed that replaces the coolant temperature feedback signal with one more strongly related to in-cylinder temperatures. Equation
2.6 shows the weighted summation of cylinder wall and cylinder head temperature that is used for temperature feedback.
Tac = w1Tc2 + w2THm (2.6)
Since the feedback signal shown in Equation 2.6 is more closely related to in-cylinder events than Tcool, feedback based on this signal promotes optimal combustion tem- peratures. Thermal stresses within the engine are reduced as well, and control design is not compromised by using a feedback signal with a very long time response.
Simulations are used to evaluate the performance of each control architecture with respect to the baseline vehicle. During each 15 minute simulation, the engine speed is varied from 1500 RPM, to 2000 RPM and then to 2500 RPM. Equation 2.7 shows the linear control strategy used to simulate the wax thermostat used in the conventional
36 vehicle. Figure 2.22 shows the simulation results using the conventional thermostat
◦ ◦ when Tmin = 95 C and Tmax = 105 C. It is seen that the coolant experiences peak-
to-peak temperature fluctuations of 3.0◦C, while the cylinder wall temperature varies
5.0◦C peak-to-peak. The temperature variation of the piston and exhaust valve face are much more significant.
0 if(Tcool < Tmin) ¯ ht = (Tcool − Tmin)/(Tmax − Tmin) if(Tmin < Tcool < Tmax) (2.7) 1 if(Tcool > Tmax)
Figure 2.22: Simulation Results Using Conventional Thermostat [12]
37 The simulation results using the active TMS with the first control strategy are shown
in Figure 2.23. Peak-to-peak fluctuations in coolant temperature are reduced to 2.4◦C, while fluctuations in the other temperatures appear unchanged from those seen with the conventional thermostat.
Figure 2.23: Simulation Results Using Active TMS and Coolant Temp. Feedback [12].
Figure 2.24 shows the results of the simulation using the feedback signal based on
estimated cylinder wall and head temperature. It is shown that the peak-to-peak
38 temperature variations in the cylinder wall are reduced to only 2.8◦C, while the effects on the other temperatures are minimal.
Figure 2.24: Simulation Results Using Active TMS and Cylinder Head and Wall Temp. Feedback [12]
The same researchers at Clemson University also propose another TMS control strat- egy that is focused on minimizing actuator energy consumption [33]. This strat- egy entails using the electronic thermostat to regulate coolant temperature and only increasing the coolant pump speed when the valve is fully open. The thermostat
39 position is commanded by a three dimensional look-up table that is a function of coolant mass flow rate and engine heat rejection. This control strategy minimizes the coolant pump speed, which minimizes energy consumption. Transient experimental results on a similar test bench as used in [12] show that the reference temperature tracking performance of the controller proposed is only marginally improved over the controller previously discussed. The true benefit of this controller is the reduced fuel consumption due to reduced coolant pump speed, but no fuel consumption results are shown. Coolant pump energy consumption results are also not reported.
The work in [12] and [33] shows a TMS control strategy that is best suited for very simple TMSs. Even with the interaction terms shown in Equation 2.2, the addition of more actuators to the system makes the design of a suitable controller of this fashion very difficult. Additionally, the control effort of the actuators is not shown in the above study, so large changes in control effort and chatter may be experienced with this strategy.
Nonlinear Model-Based TMS Control
Reference [13] presents a nonlinear controller that is used to control the TMS shown in Figure 2.25. This paper shares authors and many similarities with [12]. The same mathematical models are used, with the addition of current and speed dynamics for the electric radiator fan. A Lyapunov-based nonlinear control algorithm is designed for precise tracking of reference coolant temperature and disturbance rejection.
The test bench shown in Figure 2.26 is used to test the performance of the nonlinear controller. The heaters with maximum heat output of 12 kW are used to replicate the heat produced by an engine. Equation 2.8 shows the dynamic reference temperature
◦ ◦ used for the experiment, where Tsp = 66 C,T0 = 2.0 C, and T = 90 seconds. For
40 Figure 2.25: Schematic of TMS Considered in [13]
this experiment, the radiator fan and coolant pump operate at fixed speeds, and the heaters produce a constant 11.0 kW of heat, to simulate a part-load highway driving event. To protect the valve, the valve postion was limited to 5% < H < 95% for this test.
Ted = Tsp + T0sin(2πt/T ) (2.8)
Figure 2.27 shows the experimental results. The valve position range is 5% < H <
60% for this test. Figure 2.27 shows very good reference temperature tracking per- formance. However, it is noted that the only actuator commanded by this controller was the thermostatic valve. The coolant pump and radiator fan were operated at constant speed and were not actively controlled. This control strategy assumes that the coolant pump and radiator fan operate at constant speeds for a given scenario and the thermostat valve is used for disturbance rejection. This control logic is not
41 Figure 2.26: Schematic of Experimental Test Set-up [13]
energy efficient, as the speed of the pump and fan should be minimized to conserve energy [33].
42 Figure 2.27: Simulated Control Performance Over Time [13] 43 2.4 TMS Control Design Methodology
The focus of this Thesis is the design of a TMS controller for the fluid conditioning phase. First, a model of the prototype TMS is constructed. This model of the TMS was developed at OSU and is integral to the design of both the feed-forward and feedback controller. To find the open-loop actuator positions, a design of experiments is conducted for combinations of actuator positions at several engine operating points of interest, using the plant model. A cost function is minimized at each engine operating point to select the optimum combination of actuator positions. Special care is taken to choose actuator position combinations that provide improved fluid reference temperature tracking, as well as minimize actuator energy consumption.
This open-loop control design process is completed over the entire engine operating range of interest.
As a preliminary step to access the control authority of the TMS on the controlled variables, a simple feedback controller is implemented. Proportional and Integral
(PI) feedback controllers are added to each actuator command. The input to these controllers is temperature tracking error. The final TMS controller combines the feed- forward maps of each actuator position with PI feedback controllers. The analysis of the performance of this TMS controller will serve as a feasibility study to investigate what level of TMS control is possible using simple PI feedback. Additionally, this simple control structure will provide Chrysler Group LLC with a controller that can be easily and immediately implemented in the Engine Control Unit (ECU) of the pro- totype powertrain and tested. This work will also pave the way for the development of more advanced TMS controllers, in the future.
44 Chapter 3: Modeling of a Thermal Management System
The models developed are described in this chapter. An overview of the modelled
Thermal Management System is given, as well as the previous work completed which contributes to these models. The modelling techniques used to generate these physics- based thermodynamic models are detailed.
3.1 Overview of Thermal Management System
The TMS of interest consists of a number of heat exchangers, coupled by a common coolant flow network and engine thermal model. A schematic of the TMS for the
Chrysler prototype vehicle is shown in Figure 3.1. The heat exchangers shown are categorized into either ”fast response” or ”slow response” units. The fast response heat exchangers are characterized by the use of two working fluids that are liquids and have similar specific heats. The heat capacity of each liquid is significantly higher than that of the metal contained in the heat exchanger itself. This means that a change in temperature of one fluid causes a very quick response in the other
fluid. The fast response heat exchangers in the Chrysler TMS are the transmission oil heater and engine oil cooler. Both liquid-liquid heat exchangers exchange heat between engine coolant and either transmission oil or engine oil. The slow response heat exchangers utilize a liquid as one working fluid, and ambient air as the other. The
45 difference in heat capacities of the two working fluids necessitates the modelling of the temperature dynamics of the heat exchanger walls, themselves. The radiator and cabin heater core are both slow response heat exchangers that use air to cool engine coolant. The transmission oil cooler is used to transfer heat from the transmission oil to ambient air.
Figure 3.1: Prototype Vehicle TMS Configuration
The thermal dynamics of the Exhaust Gas Recirculation Cooler are also modelled.
This heat exchanger uses engine coolant to cool a portion of the exhaust gas before they are recirculated to the intake of the engine. The difference in heat capacities between the engine coolant and exhaust gas requires the temperature dynamics of
46 the heat exchanger walls to be modelled, as well as those of both working fluids. This heat exchanger is different than the slow response heat exchangers, because it is a shell and tube unit, with both working fluids flowing inside. The fluids are separated from one another on the inside by the heat exchanger walls and from the ambient air by a metal shell. This configuration is different than the radiator, for example, which contains engine coolant within the heat exchanger shell, and simply allows ambient air to flow over the outside of the heat exchanger.
A coolant flow network model is employed which uses the electrical circuit analogy to predict the flow of coolant through each heat exchanger. This model is implemented as a look-up table and does not include any system dynamics, with the model inputs being the position of all flow control valves, as well as coolant pump speed and coolant temperature. A coolant mixing model is also included, to determine the temperature of coolant entering the coolant pump, after coolant exiting all heat exchangers has mixed together.
An engine thermal model with four thermal masses is used as well. The four thermal masses represent the metallic parts of the engine itself and exchange heat between the combustion gasses, ambient air, engine coolant, engine oil, and themselves. This model is particularly important, as it couples engine operation to the heat exchanger model inputs.
A transmission thermal model couples the operating conditions of the transmission with the thermal dynamics of the transmission oil. This is accomplished by utilizing a model with three thermal masses. The thermal dynamics of the transmission in- ternals, transmission oil sump, and transmission case are modelled. Heat generated
47 from friction between transmission gears and the torque converter provides heat to the transmission thermal masses and transmission fluid.
3.2 Thermal System Modeling Approaches
High fidelity models of the TMS, which will be employed for the optimization and control design for the prototype vehicle, are constructed so that the TMS architec- ture and control strategies can be optimized before a test vehicle exists to conduct experimental testing. This requires a high-order TMS model for accessing the effects of changing control strategies or system architecture on vehicle fuel economy.
3.2.1 Lumped Parameter Modeling
A trade-off exists between model fidelity and computational time. Detailed models are used at the component level, during design of a single part of subassembly of the vehicle. For example, 3-Dimensional CFD analysis can be conducted when designing a radiator cooling fan, as is the case in [34]. This detailed simulation shows a finely discretized pressure distribution along the rotating fan blades and is a necessary part of the product design and optimization process. The mesh used on each element of the fan is very fine and thus produces many individual nodes that a solution is obtained at for each simulation. However, these models are extremely cumbersome to create, calibrate, and validate. Simulation time of such a model is also very long and often requires many computer processors to run. Lumped parameter modeling is used when optimized components are integrated into a larger system and detailed analysis of each component is no longer needed. This is the case for the TMS of interest. Since all of the individual components (radiator, EGRC, etc.) are thoroughly optimized, lumped parameter representations suffice for the purpose of system level simulation.
48 This allows the radiator fan model to be reduced to a simple 0-dimensional model which predicts air flow through the fan based on vehicle speed and fan speed. In the following subsections, the methods used to model each element of the TMS are shown.
3.2.2 Lumped Thermal Capacitance Method
The lumped thermal capacitance model is a 0-D model that assumes that temperature is uniform throughout the modeled mass. Using this assumption, 1-D heat flow is not considered and a single temperature for the mass is computed using an energy balance [35]. This model vastly simplifies heat transfer calculations of complex heat exchangers and other parts. These models are calibrated with experimental data, in order to retain the accuracy of the model.
3.2.3 Receivers
Figure 3.2: Mean Value Model of Receiver [14]
Using the conservation laws (for mass and energy), thermodynamic control volumes are modeled as receivers. Assuming that the fluid properties of gases are homogenous throughout the receiver and that mass flow rate remains constant through a given cross-sectional area (0-D fluid flow), applying conservation of mass to the receiver results in the following equation:
49 dm X X = m˙ − m˙ (3.1) dt in out
Wherem ˙ in andm ˙ out represent mass flow rate into and out of the receiver, respectively.
Assume that the following holds true:
• Internal energy is not affected by temperature variations
• Inlet and outlet fluid volumetric flow rates at the same
• Gravitational effects are negligible
• The volume is static, therefore no moving parts exist
Using the previous assumptions and applying conservation of energy, Equation 3.2 is used to represent the temperature dynamics of the receiver.
dT h X i mc = m˙ h − m˙ h + Q˙ (3.2) v dt in in out out ˙ Where hin and hout represent fluid enthalpies, and Q represents heat rejected to the working fluid.
The previous simplifications and Equation 3.2 are used to model the thermal dynamics and fluid flow through each heat exchanger modelled.
3.3 Models Previously Developed
Each submodel of the thermal management system shown in Figure 22.15 was previ- ously modelled by other graduate students at OSU, as detailed in [14],[36], [37], and
[38]. However, these models were characterized for use with the thermal management system employed on the current production vehicle, equipped with the 3.6L V6 engine
50 and 6 speed automatic transmission. These models were developed for this platform because experimental calibration and validation data are readily available for not only each submodel, but the entire system itself. After the model was sufficiently cal- ibrated, it was used to optimize the rapid warm-up controls for the TMS, as described in [11]. As shown in Figure 3.3, the TMS architecture for the production engine bares many similarities to that of the prototype platform. The same submodels are present on each system, but the actuators employed are different. The production engine is equipped with a simple mechanical thermostatic valve to control coolant flow to the radiator. This package also contains a conventional coolant pump, coupled to the crankshaft by a belt and pulleys. The prototype TMS contains a thermostatic valve which can either open mechanically, or with assistance from an electrical heating circuit inside the wax pellet. The coolant pump used on the prototype engine can also be driven by a belt and pulley connection to the crankshaft, or use a clutch to decouple from this system and be driven electrically.
3.3.1 Engine Thermal Model
This model captures the first order termperature dynamics of the engine thermal masses, engine oil in the oil sump, and coolant exiting the engine. A description of the four thermal masses is given below, and also shown in Figure 3.4. Figure 3.5 ˙ shows the engine thermal model input and output variables, where Qfr represents ˙ the heat generated due to friction within the engine. The term Qgas is the heat added to the hot masses from the combustion gasses..
• Mass 1 - ”hot masses” or areas in contact with combustion gasses (top of piston,
intake and exhaust valves, cylinder walls, exhaust ports)
51 Figure 3.3: Production Vehicle TMS Configuration
• Mass 2 - ”cranktrain” or rotating assembly (crankshaft, connecting rods, bear-
ings, bearing caps, camshafts)
• Mass 3 - ”sump”, consists of engine oil sump, sump ladder assembly, oil pump,
and crankshaft balancer
• Mass 4 - ”cold masses”, or outside of cooling jacket, engine block, engine head,
and valve cover
52 Figure 3.4: Thermal Masses Included in ETM
Equation 3.3 represents the thermal dynamics of the hot engine masses, which receive heat from the hot combustion gases, as well as engine friction. Thermal mass 1 also exchanges heat with the engine coolant, engine oil, and thermal mass 2.
T1 1 ˙ ˙ 1 = Qgas + αQfr − U1→oil(T1 − Toil) − U1→clnt(T1 − Tclnt) − (T1 − T2) dt m1c1 R1→2 (3.3) ˙ ˙ Parameters Qgas and Qfr represent heat generated due to combustion and friction, respectively. The parameter U represents the heat transfer coefficient for heat transfer
53 Figure 3.5: Engine Thermal Model Block Diagram
between various engine fluids and thermal masses and variable R accounts for thermal resistance between thermal masses. The term α is the fraction of heat generated from
engine friction that flows to engine thermal mass 1.
The temperature dynamics of the cranktrain are shown in Equation 3.4. It can be
seen that thermal mass 2 receives heat from engine friction and also exchanges heat
with the engine oil and mass 1.
T2 1 ˙ 1 = βQfr + (T1 − T2) − U2→oil(T2 − Toil (3.4) dt m2c2 R1→2
In Equation 3.4, β represents the portion of the heat produced by friction that is
transmitted to engine thermal mass 2.
Equation 3.5 depicts the temperature dynamics of the engine oil pan and attached
peripherals, which exchange heat with the engine oil inside the pan and the ambient
air on the outside of the pan.
T3 1 = [Uoil→3(Toil − T3) − U3→amb(T3 − Tamb)] (3.5) dt m3c3
54 The thermal dynamics of thermal mass 4 are shown in Equation 3.6. This ”cold”
mass exchanges heat with the engine coolant inside the engine, and the ambient air
outside the engine.
T4 1 = [Uclnt→4(Tclnt − T4) − U4→amb(T4 − Tamb)] (3.6) dt m4c4
Equation 3.7 shows the first order temperature dynamics for the engine coolant exiting
the engine. The coolant exchanges heat with mass 1 and mass 4, as previously
mentioned.
Tclnt 1 = [m ˙ clntcpclnt (Tclntin − Tclnt) + U1→clnt(T1 − Tclnt) − Uclnt→4(Tclnt − T4)] dt mclntcclnt (3.7)
The engine oil temperature dynamics are shown in Equation 3.8 and rely on heat transfer between the engine oil and thermal masses 2 and 3, as well as heat generated due to friction.
Toil 1 ˙ = [m ˙ oilcpoil (Toilin − Toil) + (1 − α − β)Qfr dt moilcoil (3.8)
+U1→oil(T1 − Toil) + U2→oil(T2 − Toil) − Uoil→3(Toil − T3)]
The six equations which describe the temperature dynamics of the engine thermal model are all linked together. Most importantly, these equations are linked to both ˙ ˙ the engine operation, through the variables Qfr, Qgas, and others, as well as the rest of the thermal mangement system, through the temperatures and flow rates of the engine oil and coolant. To ensure the accuracy of the engine thermal model, all data for the mass and geometry of all thermal masses was supplied by Chrysler Group
LLC. Experimental data was also supplied, in order to calibrate the heat transfer coefficients shown in the governing equations of the engine thermal model. Section
3.5.1 of this document details the experimental calibration and validation procedure.
55 3.3.2 Slow Response Heat Exchangers
Each slow response heat exchanger is divided into discrete lumps, with each lump
being comprised on a single liquid node, heat exchanger wall node, and surface node.
For the case of the radiator and CHC, the liquid is engine coolant. For the TOC,
the liquid is transmission oil. The slow response heat exchangers previously modelled
and the number of lumps within each model are listed below.
• Radiator - 3 lumps
• TOC - 3 lumps
• CHC - 2 lumps
All of the slow response heat exchangers are modelled in the same way, so a single block diagram showing the inputs and outputs of each model is shown in Figure 3.6.
The term Vface represents the velocity of air that impacts the heat exchanger.
Figure 3.6: Slow Response Heat Exchanger Block Diagram
Equation 3.9 shows the temperature dynamics of the liquid node of the slow response heat exchanger model. These temperature dynamics result from an energy balance
56 for the liquid node, which accounts for heat transfer from liquid in the previous node,
as well as heat transfer to the heat exchanger walls, as outlined in [39].
β Tliqj n Cf m˙ o C”liq = m˙ liqcpliq (Tliqj−1 − Tliqj ) − (Tliqj − Twj ) (3.9) dt Aface C3
Terms β, C1, C2, and C3 are calibration coefficients, while Aface is the frontal area of
the heat exchanger. The parameter n represents the number of lumps in the radiator
model andm ˙ o is the mass flow rate of coolant divided by the length of the heat
exchanger.
The heat exchanger wall temperature dynamics are repesented by Equation 3.10.
β Twj Cf m˙ o 1 C”w = (Twj − Tliqj ) − (Twj − Tsj ) (3.10) dt C3 C2
Equation 3.11 shows the temperature dynamics of the surface node of the heat ex-
changer.
Tsj 1 C”s = (Twj − Tsj ) − ρaircpair VfacePa(Tsj − Tairin ) (3.11) dt C2 Experimental data was supplied by each heat exchanger OEM. Part of this data was used to calibrate the coefficients β, C1, C2, and C3 , while the remaining data was used for validation of the calibrated model.
3.3.3 Fast Response Heat Exchangers
The TOH and EOC are modelled as fast response heat exchangers. The effectiveness-
NTU method is used for these models, as described in [35]. Figure 3.7 shows the inputs and outputs of these models.
The Number of heat Transfer Units (NTU) is calculated using Equation 3.12.
UA NTU = (3.12) Cmin 57 Figure 3.7: Fast Response Heat Exchanger Block Diagram
The variable UA represents the overall heat transfer coefficent. The term Cmin rep- resents the minimum heat capacity of the working fluids.
The minimum Capacitance Ratio (CR) is calculated as the minimum of Equation
3.13.
m˙ c m˙ c CR = clnt vclnt or oil voil (3.13) m˙ oilcvoil m˙ clntcvclnt The calculated NTU and CR are then used to calculate the heat exchanger effective- ness, as shown in Equation 3.14.
1 − e−NTU[1−CR] ε = (3.14) 1 − CRe−NTU[1−CR] The calculated heat exchanger effectiveness is used to calculate the temperature of both working fluids. Equation 3.15 represents the first order temperature dynamics of the coolant exiting the heat exchanger.
dTclnt m˙ clntcpclnt = [(Tclntin − Tclnt) + εCR(Toilin − Tclntin )] (3.15) dt mclntcvclnt The oil temperature dynamics are represented by Equation 3.16.
58 dToil m˙ oilcpoil = [(Toilin − Toil) + εCR(Toilin − Tclntin )] (3.16) dt moilcvoil The look-up tables for heat exchanger effectiveness and CR implemented in each fast response heat exchanger model were calibrated and validated using experimental data from each heat exchanger OEM.
3.3.4 Transmission Thermal Model
Figure 3.8 shows the input/output structure of the Transmission Thermal Model
(TTM). This thermal model receives the heat generated from the transmission and ˙ ˙ torque converter (Qtrans and QTC , respectively) from the transmission mechanical model. Engine speed, turbine torque, gear selected, and torque converter lockup status are other inputs also received from the mechanical model. Finally, the temper- ature of the transmission oil returned from the TOH and/or TOC is also used as a model input as well. All of these inputs are used to model the temperature dynamics of the three major parts of the transmission:
• Transmission internals - includes all gears, shafts, clutches, pumps, and actua-
tors
• Torque converter - transmission torque converter pump and turbine
• Transmission sump/case - transmission case and transmission oil sump
Equation 3.17 represents the temperature dynamics of the transmission internals. It can be seen that the internals receive heat from the transmission friction and also exchange heat with the transmission oil.
59 Figure 3.8: Transmission Thermal Model Block Diagram
dT C ti = Q˙ + c m˙ (T − T ) (3.17) ti dt trans p TOti TOin ti
Equation 3.18 models the thermal dynamics of the torque converter, as it receives heat
generated from its own inefficiencies, and also exchanges heat with the transmission
oil.
dT C TC = Q˙ + c m˙ (T − T ) (3.18) TC dt TC p TOTC TOin TC
The transmission sump/case also displays first order temperature dynamics, as shown in Equation 3.19. This lump of the TTM exchanges heat with the torque converter and transmission internals on the inside, and the ambient air on the outside.
dT C sc = c m˙ (T − T ) + c m˙ (T − T ) − UA (T − T ) (3.19) sc dt p TOTC TC sc p TOti ti sc amb sc amb
The mass of each lump in the TTM was provided by Chrysler Group LLC. A valida- tion procedure was carried out on the transmission thermal model, by ensuring that
60 transmission sump temperature predicted by the model matched those of experimen-
tal data provided by Chrysler.
3.4 Updated Models
The TMS submodels in the previous section were carried over form the production
vehicle TMS model to the prototype vehicle TMS model. Minor changes were made,
such as updating the engine thermal model for the thermal masses of the prototype
engine, for instance, but the overall model structure and calibration parameter re-
mained the same. The following TMS submodels underwent significant updates in
model structure so that they could accurately model the behavior of the prototype
vehicle TMS:
• Coolant Flow Network and coolant pump
• Electronic Thermostat Model
• Radiator Fan Model
• EGR Cooler Thermal Model
While the EGR cooler used on the production vehicle and prototype vehicle platforms are the same, this model was recalibrated after additional experimental calibration data was supplied to OSU, to simply improve its accuracy. This process is described in later sections of this chapter. The coolant flow network for the prototype engine reflects the new coolant pump used, as well as different flow losses through the engine itself. The thermostat model is changed to capture its performance both in mechanical mode, as well as electrical mode. The radiator fan model was created in order to accurately model the air flow through the radiator.
61 3.4.1 Coolant Flow Network
The Coolant Flow Network (CFN) is a static model that consisting of a look-up table.
This table gives the flow rate of coolant through each branch of the CFN, based on
the current position of each of the actuators that control coolant flow. A schematic
of the CFN input/output structure is shown in Figure 3.9.
Figure 3.9: Coolant Flow Network Block Diagram
The look-up table within the CFN is populated using the electrical resistance fluid
flow analogy. Equation 3.20 shows the fluid equivalent of Ohm’s Law.
qR = ∆p (3.20)
Equation 3.20 holds true when q represents volumetric fluid flow rate, R is fluid flow resistance, and ∆p is fluid pressure loss across the flow resistance.
Equation 3.20 is used in conjunction with Kirchoff’s Current Law (KCL) and Kir- choff’s Voltage Law (KVL) to create an equivalent electrical circuit to represent the
CFN, as shown in Figure 3.11. The fluid resistances through heat exchangers and
62 valves in each branch are calculated according to Equations 3.21 and 3.22, respec-
tively.
RHEXi = C1HEXi µc + C2HEXi ρcqi (3.21)
The terms µc and ρc account for fluid viscosity and viscosity, respectively. The vari-
ables C1HEXi and C2HEXi are calibration coefficients that are derived from experi- mental flow data for each heat exchanger.
Kvalvei ρcqi Rvalvei = 2 (3.22) 2Aflow
Variable Kvalvei represents the empirically calculated discharge coefficient for valve i,
at a particular opening.
The pressure rise across the coolant pump is determined using the data shown in
Figure 3.10, as supplied by Chrysler. Additionally, mechanical power conusmption
curves were supplied for the coolant pump, as well. When the pump operates in
electrical mode, the coolant flow rate and pressure rise is the same for a given coolant
pump speed. However, an additional electrical to mechanical energy conversion effi-
ciency is used to obtain the electrical power required, from the calculated mechanical
power. The mechanical to electrical energy conversion efficiency of the alternator is
then used to determine the power the pump requires from the alternator. Since the
alternator is coupled to the crankshaft via a belt and pulley system, the calculated
alternator power must be supplied by the engine.
Equation 3.23 shows the equivalent electrical circuit in matrix form.
63 Figure 3.10: Normalized Coolant Flow vs. Pressure Rise for Different Pump Speeds
−1 −1 −1 −1 −1 1 q1 0 −R1 R2 0 0 0 0 q2 0 0 −R2 R3 0 0 0 q3 0 = (3.23) 0 0 −R3 R4 0 0 q4 0 0 0 0 −R4 R5 0 q5 0 R1 0 0 0 0 R6 q6 ∆ppump The solution for Equation 3.23 must be calculated iteratively, as the fluid resistance through each branch depends on the flow through each branch, which is unknown.
To start the iteration, a flow through each branch is assumed, based on experimental data. The fluid resistance through each branch is calculated, for this assumed flow rate and given set of actuator positions. The assumed flow through the coolant pump and the specified pump speed is then used to determine a pressure rise across the coolant pump. The calculated flow resistances and pressure rise across the pump are then used with Equation 3.23 to calculate the flow through each branch of the CFN.
64 Figure 3.11: Electrical Analogy Represenation of Coolant Flow Network
The calculated flows serve as the starting point for the next iteration. This process is repeated until the difference between calculated coolant flows through the branches between iterations converges.
Figure 3.12 shows the normalized coolant flow rate through all branches of the CFN as EGRC CV position is varied. This example case was carried out at conditions which resemble typical actuator positions when the vehicle is fully warmed-up. It can be seen that since the thermostat is 50% open, it receives most of the coolant flow.
The flow to the EGRC varies nonlinearly with coolant valve position, with openings of more than 50% yielding very little additional coolant flow. It is important to note that the sum of the coolant flow through each heat exchanger is equal to the coolant
flow through the coolant pump, as expected.
65 T−stat @ 100%, 3WV @ 0%, Temperature = 379 K = 105oC Pump Speed = 3500 1 EGR Cooler 0.9 Radiator EOC 0.8 TOH 0.7 CHC Pump 0.6
0.5
0.4
0.3
Normalized Flow Rate − All loops 0.2
0.1
0 0 20 40 60 80 100 EGR Valve Opening [%]
Figure 3.12: Normalized Coolant Flow to All Branches with Varying EGRC CV Position
3.4.2 Electronic Thermostat
The thermostat model for the prototype engine is divided into two modes: mechanical and electrical. Figure 3.13 shows the block diagram of the thermostat model.
Figure 3.13: Thermostat Model Block Diagram
66 It can be seen that the opening and closing dynamics of the thermostat in the pro-
totype engine are first order in nature, where K represents the gain of the transfer function, and τ represents the time constant. The steady-state thermostat displace- ment increases with increasing coolant temperature. The time constant for the ther- mostat opening and closing changes with coolant temperature and operating mode.
A logic block is also included in the thermostat model, to choose between when the thermostat should be opening or closing and if it is operating in mechanical mode or electrical mode. Four seperate tables for determining the time constant and steady- state thermostat position, based on coolant temperature are implemented. These tables correspond to thermostat opening in both mechanical and electrical mode, as well as thermostat closing in both mechanical and electrical mode.
All data for thermostat steady-state opening and closing positions as well as time constants is taken from data supplied by Chrysler Group LLC. Figure 3.14 shows the normalized steady-state thermostat positions for both thermostat opening and closing with varying temperature and thermostat mode. As expected, the thermostat opens earlier in electrical mode, due to the heating of the wax pellet. As can be seen, steady-state thermostat displacement data for the mechanical opening of the thermo- stat was not supplied for very high temperatures. However, the data supplied does include all expected engine operating temperatures. The normalized time constant of the thermostat at different operating points is shown in Figure 3.15. As expected, the opening time constant decreases with increasing temperature, while the oppisite is true for thermostat closing. Also, the opening time constant is lower when the thermostat is in electrical mode. However, the closing time constant is larger when in electrical mode.
67 1
0.9 Mech. Mode Opening Elec. Mode Opening 0.8 Mech. Mode Closing Elec. Mode Closing 0.7
0.6
0.5
0.4
0.3 Thermostat Opening Fraction 0.2
0.1
0 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Normalized Coolant Temperature
Figure 3.14: Thermostat Model Steady-State Opening
1
0.9
0.8
0.7
0.6 Mech. Mode Opening Elec. Mode Opening 0.5 Mech. Mode Closing 0.4 Elec. Mode Closing
0.3
0.2 Normalized Thermostat Time Constant
0.1
0 0.75 0.8 0.85 0.9 0.95 1 Normalized Coolant Temperature
Figure 3.15: Thermostat Model Time Constant
3.4.3 Radiator Fan
The radiator fan is modelled as a static look-up table. The velocity of air passing through the fan is a look-up table based on vehicle speed and radiator fan speed,
68 as shown in Figure 3.16. A normalized table of the output of this model is shown in Figure 3.17. The data which populates this table was supplied by Chrysler LLC.
Data was also supplied to predict radiator fan power consumption, as a function of fan speed.
Figure 3.16: Radiator Fan Block Diagram
1
0.8
0.6
0.4
0.2 Normalized Air Flow Rate 0 1 1 0.8 0.5 0.6 0.4 0.2 0 0 Normalized Vehicle Speed Normalized Fan Speed
Figure 3.17: Normalized Radiator Fan Flow
69 3.5 Modeling of Exhaust Gas Recirculation Cooler Thermo- dynamics
The Exhaust Gas Recirculation Cooler (EGRC) allows exhaust gas to transfer heat to the coolant, before the gas is routed to the inlet of the turbocharger compressor.
The plumbing of this shell and tube heat exchanger is shown in Figure 3.18. It is very important to have a high fidelity model of the EGRC, as the temperature of the
EGR entering the intake tract has a significant impact on engine performance and fuel economy. Additionally, the heat the EGRC transfers to the coolant impacts the rest of the thermal management system. The thermal capacitance of the two working
fluids in the EGRC (coolant and exhaust gas) are very different from one another.
Since the thermal capacitance of the heat exchanger walls is also very different from that of both fluids, the lumped capacitance is used to discretize the EGRC model into three nodes. The EGRC model is comprised of seperate nodes for the temperature of the coolant exiting the heat exchanger, the heat exchanger walls, and the exhaust gas exiting the heat exchanger. Figure 3.19 shows the block diagram for the EGRC thermal model.
Figure 3.18: Shell and Tube EGRC Architecture [15]
70 Figure 3.19: EGR Cooler Block Diagram
An energy balance is written for each of the three nodes. The resulting first order
temperature dynamics for the coolant node are shown in Equation 3.24. [40].
dTclnt 1 h Twall − Tclnt = − ((Tclnt + Tclntin )/2 − Tamb)hambAshell dt mclntcvclnt + mshellcvshell Rclnt + Rwall i +m ˙ clntcvclnt (Tclntin − Tclnt) (3.24)
The product hambAshell represents the heat transfer coefficient between the EGRC shell and the ambient air.
Equation 3.25 represents the temperature dynamics of the heat exchanger wall node.
dT 1 h T − T T − T i wall = clnt wall + clnt wall (3.25) dt mwallcvwall Rclnt + Rwall Rexh + Rshell The temperature dynamics of the exhaust node of the EGRC model are shown in
Equation 3.26.
dTexh 1 h Twall − Texh i = +m ˙ exhcpexh (Texhin − Texh) (3.26) dt mexhcvexh Rexh + Rwall 71 Equation 3.27 is used to estimate a ratio of the thermal power of the exhaust flowing
through the EGRC, to that of the coolant flowing through.
m˙ exhcpexh (Texhin − Tclnt) Eratio = (3.27) m˙ clntcpclnt (Tclntboil − Tclntin )
The term Tclntboil is used to represent the boiling temperature of the coolant inside the EGRC, at the modelled coolant temperature and pressure.
This ”energy ratio” calculated in Equation 3.27 is used as a constraint on the EGRC operation, for durability purposes. When the energy ratio is too high, hot exhaust can cause localized boiling of the coolant inside the EGRC or damage the heat exchanger itself. This constraint in EGRC operation is considered when designing the TMS controller and is discussed in greater detail in Chapter 4.
3.5.1 EGRC Model Calibration and Validation
The convective thermal resistances, Rclnt and Rexh shown in Equations 3.24,3.25, and
3.26, are calibrated using experimental data. During steady-state experimentation,
the model inputs in Figure 3.19 are individually varied in order to carry out a Design
of Experiments (DoE). The experimental results from the DoE performed by the
EGRC Original Equipment Manufacturer (OEM) are used to calibrate each thermal
resistance. Equation 3.28 shows the relationship used to calculate the overall heat
transfer coefficient of the model, as the thermal resistance of each individual node.
1 1 δ 1 = Rexh + Rwall + Rclnt = + + (3.28) {UA} Ahexh AKwall Ahclnt It is clear that the conductive thermal resistance of the wall node is simply a func-
tion of wall thickness, δ, its area, and thermal conductivity. Since all geometrical
72 parameters of the wall are measured and the thermal conductivity is calculated using a polynomial fit to thermal conductivity vs. wall temperature, there are no calibra- tion parameters for the thermal resistance of the wall. However, the convective heat transfer coefficient of both the exhaust and coolant is calculated using Equation 3.29.
1/3 βfluid CcalKfluidP rfluidGfluid hconv = (3.29) fluid βfluid µfluid
The parameters Cfluid and β are calibration coefficients that are different for each
fluid. Prandtl number (Pr), mass velocity (Gfluid), Kfluid, and µfluid are all calculated from measured mass flow rates, areas, and temperatures.
The calibration coefficients are constant for all operating points and are calculated by first calculating the necessary thermal resistance in each fluid node, given exper- imental values for inputs and outputs. Each parameter other than the calibration coefficients in Equation 3.29 is then calculated. A least squares curve fit is then car- ried out on the calibration coefficients, Cfluid and β. The values of Cfluid and β for each fluid are shown in Table 3.1.
Table 3.1: EGRC Calibration Coefficients
Fluid Cfluid β Coolant 9.08e9 -1.04 Exhaust 3.96e7 -0.57
The inputs to the DoE performed by the EGRC OEM are shown in Figure 3.20.
Figure 3.22 shows the exhaust outlet temperature during this DoE. The steady-state exhaust outlet temperature predicted by the calibrated EGRC model is also shown.
73 Figure 3.21 shows the same results comparison for the coolant at the EGRC outlet.
No experimental data was provided for the heat exchanger wall temperature, but this
simulated temperature is between the temperature of the exhaust and that of the
coolant for all scenarios.
Figure 3.20: Experimental Inputs for EGRC Calibration
The accuracy of the calibrated EGRC model is validated on another set of exper- imental data. The experimental data used in this validation was taken from tests of the prototype engine on an engine dynamometer. Engine operation was varied during the tests and values were recorded for the temperature of coolant entering the
EGRC, as well as the temperature of exhaust entering and exiting. Mass flow rate
74 135 Coolant Temp − Supplier Data Coolant Temp − Model 130
125
120
115
110 Coolant Temperature [deg C]
105
100 1 2 3 4 5 6 7 8 9 Data Point #
Figure 3.21: Experimental and Simulated Coolant Temperature Data for EGRC Cal- ibration
of exhaust through the EGRC is estimated by the ECU and recorded in the data, as well. A look-up table is created for each of these parameters, based on engine speed and throttle opening. The output of each of these look-up tables is shown in Figure
3.23. These values are sent to the EGRC model, as a DoE of engine operating condi- tions is executed using the complete model of the prototype dyno engine TMS. This model uses a coolant flow network model, calibrated with experimental data, to esti- mate coolant flow to the EGRC. Figure 3.24 shows a comparison of the steady-state experimental exhaust temperature at the EGRC outlet, to the temperature predicted by the EGRC model. A histogram of the error of the model predictions is shown in Figure 3.25. Experimental data for wall temperature and coolant temperature at
75 160 Exh. Temp − Supplier Data 155 Exh. Temp − Model
150
145
140
135
130
125 Exhaust Temperature [deg C] 120
115
110 1 2 3 4 5 6 7 8 9 Data Point #
Figure 3.22: Experimental and Simulated Exhaust Temperature Data for EGRC Calibration
the outlet of the EGRC was not recorded for the given data. The accuracy of the exhaust temperature prediction of the EGRC model is very good. Possible sources of error include error in estimating the mass flow rate of coolant to the EGRC, using the model of the coolant flow network. It is also good that the model consistently over estimates the temperature of exhaust exiting the EGRC. When developing TMS controls which minimize exhaust outlet temperature using this model, the controls tend to over-cool the EGR on the actual engine, which is favorable to accidentally under-cooling the exhaust and damaging the engine.
76 Figure 3.23: Experimental Inputs for EGRC Validation
The EGRC model is now ready for use in the complete TMS model. A similar calibration and validation procedure was completed for all remaining TMS submodels updated from the production vehicle platform.
77 130 Exh. Temp − Dyno Data Exh. Temp − Model
C] 125 o
120
115
110
105
Temperature of Exhaust Exiting EGRC [ 100
95 0 10 20 30 40 50 60 Data Point #
Figure 3.24: Validation of EGRC Exhaust Outlet Temperature Model
15
10
5 Frequency of Occurence
0 −0.5 0 0.5 1 1.5 2 2.5 3 % Error of EGR Outlet Temperature in Deg. C
Figure 3.25: Histogram of Exhaust Temperature Prediction Error
78 3.6 Complete TMS Model Results
Following the calibration and validation of each of the TMS submodels, these sub- models are combined to form the complete vehicle TMS. The complete block diagram of the TMS model is shown in Figure 3.26.
Figure 3.26: Complete TMS Block Diagram
The TMS model is combined with the mechanical engine and transmission models, as well as the vehicle dynamics, air conditioning system, and electrical system model.The
79 engine mechanical model simulates the dynamics of the engine air pathways and sub- sequent torque production. The transmission mechanical model accurately represents the behavior of the transmission and torque converter during gear changes and ac- celeration, as well as steady-state operation. Including an accurate vehicle dynamics model is important, as this model predicts how the vehicle accelerates, as a function of the powetrain operation. The electrical system model captures the behavior of the vehicle’s lead-acid battery, alternator, and voltage regulator, as shown in [41].
The air conditioning model is used to represent the behavior of the compressor, evao- porator, condensor, and all actuators in the system, and is detailed in [42]. These models combined with the control algorithms for all actuators complete the Vehicle
Energy Simulator (VES), as shown in Figure 3.27. This forward-looking model also uses a ”driver” model to actuate the throttle and brake pedal of the vehicle in order to match any vehicle velocity trace supplied. The VES combines the models of all of the vehicle systems to create a single simulator which is capable of predicting a large number of vehicle operating parameters during a given drive cycle. Most im- portantly, the VES is used to predict the fuel consumption of the vehicle during an
FTP drive cycle. This is extremely important, as it allows for the evaluation of the impact a different control strategy for any of the systems may have on vehicle fuel consumption.
80 Figure 3.27: Vehicle Energy Simulator Hierarchy
Figure 3.28 shows the velocity trace that a vehicle must follow for the FTP drive cycle. This test begins with the vehicle at ambient temperature and consists of an Urban Dynamometer Driving Schedule (UDDS) test, followed by a Highway Fuel
Economy Driving Schedule (HWFET) test [43]. The test is used by the Environmental
Protection Agency (EPA) to evaluate vehicle fuel economy and emissions ratings [43].
The FTP is used to represent a real-world driving cycle, so the vehicle velocity varies considerably, with many instances of idling during the urban driving portion. The average vehicle speed during the FTP is 9.48 m/s (21.2 mph) [43].
81 30
25
20
15
Vehicle Velocity [m/s] 10
5
0 0 200 400 600 800 1000 1200 Time [s]
Figure 3.28: Vehicle Velocity During FTP
3.6.1 FTP Engine Operating Range
Figure 3.29 shows the engine speed that the Chrysler Town and Country equipped with the Alpha 2 engine maintained during the FTP drive cycle. The throttle opening during the test is shown in Figure 3.30.
82 5000
4500
4000
3500
3000
2500
2000 Engine Speed [RPM] 1500
1000
500
0 0 200 400 600 800 1000 1200 Time [s]
Figure 3.29: Engine Speed During FTP
0.9
0.8
0.7
0.6
0.5
0.4
0.3 Throttle Opening [Fraction] 0.2
0.1
0 0 200 400 600 800 1000 1200 Time [s]
Figure 3.30: Throttle Opening During FTP
83 3.6.2 TMS Inputs
The Friction Mean Effective Pressure (FMEP) of the engine is a measure of the fuel energy delivered to the engine that is lost due to friction between rotating components of the engine. FMEP is a source of fuel consumption that can be minimized by an intelligent TMS, as it is directly proportional to engine oil temperature. FMEP is calculated within the VES according to Figure 3.31, where the Shayler factor shown is calculated using Equation 3.30.
0.24 µoil ρoilref F actorShayler = (3.30) ρoil µoilref
Figure 3.31: FMEP Calculation
As shown in Figure 3.31, the Shayler factor is multiplied by the FMEP calculated for fully warmed-up conditions, in order to account for the increase in rubbing friction
84 when the engine oil is cold and therefore more viscous. Figure 3.32 shows the FMEP of the Alpha 2 engine during a simulated FTP drive cycle. It can be seen that the magnitude of the FMEP generally decreases during the first 400 seconds of the simulation, due to the warm-up of the engine oil. Similarly, the efficiency of the automatic transmission of the vehicle also has a dependency on fluid temperature.
Figure 3.33 shows the power conversion efficiency of the transmission during the
FTP. It can be seen that the transmission efficiency is much more dependent on transmission operation, and not transmission fluid temperature. The FMEP of the engine and efficiency of the transmission are two important inputs to the TMS.
4.5
4
3.5
3
2.5
2 FMEP [bar]
1.5
1
0.5
0 0 200 400 600 800 1000 1200 Time [s]
Figure 3.32: Friction Mean Effective Pressure During FTP
85 1
0.9
0.8
0.7
0.6 Transmission Efficiency [Fraction] 0.5
0.4 0 200 400 600 800 1000 1200 Time [s]
Figure 3.33: Transmission Efficiency During FTP
3.6.3 TMS Outputs
The temperature of the coolant, engine oil, and transmission oil during the simulated
FTP are shown in Figure 3.34. For this baseline simulation of the vehicle with the prototype powertrain, the coolant pump and thermostat are left to operate in me- chanical mode only. The three way valve is open only 15% and thus diverts most of thel coolant flow to the CHC. The EGRC coolant valve is kept at a minimum opening of 25%. It can be seen that during this baseline simulation, the engine coolant warms up first, as it receives heat from combustion through the cylinder walls. The target coolant temperature of 105oC is acheived after 462 seconds. The coolant exchanges heat with the engine oil by means of the Engine Oil Cooler, causing the engine oil to reach its target temperature of 105oC after 1031 seconds. The engine oil also receives heat from the previously mentioned friction within the engine. The transmission fluid
86 is heated by friction within the transmission, as well as from heat transferred from coolant in the TOH. The heat transferred to the transmission oil is enough to warm the oil to its target temperature of 80oC, after 675 seconds. At this time the three- way valve is closed, as a thermostatic valve inside the transmission oil lines opens and sends all transmission oil flow to the TOC, and closes off flow to the TOH. This is done in an effort to maintain the transmission oil temperature between 80oC and
90oC, after the initial rapid warm-up phase.
Figure 3.35 shows the temperature of exhaust gas exiting the EGRC. As this gas is recirculated to the engine intake tract, its temperature is critical to engine opera- tion. It can be seen that the EGRC is extremely effective and maintains an EGR temperature only slightly above the coolant temperature.
110
100
90
80 C] o 70
60 Coolant at Engine Outlet Engine Oil in Sump Temperature [ 50 ATF in Sump
40
30
20 0 200 400 600 800 1000 1200 Time
Figure 3.34: Engine and Transmission Fluid Temperatures During FTP
87 120
110 C] o 100
90
80
70
60
50
40 Exhaust Temperature at EGRC Outlet [ 30
20 0 200 400 600 800 1000 1200 Time
Figure 3.35: EGR Temperature During FTP
3.6.4 TMS Actuator Positions
With the thermostat left to operate in mechanical mode only, it begins opening at
105oC, and then opens and closes in a regular saw-tooth pattern after the coolant is fully warmed-up. This behavior during the FTP is shown in Figure 3.36, and produces a similar saw-tooth pattern in the coolant temperature, after the initial warm-up, as shown in Figure 3.34. Figure 3.37 shows the coolant speed during the simulation, which is mechanically coupled to the crankshaft at all times. The coolant pump rotates 1.34 times faster than the crankshaft, due to the ratio between the pulleys on each device. The rotational speed of the single 650 W radiator fan is shown in Figure 3.38. The fan operates at three discrete speeds, in accordance with a rule-based control architecture that increases fan speed as coolant temperature rises
88 higher above its target. This replicates the control structure implemented in the production vehicle and is therefore applicable to this baseline simulation.
Overall, the performance of the baseline TMS and controller is not ideal. The TMS is sized to adequetely cool the powertrain during even the most extreme conditons. Due to this, in many areas of engine operation, the TMS overcools the fluids. This reduc- tion in coolant temperature causes the thermostat to begin to close. By the time the thermostat begins closing, the engine operating point has changed and the thermostat needs to open again. This causes undesirable oscillations in coolant temperature.
0.16
0.14
0.12
0.1
0.08
0.06
Thermostat Opening [Fraction] 0.04
0.02
0 0 200 400 600 800 1000 1200 Time [s]
Figure 3.36: Thermostat Opening During FTP
89 7000
6000
5000
4000
3000
2000 Coolant Pump Speed [RPM]
1000
0 0 200 400 600 800 1000 1200 Time [s]
Figure 3.37: Coolant Pump Speed During FTP
2000
1800
1600
1400
1200
1000
800 Fan Speed [RPM] 600
400
200
0 0 200 400 600 800 1000 1200 Time [s]
Figure 3.38: Radiator Fan Speed During FTP
90 3.6.5 Fuel Consumption
Fuel consumption is the most important metric predicted by the VES, as the overall goal of the research project is to reduce fuel consumption during the FTP drive cycle. Figure 3.39 shows the cumulative fuel consumed by the vehicle during the simulated FTP cycle, which is a total of 0.95 kg. This fuel economy prediction is a consequence of vehicle operation and its effects on each vehicle subsystem. As such, the engine FMEP and transmission efficiency both have a significant impact on the fuel consumption predicted by the VES. This means that changes in TMS control strategy will have an immediate effect on the fuel consumption predicted by the VES.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Cumulative Fuel Consumption [kg] 0.2
0.1
0 0 200 400 600 800 1000 1200 Time [s]
Figure 3.39: Fuel Consumption During FTP
91 Chapter 4: Thermal Management System Control Development
This chapter aims to explain the TMS controller designed for use during the fluid conditioning phase of vehicle operation. The basic goals for the TMS controller as well as the design methodology are outlined. This controller utilizes open-loop actuator control coupled with feedback control. The control design methodology involves utilizing both open-loop and closed-loop control. System analysis is first performed to decide the control authority of each TMS actuator. Next, a DoE of
TMS actuator positions is carried out at a variety of steady-state engine operating conditions, using the complete nonlinear TMS model. The optimal actuator positions are selected by minimizing a cost function and then used as the feed-forward portion of the TMS controller. Simulations are then carried out with the open-loop controller, to test its performance. Rule-based controls are implemented with PI feedback on each actuator, for closed-loop control. The PI controllers correct the actuator positions, based on error between the desired and actual coolant temperature.The performance of the closed-loop TMS controller derived is compared to that of the baseline controller used by Chrysler Group LLC.
92 4.1 Control Objectives and Methodology
Fuel consumption can be reduced by allowing the engine fluids to operate at an el- evated temperature. In particular, the higher the temperature of the engine oil and transmission oil, the less friction will be experienced within the engine and transmis- sion. However, maintaining elevated fluid temperatures requires more robust TMS control, as the elevated temperatures are inherently closer to critical temperatures that may cause engine damage. Figure 4.1 shows the consequences of poor thermal management. As the coolant temperature overshoots its target, the cylinder wall temperatures rise and engine knock could occur. Engine knock can cause engine damage and will cause the ECU to retard spark timing, thus reducing fuel economy.
Fuel economy is further reduced when the coolant temperature oscillates below that of the target temperature. The lower coolant temperature will lower the engine oil temperature, which increases frictional losses.
Figure 4.1: Effects of Fluid Temperature Oscillations [16]
93 The TMS controller must use the coolant pump, thermostat, radiator fan, three-way valve, and EGRC coolant valve to meet the control objectives set by Chyrsler Group
LLC in the following list. Additionally, the controller must provide robust operation in all operating ranges and be easy to implement in the ECU. The following list shows the control objectives of the TMS controller:
1. Maintain EGR temperature below threshold shown in Figure 4.2 and EGRC
energy ratio below 0.35.
2. Maintain coolant temperature at 105◦C, while minimizing temperature fluctu-
ations.
3. Prevent rapid switching of actuators.
4. Minimize actuator energy consumption.
A basic control strategy for each actuator was determined. Since the thermostatic valve inside the transmission oil line is open during fully warmed-up operation, all transmission oil will flow to the TOC, and none will flow to the TOH. For this reason, the TWV can be set to divert all coolant to the CHC. This means that the coolant and transmission oil circuits are completely decoupled. Since the transmission oil temperature is now maintained entirely by air flow to the TOC, the entire transmission thermal model and accompanying heat exchangers can be omitted from the TMS model used to develop fluid conditioning controls. Air is supplied to the TOC due to air flowing around the vehicle as it drives, as well as radiator fan actuation. It has been seen during experimental testing on similar powertrains that if the radiator fan is used enough during the FTP drive cycle such that the engine coolant temperature
94 is maintained at its target temperature, the transmission oil temperature will also be kept at an acceptable level (below 100◦C). Also, no goal was put on engine oil temperature for the controller design because it has also been observed that if the coolant temperature targets are met, the engine oil temperature will also remain at an acceptable level (below 125◦C) during FTP operation, because excess heat in the engine oil is transferred to the coolant, via the EOC. In this way, the proposed controller is cascading in nature in that coolant temperature is actively controlled, which will indirectly satisfy safety constraints on engine oil and tranmission fluid temperatures.
150
145
140 C] o 135
130
125
120
115 Exh. Temp. at EGRC Outlet [ 110
105
100 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 Engine Speed [RPM]
Figure 4.2: Maximum EGR Temperature at EGRC Outlet
It is important to maintain the EGR temperature below the thresholds shown in
Figure 4.2, to prevent engine damage due to engine knock associated with elevated combustion chamber temperatures. The energy ratio constraint of 0.35 must be
95 maintained, to prevent localized coolant boiling inside the EGRC, as well as warping of the heat exchanger walls. To satisfy the EGR temperature constraints and energy ratio constaint, the EGRC Coolant Valve (EGRC CV) is actuated according to a controller developed in [38]. This controller is described by Equation 4.1.
τERf − ER p αEGRCCV = 1 − (1 − αEGRCCVmin ) (4.1) τERf − min(ER, τERs ) s + p
This controller compares the actual EGRC energy ratio to an upper and lower thresh- old for the energy ratio. The EGRC CV is opened as the energy ratio approaches these thresholds. As the valve opens and allows more coolant to flow through the
EGRC, the energy ratio decreases. By only opening the EGRC CV more when needed to maintain a safe EGRC energy ratio, more of the coolant can be diverted to other heat exchangers. This allows for more efficient use of the available coolant to cool the engine and engine oil.
In Equation 4.1, a value of 0.25 is used for the lower safety threshold for the energy
ratio, as represented by τERs . The variable τERf represents the higher threshold on the energy ratio constraint, which is 0.35. As the current energy ratio approaches the thresholds, the controller opens the EGRC CV, in order to decrease the energy ratio. The default opening of the CV is the minimum EGRC CV opening and is
represented by the variable αEGRCCVmin . The chosen value of 0.25 maintains a minimal opening of the EGRC CV that will maintain a safe EGRC energy ratio at most engine operating conditions. The transfer function shown in Equation 4.1 is used to filter the commanded EGRC CV position. A value of 10 is used for the parameter p, of this transfer function.
96 The EGRC CV controller shown in Equation 4.1 ensures both the energy ratio con- straint and the EGR temperature constraints are not violated, even at varying engine operating conditons and actuator positions. This is because it was observed that when the controller is used to hold the energy ratio below the maximum acceptable value of 0.35, the EGR temperature always remains below the maximum acceptable
EGR temperatures shown in Figure 4.2. In this way, the EGRC CV controller shown in Equation 4.1 is used to actively maintain the desired EGRC energy ratio, which indirectly ensures that the EGR temperature targets are met as well.
The remainder of this chapter details the TMS controller designed to actuate the thermostat, coolant pump, and radiator fan in order to meet the control objectives.
For the control of these actuators, open-loop control is coupled with simple PI feed- back control, to investigate the performance of a simple control struture, before more complex controllers are designed. Additionally, this control structure is very eas- ily implemented inside the Engine Control Unit (ECU) of the prototype vehicle at
Chrysler Group LLC. The following sections explain the details of this control design process and evaluate its performance. This work will lead to future investigations of more complex TMS controller designs.
4.2 System Analysis
System analysis was completed to determine the control authority of each TMS ac- tuator. This was done to determine which areas of engine operation would be ideal to use each actuator. In order to accomplish this, the heat rejected from the en- gine to the coolant at each operating point was analyzed, as presented in Figure 4.3.
Neglecting any heat added to the coolant from the other heat exchangers, the heat
97 rejection values shown here represent the heat that must be rejected to the radiator to maintain a constant engine coolant temperature. A contour plot of this same heat rejection data is shown in Figure 4.4, with the operating points of the FTP drive cycle plotted as well.
120
100
80
60
40
20
0 Total Heat Rejection to Coolant[kW] 5000 4000 100 80 3000 60 2000 40 1000 20 0 Engine Speed [RPM] Throttle [%]
Figure 4.3: Heat Rejected to Coolant from Engine
98
100 75
25
50 90
45 70
20
65 40
90
35 80 60
85
80
55 30 25
75
25 50 60
70 45 25
20
65 40
95
90 60 35
85 99 80 Throttle [%]
55 30
75 40 70 65 60 50 55 45 40
Total Heat Rejection to Coolant [kW] Total Heat Rejection 50 35 25 45 30 40 20 20 20 35 25 30 15 20 25 15 10 20 15 10 5 510 5 0 0 0 0 C and a constant thermostat opening corresponding to this coolant ◦
3000 2500 2000 1500 1000 5000 4500 4000 3500 Engine Speed [RPM] Speed Engine s to the radiator, due to an additional cooling fan in the test cell, is also assumed. Figure 4.4: Heat Rejected to Coolant from Engine with FTP Operating Points / The heat rejected to the coolant atheat each rejected operating from the point coolant is to then the comparedFigures radiator, with 4.5 for and the a 4.6, given show the sent heat of rejected actautor frommechanical positions. the thermostat engine coolant operation, to and the radiator electrical for thermostatThese operation, plots respectively. were generated by assuming athe constant radiator of temperature 105 of coolant entering temperature and the respective thermostat operating mode. A Constantm air flow of 0.5 A DoE of steady-state coolant pump speedsusing and the radiator radiator fan model, speeds and was the carried heat out rejected to the radiator was calculated. Heat Rejection to Radiator with Thermostat in Mech. Mode 80
70 fan off fan at 1000 rpm fan at 1500 rpm 60 fan at 2000 rpm fan at 2500 rpm 50 fan at 2800 rpm
40
30
Heat Rejected to Radiator [kW] 20
10
0 0 1000 2000 3000 4000 5000 6000 7000 Coolant Pump Speed [RPM]
Figure 4.5: Heat Rejected to Radiator With Mechanical Thermostat Actuation
Heat Rejection to Radiator with Thermostat in Elec. Mode 80 fan off fan at 1000 rpm 70 fan at 1500 rpm fan at 2000 rpm 60 fan at 2500 rpm fan at 2800 rpm 50
40
30
Heat Rejected to Radiator [kW] 20
10
0 0 1000 2000 3000 4000 5000 6000 7000 Coolant Pump Speed [RPM]
Figure 4.6: Heat Rejected to Radiator With Electric Thermostat Actuation
100 It can be observed from Figures 4.5 and 4.6 that multiple actuator combinations are possible for a given radiator heat rejection requirement. This is done by first selecting an engine operating point of interest and noting the amount of heat the engine produces at this condition, using Figure 4.3. A horizontal line is then drawn on Figures 4.5 and 4.6, at this same level of heat rejection. Each point of intersection of this horizontal line and the curves representing constant radiator fan speed correspond to a set of actuator positions that would satisfy the given heat rejection requirement.
However, it can be seen that some actuator combinations will clearly result in less actuator energy consumption than others. For example, Figures 4.5 and 4.6 show that there is a large benefit to electrically heating the thermostat. Electrifying the thermostat consumes very little energy and increases the heat rejected to the radiator for a given coolant pump and fan speed. This allows for an energy consumption savings by down-speeding the coolant pump and radiator fan. However, it can be seen in Figure 4.4 that in many engine operating conditions experienced during the
FTP drive cycle that are at or near idle conditions, the heat rejected by the engine is less than the lowest value of heat rejected to the radiator with the thermostat in electrical mode. This means that the thermostat must be de-energized in these zones, to prevent overcooling of the engine fluids. On the other hand, some of the operating points of the FTP show heat rejection values higher than the maximum heat that can be rejected to the radiator with the thermostat in mechanical mode. This means that the thermostat must be electrified in these zones, to prevent overheating of the coolant. Additionally, some zones of Figure 4.3 show an engine heat rejection greater than the highest possible heat rejection to the radiator shown in Figure 4.6, where the thermostat is operated electrically. However, these radiator heat rejection values
101 are calculated assuming a vehicle on a stationary chassis dynamometer. A vehicle operating at high engine speed and load will quickly accelerate, thereby increasing the air flow to the radiator for all fan speeds.Therefore, these heat rejection requirements are still attainable during real-world driving.
Another key observation that can be gleaned from Figures 4.5 and 4.6 is that when the radiator fan is off, the heat rejected to the radiator is very insenstive to changes in coolant pump speed. This is because when the radiator fan is off, air is only supplied to the radiator by the external cooling fan, at a very low speed. It is immediately obvious that in these conditions that the radiator fan is off, the coolant pump speed should be minimized, to minimize its energy consumption.
These observations are used to shape future controller design. It was observed that, in general, the thermostat should be electrified in high load/high engine speed operation.
Also, special care must be taken to avoid overspeeding the coolant pump in regions that yield very little additional radiator performance for increased coolant pump speed. In these regions, the coolant pump speed should be minimized and the radiator fan speed should be increased.
4.3 Baseline TMS Controller
The baseline TMS controller for the fluid conditioning phase replicates the control used on the production vehicle during fully warmed-up operation. Simulations are carried out using the baseline controller and the prototype TMS model, in order to establish a benchmark for the TMS controller designed in this work. Using the base- line TMS architecture, the coolant pump and thermostat both operate in mechanical mode. The three-way valve diverts all coolant to the CHC and the EGRC CV is
102 controlled according to Equation 4.1. The radiator fan utilizes a rule-based control structure that increases fan speed with increasing coolant temperature, as shown in
Equation 4.2. The first and second rules in this strategy result in hysterisis in fan operation. This is because the fan is turned on when the coolant temperature exceeds
106◦C, but not turned off until the coolant temperature falls below 104◦C. Since it is desired to simulate the vehicle behavior during FTP testing on a chassis dynamome- ter, only a small air flow of 0.5 m/s is assumed to be provided by an additional fan in the test cell.
◦ 0 if Tclnt < 104 C ◦ 1000 RPM if Tclnt > 106 C ωfan = ◦ (4.2) 2000 RPM if Tclnt > 108 C ◦ 2500 RPM if Tclnt > 110 C FTP drive cycle simulations were carried out using the VES and the baseline TMS controller previously described. The performance of the baseline TMS controller is analyzed after the coolant reaches operating temperature (275 seconds). The coolant and EGR temperatures during the fully-warmed up portion of these simulations are shown in Figure 4.7 and Figure 4.8, respectively. Figure 4.8 shows that the maximum
EGR temperature is not exceeded during the simulated FTP, except at idle conditons.
However, the maximum EGR temperature at idle speed should be ignored, since these temperatures are below the desired coolant temperature. This is because when the
EGRC walls are warmed up, the EGR can not possibly be cooled to a temperature below that of the coolant.
103 109
108.5
108
C] 107.5 o
107
106.5
106
105.5 Coolant Temperature [
105
104.5
104 400 600 800 1000 1200 Time
Figure 4.7: Engine Coolant Temperature With Baseline TMS Controller
145
140 Baseline 135 Maximum
C] 130 o
125
120
115 EGR Temperature [
110
105
100 400 600 800 1000 1200 Time
Figure 4.8: EGR Temperature With Baseline TMS Controller
104 Table 4.1 shows that the Root Mean Squared (RMS) coolant temperature tracking error during fully-warmed operation is 1.01◦C. RMS Error is calculated according to
Equation 4.3, by taking the square root of the average squared coolant temperature tracking error. The standard deviation and maximum of this error are 0.80◦C and
2.5◦C, respectively.
rP 2 (Tcool − Tcool ) RMSE = ref (4.3) n
Table 4.1: Baseline Coolant Temp. Tracking Error
Controller RMS Error [◦C] Std. Dev. [◦C] Max. Error [◦C] Baseline 1.04 0.80 8.84
Figures 4.9, 4.10, and 4.11, show the simulated pump speed, fan speed, and thermostat position, respectively. The coolant pump speed is dictated by engine speed, as the coolant pump is in mechanical mode. The thermostat shows small openings of less than 10% during most of the simulation, as it is also operating in mechanical mode.
105 0.14
0.12
0.1
0.08
0.06
0.04 Thermostat Opening [Fraction]
0.02
0 400 600 800 1000 1200 Time [s]
Figure 4.9: Thermostat Opening With Baseline TMS Controller
7000
6000
5000
4000
3000
2000 Coolant Pump Speed [RPM]
1000
0 400 600 800 1000 1200 Time [s]
Figure 4.10: Coolant Pump Speed With Baseline TMS Controller
106 2000
1800
1600
1400
1200
1000
800 Fan Speed [RPM] 600
400
200
0 400 600 800 1000 1200 Time [s]
Figure 4.11: Radiator Fan Speed With Baseline TMS Controller
Table 4.2 summarizes the energy consumption of these actuators over the entire simu-
lated drive cycle, including the warm-up phase. The variable Epump represents the en-
ergy consumed by the coolant pump during the simulation, while the energy consumed
by the fan is Efan. The term Etotal describes the energy consumed by both actuators, which is converted into an Ecuivalent Actuator Fuel Consumption, mEAF C .These re-
sults serve as the baseline scenario that all TMS controllers developed by OSU are
compared to.
Table 4.2: Baseline Actuator Energy Consumption
Controller Epump [kJ] Efan [kJ] Etotal[kJ] mEAF C [kg] Baseline 125.63 102.25 227.88 0.01
107 4.4 Open-Loop Control Design
Optimal steady-state TMS actuator positions were found by conducting simulations at different engine operating points, and then used as Feed-Forward (FF) maps for each actuator position. A DoE was carried out by initializing the TMS at fully warmed-up conditions, and then allowing the engine to operate at constant speed and load. The radiator fan speed was set to a constant value and the coolant pump begins in mechanical mode. The coolant pump’s speed is corrected with a PI controller, based on error between actual coolant temperature and the desired temperature of 105◦C.
The coolant pump speed is varied during each simulation to remove one Degree of
Freedom (DoF) from the DoE and thus reduce the simulation time required. This is because the coolant pump speed is continuously varying when operating in electrical mode and would thus require a very fine DoE of pump speeds to find the ideal value.
The radiator fan speed is left as a DoE variable because Chrysler expressed a desire to use the fan only at a finite number of speeds and not continuously vary the fan speed. To prevent oscillations in coolant temperature, the thermostat position was set to a constant position. For low throttle openings, the thermostat opening is 10%, which corresponds to its opening at 105◦C, when operating in mechanical mode.
The thermostat position was set to a constant 60% opening during electrical mode operation. The thermostat operating mode for each simulation was determined before the DoE was carried out, through system analysis, and is shown as a function of engine operation in Figure 4.12. The analysis which determined the optimal thermostat mode for each operating point is explained in the previous section.
108 1
0.8
0.6
0.4
Thermostat Mode 0.2
0 4000 3000 100 80 2000 60 1000 40 20 0 0 Engine Speed [rpm] Throttle Opening [%]
Figure 4.12: Open-Loop Thermostat Actuation (1=electrical, 0=mechanical)
Each simulation in the DoE is run until the engine coolant temperarture stabilizes at
105◦C. Engine speed is varied between tests, between 600 and 4400 RPM. At each of these engine speeds, throttle is varied between 4,15,30, and 100% opening. Radiator fan speed was varied at each engine speed and load combination between values of
0, 1000, 1500, 2000, 2500, and 2800 RPM. This DoE of inputs is summarized in
Table 4.3. After all simulations were completed, the final position of each actuator for each data point was compiled. The cost function, shown in Equation 4.4, is dependent on steady-state coolant temperature tracking error, as well as actuator energy consumption. This cost function was evaluated for each DoE scenario and the optimal combination of actuator positions was selected for each engine operating point. This is done by minimizing the cost function at each engine operating point, as shown in Equation 4.5.
109 Table 4.3: DoE Operating Points
Parameter Min. Max. Number of Points Throttle [%] 4 100 4 N [RPM] 600 4400 10 Fan Speed [RPM] 0 2800 6
Tcool − Tcoolref Cf = α1 + α2(Ppump + Ptstat + Pfan) (4.4) Tcoolref
∗ u = argmin(Cf ) (4.5)
The cost function takes actuator energy consumption into consideration because Fig- ures 4.3 through 4.6 show that different combinations of actuator positions exist that can satisfy the same heat rejection demands of the engine at a given engine operating point. However, even though these solutions may all result in zero coolant tempera- ture tracking error, the actuator energy consumption for each case will differ. This is because the actuator power consumption data shown in Tables 4.4 and 4.5 show that an energy consumption tradeoff exists for different combinations of TMS actuator positions.
110 Table 4.4: Coolant Pump Power Consumption
Pump Speed Power Required in Power Required in [RPM] Mech. Mode [W] Elec. Mode [W] 500 27 52 1000 24 45 1500 36 67 2000 62 117 2500 92 174 3000 139 263 3500 206 N/A 4000 290 N/A 4500 393 N/A 5000 521 N/A
Table 4.5: Radiator Fan Power Consumption
Fan Speed [RPM] Power Required [W] 500 42 1000 82 1500 197 2000 387 2500 721 2800 956
Table 4.4 shows the power consumption of the coolant pump at different speeds.
A cost to run the pump in mechanical mode is given, as supplied in experimental data. The electrical power is found by dividing the mechanical power required by the electrical-to-mechanical energy conversion efficiency of the electric motor of the
111 coolant pump. This resulting electrical power is then divided by the mechanical-to- electrical energy conversion efficiency for the alternator. This final power consumption value represents the mechanical power required at the crankshaft of the engine to op- erate the coolant pump in electrical mode. Using this value, the power consumption of the pump in mechanical and electrical modes can be directly compared in terms of crankshaft power. The alternator energy conversion efficiency used for these cal- culations is assumed to be a constant 62% for scenarios shown in Table 4.4. This is because the alternator is operated at relatively low shaft speeds and electrical cur- rents during the FTP drive cycle, so the energy conversion efficiency of the alternator does not change much. The power consumption of the radiator fan is shown in Table
4.5. This power consumption is taken from experimental fan power consumption data provided by Chrysler Group LLC. Since this data was measured at the fan itself, the power was divided by the mechanical-to-electrical conversion efficiency of the alterna- tor, to yield the values shown in Table 4.5. Again, the electrical power consumption shown is the power requirement at the engine crankshaft.
The feed-forward maps of coolant pump speed, radiator fan speed, and thermostat actuator are shown in Figures 4.13, 4.14, and 4.12, respectively. The overall shape of each of the feed-forward maps is smooth and shows the expected trends. It can be seen that when the engine is at or near idle conditions, the fan and thermostat are deactivated, and the coolant pump speed is minimized. However, as throttle opening increases at low engine speeds, in Figure 4.13, the coolant pump speed increases, then decreases sharply and finally begins increasing again. This decrease in pump speed corresponds to the actuation of the electric thermostat and radiator fan. This same pattern is also seen for increasing engine speed at low throttle openings. This
112 is because even though the heat rejection to the radiator is not sensitive to changes in coolant pump speed when the radiator fan is off, there are still some situations in which it is beneficial to increase the coolant pump speed slightly in order to avoid actuating the radiator fan.
6000
5000
4000
3000
2000
1000 Coolant Pump Speed [rpm] 0 4000 3000 100 80 2000 60 1000 40 20 0 0 Engine Speed [rpm] Throttle Opening [%]
Figure 4.13: Open-Loop Coolant Pump Speed
113 3000
2500
2000
1500
1000
500 Radiator Fan Speed [rpm] 0 4000 3000 100 80 2000 60 1000 40 20 0 0 Engine Speed [rpm] Throttle Opening [%]
Figure 4.14: Open-Loop Radiator Fan Speed
The open-loop controller developed uses the feed-forward maps for coolant pump and radiator fan speed shown in Figures 4.13 and 4.14, respectively. As the map of thermostat operation shown in Figure 4.12 is only a binary signal, that has a single continuous zone in which it is actuated, this table is converted into a rule- based controller. The actuation of the thermostat and radiator fan also have rule- based controls which are related to the current engine coolant temperature. To this measure, the thermostat is electrified if the current throttle opening and engine speed are within the zone for electrification shown in Figure 4.12, or if coolant temperature exceeds 107◦C. Additionally, the values of the radiator fan speed map specified in
Figure 4.14 are only used if the coolant temperature is above 106◦C, thus activating the radiator fan. After activation, the radiator fan operates according to Figure 4.14 until coolant temperature falls below 105◦C. For this reason, the open-loop controller
114 designed is not completely open-loop, as the rule-based control relies on feedback from the coolant temperature. However, the values specified in the actuator feed-forward maps are not altered by feedback control in any way, the tables are simply enabled or disabled based on coolant temperature. This is necessary because the feed-forward maps were derived for steady-state engine operation, after the temperature of each of the masses of the engine thermal model had converged to a constant value. As the thermal inertia of the engine is very large, it takes several hundred seconds for the engine thermal model to reach equilibrium. Since the FTP drive cycle consists of very rapidly changing engine operation, the radiator fan and thermostat operation must not be activated immediately, to prevent overcooling of the engine fluids. A Low Pass
Filter (LPF) is also used to smooth the throttle opening and engine speed signals that serve as the inputs to the feed-forward maps. This promotes smooth actuator operation by reducing rapid spikes in the controller inputs that have little impact on the coolant temperature, due to the previously mentioned engine thermal dynamics.
The block diagram of the open-loop radiator fan controller is shown in Figure 4.15.
The logic for enabling and disabling the fan is shown, as are the feed-forward map of fan speed and PID controller. The desired fan speed is sent to a rounding function which rounds the desired fan speed to the nearest 500 RPM. This is done to satisfy the desire of Chrysler to have the fan operate at only discrete speeds, and not on a continuous basis.
115 Figure 4.15: Block Diagram of Open-Loop Radiator Fan Controller
Figure 4.16 shows the block diagram of the open-loop coolant pump controller. It can be seen that logic gates enable the coolant pump to switch to mechanical mode if the desired coolant pump speed is within 5% of the value of the coolant pump speed in mechanical mode. Switching to mechanical pump mode in these conditons saves energy. The pump is also operated mechanically if both the desired pump speed and the mechanical pump speed exceed the maximum pump speed in electric mode (3000
RPM).
116 Figure 4.16: Block Diagram of Open-Loop Coolant Pump Controller
Logic is also implemented in both the fan and pump controllers to prevent rapid on/off switching. For the case of the coolant pump, whenever the pump enters electrical mode, a counter begins. The pump is not able to switch back to mechanical mode until at least two seconds have passed. For the radiator fan, a different speed can only be selected every three seconds.
4.4.1 Open-Loop Controller Performance
The TMS model combined with the open-loop controller developed is subjected to a simulated FTP cycle, beginning from ambient conditions. For this simulation, the three-way valve and the EGRC CV are controlled in the same way as for the baseline controller. The open-loop simulation results are compared to those of the baseline case after the coolant reaches 105◦C in both simulations. It can be seen in Figure 4.17,
that the coolant temperature tracking error is smaller with the open-loop controller.
117 This is especially true at the very beginning of steady-state operation, where a large temperature overshoot of 8.84◦C is present in the baseline case. Statistics regarding coolant temperature tracking error during each simulation is shown in Table 4.6. It can be seen that the Root Mean Square (RMS) error is reduced by 0.29◦C for the open-loop control strategy. However, both control strategies display little temperature tracking error.
109 Baseline Open−Loop 108 C] o 107
106
105 Coolant Temperature [
104
103 400 600 800 1000 1200 Time
Figure 4.17: Open-Loop Coolant Temperature During Simulated FTP
Table 4.6: Open-Loop Coolant Temp. Tracking Error
Controller RMS Error [◦C] Std. Dev. [◦C] Max. Error [◦C] Baseline 1.04 0.80 8.84 Open-Loop 0.75 0.69 7.36
118 The EGR temperature at the EGRC outlet is shown in Figure 4.18. It is observed that the maximum EGR outlet temperature is not exceeded during either simulation, except at idle conditions. This is because the maximum EGR temperature at idle conditions is less than the desired coolant temperature of 105◦C. Therefore, the EGR temperatures above the maximum allotted temperatures should be ignored at idle.
145 Baseline 140 Open−Loop Maximum 135
C] 130 o
125
120
115 EGR Temperature [
110
105
100 400 600 800 1000 1200 Time
Figure 4.18: Open-Loop EGR Temperature During Simulated FTP
Figure 4.19 shows the coolant pump speed during the FTP, while the radiator fan speed is shown in Figure 4.20. The thermostat opening during the cycle is shown in Figure 4.21. It can be seen that because the thermostat is often actuated elec- trically, as shown in Figure 4.22, the average thermostat opening is much greater for the open-loop controller. This greater thermostat opening is the reason that the speed of the coolant pump and radiator fan is often less for the simulation conducted
119 with the open-loop controller. This is also the reason the large overshoot in coolant temperature seen in the baseline case is not present when the open-loop controller is employed. The simulated coolant pump operating mode is shown in Figure 4.23.
Please note that for both the pump and fan operation, a value of zero corrsponds to mechanical mode, while a one corresponds to electrical actuation.
7000 Baseline Open−Loop 6000
5000
4000
3000
2000 Coolant Pump Speed [RPM]
1000
0 400 600 800 1000 1200 Time [s]
Figure 4.19: Open-Loop Coolant Pump Speed During Simulated FTP
120 2000 Baseline 1800 Open−Loop
1600
1400
1200
1000
800 Fan Speed [RPM] 600
400
200
0 400 600 800 1000 1200 Time [s]
Figure 4.20: Open-Loop Radiator Fan Speed During Simulated FTP
0.4
0.35
0.3
0.25
0.2
0.15
Thermostat Opening [Fraction] 0.1
0.05 Baseline Open−Loop 0 400 600 800 1000 1200 Time [s]
Figure 4.21: Open-Loop Thermostat Opening During Simulated FTP
121 1
0.9
0.8
0.7
0.6 Baseline Open−Loop 0.5
0.4 Operating Mode
0.3
0.2
0.1
0 400 600 800 1000 1200 Time
Figure 4.22: Open-Loop Thermostat Operating Mode During Simulated FTP
1
0.9
0.8
0.7
0.6 Baseline Open−Loop 0.5
0.4 Operating Mode
0.3
0.2
0.1
0 400 600 800 1000 1200 Time
Figure 4.23: Open-Loop Coolant Pump Operating Mode During Simulated FTP
122 Table 4.7 shows the energy consumed by each actuator during the simulation. It can be seen that the open-loop control strategy makes more efficient use of its actuators and thus much less energy is consumed by the actuators when the open-loop control strategy is used. However, as the actuator energy consumption does not represent very much of the total energy consumed during the FTP, only 0.28% less fuel is consumed by using the open-loop control strategy.
Table 4.7: Open-Loop Actuator Energy Consumption
Controller Epump [kJ] Efan [kJ] Etstat [kJ] Etotal[kJ] mEAF C [kg] FC Red.[%] Baseline 125.63 102.25 0 227.88 0.01 0 Open-Loop 151.16 22.12 1.45 174.73 0.00 -0.28
4.5 Closed-Loop Control Design
Although the performance of the open-loop controller appears adequate, feedback control is still necessary. This is because unforseen disturbances, such as fluctations in ambient temperature or changes in engine calibration, will be encountered during the life of the vehicle. Also, the thermostat opening dynamics and thermal dynamics in the heat exchangers associated with fast transients in engine operation will lead to coolant temperature tracking error. These circumstances require a robust controller that is able to adjust the TMS actuator positions to accomadate these conditions.
For this reason, Proportional and Integral (PI) control is added to the commanded coolant pump and radiator fan speeds. The transfer function for the PI controller is shown in Equation 4.6, where the input is coolant temperature tracking error. The proportional and integral gains, Kp and Ki, respectively, are tuned separately for each
123 actuator controller. These gains are tuned to yield a controller with fast response time as well as small overshoot and oscillations.
K G(s) = K + i (4.6) p s
Since different engine operating points produce vastly different levels of heat rejection and feed-forward actuator positions, the PI controller for each actuator must be tuned for multiple engine operating points. This is because the different behavior of the system at each operating point prevents a single optimal set of PI gains to be determined for the entire engine operating range. Two case studies are presented here.
First, validation of the PI gains tuned for a slow speed ”city” type driving are shown.
Validation of the feedback controller in a higher speed ”highway” type driving scenario is also shown. All of the controller gains are used during engine operation by utilizing switching blocsk to schedule these gains, based on engine operating conditions. the
PI controllers were tuned for step responses in throttle at 1200 RPM. This engine speed is typical of light city driving during the FTP. An engine speed of 2800 RPM was selected to represent the highway driving portion. The abrupt difference in heat rejection to the coolant seen between these two operating zones necessitated that the feedback control gains be tuned for each condition.
4.5.1 City Driving Feedback Control
Figure 4.24 shows a step input of throttle opening at a constant engine speed of 1200
RPM. This represents an engine transient during city type driving. The open-loop as well as closed-loop step response of the coolant temperature is shown in Figure 4.25.
The corresponding actuator positions are shown in Figures 4.26, 4.27, and 4.28, while
124 feedback control effort from each controller during closed-loop operation is shown in
Figure 4.29. It can be seen that even during steady-state open-loop operation, a very small amount of coolant temperature tracking error still exists. This is due to the temperature dynamics of the other powertrain fluids and thermal masses, as well as thermostat opening and closing dynamics. Additionally, since the DoE used to
find the open-loop actuator positions is somewhat coarse, interpolation of open-loop actuator positions between the engine operating points simulated in the DoE may introduce error. This open-loop error also produces some steady-sate control effort, as shown in Figure 4.29.
100
90
80
70
60
50
40 Throttle Opening [%] 30
20
10
0 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.24: Step Input of Throttle at 1200 RPM
125 106
105.8
105.6 OL CL
C] 105.4 o
105.2
105
104.8
104.6 Coolant Temperature [
104.4
104.2
104 0 100 200 300 400 500 600 700 800 Time
Figure 4.25: Step Response of Coolant Temperature at 1200 RPM
The jagged appearance of the step response in coolant temperature seen in Figure
4.25 is also due to the discrete nature of the fan speed commands. Since they are
in increments of 500 RPM, a switch in fan speed produces a very large change in
coolant temperature. Additionally, when a change occurs, the rule-based logic in the
fan controller forces the fan to maintain its present speed for at least three seconds,
to prevent rapid switching of speeds.
Table 4.8 summarizes the coolant temperature tracking error during the step response.
It can be seen that the closed-loop controller reduced the Max. Overshoot from 0.76%
to 0.57%. The settling time was also reduced by some 29.5%. Settling time is defined
as the difference between when the step input is applied and the instant in which
the coolant temperature enters within ±0.5◦C of the target coolant temperature of
105◦C. This reduction in coolant temperature tracking error was due to an increase
126 in coolant pump and radiator fan speed during the step response. This is necessary because the step input forces the thermostat to switch from mechanical to electrical operation. The opening dynamics of the thermostat necessitate a higher pump and fan speed to compensate for the gradual opening of the thermostatic valve. The actuator positions during the step response are shown in Figures 4.26, 4.27, and 4.28.
Table 4.8: PI Controller Step Response Metrics City Driving
Controller Max. Overshoot [%] Settling Time [s] Open-Loop 0.76 220 Closed-Loop 0.57 312
2350
2300
2250
2200
2150
2100 OL Coolant Pump Speed [RPM] CL
2050
2000 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.26: Coolant Pump Speed During Step Response at 1200 RPM
127 3000 OL CL 2500
2000
1500
Fan Speed [RPM] 1000
500
0 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.27: Radiator Fan Speed During Step Response at 1200 RPM
0.8
0.7
0.6
0.5
0.4
0.3 OL Thermostat Opening [Fraction] CL
0.2
0.1 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.28: Thermostat Opening During Step Response at 1200 RPM
128 40 Pump 30 Fan
20
10
0
−10
−20
−30 FB Control Contribution [%]
−40
−50
−60 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.29: Control Effort During Step Response at 1200 RPM
Table 4.9 shows the controller gains used for each PI controller during city driving.
The gains on the fan speed controller are higher than those of the coolant pump controller. This is because of the high control authority offered by the radiator fan.
The high control authority of the fan is means that the coolant temperature is lowered almost immediately after the fan is turned on. The coolant pump does not have as much control authority. This is because changing coolant pump speed increases both the heat rejection to and from the coolant. The heat rejected to the coolant from the engine thermal masses increases with increasing coolant flow. This means that increasing coolant flow increases heat rejected to the radiator from the coolant, but also increases heat rejected from the engine thermal masses to the coolant, thus reducing the termperature of the thermal masses. Therefore, the fan displays a higher
129 control authority than the coolant pump. However, only operating the fan at discrete speeds produces oscillations in coolant temperature as the fan is actuated.
Table 4.9: PI Controller Gains for City Driving
Actuator Kp Ki Coolant Pump 120 0.5 Radiator Fan 300 4
4.5.2 Highway Driving Feedback Control
The step input in throttle used to tune the PI controllers for highway style driving is shown in Figure 4.30. This simulation is carried out at a constant engine speed of 2800
RPM. The resulting closed-loop and open-loop step response in coolant temperature is shown in Figure 4.31.Statistics on coolant temperature tracking error during this step response are shown in Table 4.10. It can be seen that the closed-loop controller reduces the maximum overshoot slightly. However, the settling time is greatly decreased to just 25.3% of the open-loop settling time.
130 50
45
40
35
30
25
20 Throttle Opening [%]
15
10
5
0 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.30: Step Input of Throttle at 2800 RPM
131 111
Open−Loop Closed−Loop 110
109 C] o
108
107 Coolant Temperature [
106
105
104 0 100 200 300 400 500 600 700 800 Time
Figure 4.31: Step Response of Coolant Temperature at 2800 RPM
Table 4.10: PI Controller Step Response Metrics for Highway Driving
Controller Max. Overshoot [%] Settling Time [s] Open-Loop 4.46 150 Closed-Loop 1.66 38
The acuator positons during the step response are shown in Figures 4.32, 4.33, and
4.34. It is observed that the radiator fan speed is increased greatly from its open-loop value in order to regulate the coolant temperature. However, Figure 4.32 shows that the closed-loop coolant pump speed deviates very slightly from the open-loop speed.
132 This is because the control gains for the coolant pump in this region are very small.
The closed-loop contributions to the actuator positions can be seen in Figure 4.35.
3000
2500
2000 Open−Loop Closed−Loop
1500 Coolant Pump Speed [RPM]
1000
500 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.32: Coolant Pump Speed During Step Response at 2800 RPM
133 3000
Open−Loop Closed−Loop 2500
2000
1500 Fan Speed [RPM]
1000
500
0 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.33: Radiator Fan Speed During Step Response at 2800 RPM
1
Open−Loop 0.9 Closed−Loop
0.8
0.7
0.6
0.5
0.4
Thermostat Opening [Fraction] 0.3
0.2
0.1
0 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.34: Thermostat Opening During Step Response at 2800 RPM
134 40 Pump Fan
30
20
10
0 FB Control Contribution [%]
−10
−20
−30 0 100 200 300 400 500 600 700 800 Time [s]
Figure 4.35: Control Effort During Step Response at 2800 RPM
The PI gains for each controller are shown in Table 4.11. It can be seen that the coolant pump proportional feedback gain is now zero, while the same integral gain is used as in the previous case study. This is because the fan is much more effective during high-speed engine operation. Increasing coolant pump speed at many high speed engine operating points has almost no initial effect, as shown in the previous system analysis. Control effort due to feedback control continues to build for the pump speed controller, and then leads to eventual overcooling of the coolant. The integral gain of the fan is reduced. This is because the best controller performance was acheived with a smaller integral gain that before, but a much larger proportional gain. The large proportional gain of the fan PI controller allows the fan to provide quick disturbance rejection, while the integral gain of the coolant pump controller allows the pump to correct for steady-state coolant temperature tracking error.
135 Table 4.11: PI Controller Gains for Highway Driving
Actuator Kp Ki Coolant Pump 0 0.5 Radiator Fan 500 1
4.5.3 Closed Loop Controller Structure
The block diagram of the closed-loop radiator fan controller is shown in Figure 4.36.
The logic controlling the fan is the same as that shown in the open-loop controller shown in Figure 4.15, with the exception of the added PI controller. Additional logic inside the PI controller allows for scheduling of each PI gain, based on engine operation
Figure 4.36: Block Diagram of Closed-Loop Radiator Fan Controller
136 Figure 4.37 shows the block diagram of the closed-loop coolant pump controller. The structure of this controller is different than that of the open-loop controller shown in
4.16 because of the added PI controller. The gains of this PI controller are scheduled based on engine operating condtions. This PI controller is enabled by a binary input signal that only activates the PI control of the coolant pump if the radiator fan is currently activated. This is done because, as previously established in the system analysis, increasing the coolant pump speed when the fan is off yields very little additional radiator performance. Since the open-loop actuator positions have already been optimized with respect to this effect, the open-loop coolant pump speed should not be changed when the fan is not actuated.
Figure 4.37: Block Diagram of Closed-Loop Coolant Pump Controller
137 4.5.4 Closed-Loop Controller Performance
Another simulated FTP cycle is carried out, again beginning from ambient condi- tions. The same simulation conditions as those used to validate the open-loop and baseline controllers are used for this simulation. However, the closed-loop control strategy developed in the previous section is employed to control the coolant tem- perature. The closed-loop results are compared to the results obtained with both the baseline controller and open-loop controller. Figure 4.38, shows that the coolant temperature tracking performance of the closed-loop controller is better than that of both the baseline controller and the open-loop controller. The EGR temperature at the EGRC outlet is shown in Figure 4.39. Again, EGR temperatures above the maximum threshold during idle operation should be ignored. Figure 4.40 shows the coolant pump speed during the FTP for all simulations, while the radiator fan speed is shown in Figure 4.41. The thermostat opening during all simulations is shown in
Figure 4.42.
138 109
Baseline 108 Open−Loop Closed−Loop C] o 107
106
105 Coolant Temperature [
104
103 400 600 800 1000 1200 Time
Figure 4.38: Closed-Loop Coolant Temperature During Simulated FTP
145 Baseline 140 Open−Loop Closed−Loop 135 Maximum
C] 130 o
125
120
115 EGR Temperature [
110
105
100 400 600 800 1000 1200 Time
Figure 4.39: Closed-Loop EGR Temperature During Simulated FTP
139 7000 Baseline 6000 Open−Loop Closed−Loop
5000
4000
3000
2000 Coolant Pump Speed [RPM]
1000
0 400 600 800 1000 1200 Time [s]
Figure 4.40: Closed-Loop Coolant Pump Speed During Simulated FTP
2000 Baseline 1800 Open−Loop Closed−Loop 1600
1400
1200
1000
800 Fan Speed [RPM] 600
400
200
0 400 600 800 1000 1200 Time [s]
Figure 4.41: Closed-Loop Radiator Fan Speed During Simulated FTP
140 0.45 Baseline 0.4 Open−Loop Closed−Loop 0.35
0.3
0.25
0.2
0.15
Thermostat Opening [Fraction] 0.1
0.05
0 400 600 800 1000 1200 Time [s]
Figure 4.42: Closed-Loop Thermostat Opening During Simulated FTP
1
0.9
0.8
0.7 Baseline Open−Loop 0.6 Closed−Loop 0.5
0.4 Operating Mode
0.3
0.2
0.1
0 400 600 800 1000 1200 Time
Figure 4.43: Closed-Loop Thermostat Operating Mode During Simulated FTP
141 1
0.9
0.8
0.7 Baseline Open−Loop 0.6 Closed−Loop 0.5
0.4 Operating Mode
0.3
0.2
0.1
0 400 600 800 1000 1200 Time
Figure 4.44: Closed-Loop Coolant Pump Operating Mode During Simulated FTP
The coolant temperature tracking error statistics for each simulation during fully warmed-up operation is shown in Table 4.12. It can be seen that the Root Mean
Square (RMS) error is minimized with the closed-loop control strategy, if only slightly.
Table 4.12: Coolant Temp. Tracking Error
Controller RMS Error [◦C] Std. Dev. [◦C] Max. Error [◦C] Baseline 1.04 0.80 8.84 Open-Loop 0.75 0.69 7.36 Closed-Loop 0.69 0.67 7.46
The energy consumed by each actuator during each simulation is shown in Table
4.13 . It can be seen that the actuators consume less energy than the baseline case
142 when the closed-loop strategy is utilized. However, the open-loop strategy still uses the least acuator energy. This is because the increased coolant temperature tracking performance provided by the closed-loop TMS controller is obtained by increasing the radiator fan speed in certain condtions.
Table 4.13: Actuator Energy Consumption
Controller Epump [kJ] Efan [kJ] Etstat [kJ] Etotal[kJ] mEAF C [kg] FC Red.[%] Baseline 125.63 102.25 0 227.88 0.01 0 Open-Loop 151.16 22.12 1.45 174.73 0.00 -0.28 Closed-Loop 151.18 28.04 1.45 180.67 0.00 -0.26
143 Chapter 5: Conclusions and Future Work
5.1 Conclusions
Advanced powertrain technologies are used in almost all production passenger vehi- cles to minimize vehicle fuel consumption. Increasing fuel prices and more stringent emissions regulations justify the use of advanced Thermal Management Systems for additional fuel consumption reduction. These TMSs serve to warm all engine and transmission lubricating oils quickly during a cold-start of the engine, in order to re- duce the frictional losses associated with cold, viscous, oils. During fully warmed-up operation, the advanced TMS maintains all powertrain fluids at elevated tempera- tures, again, to reduce frictional losses. However, by increasing the fluid temper- atures, the margin for error between the steady-state fluid temperatures and fluid temperatures which may cause engine damage due to engine knock or overheating is reduced. This necessitates the use of a robust TMS controller.
In an effort to reduce powertrain development time, a model-based TMS controller was developed before experimental testing of the prototype TMS was conducted. This was done by first developing, calibrating, and validating a complete Vehicle Energy
Simulator in Matlab/Simulink, for an existing production vehicle. This model was
144 then updated to reflect the prototype architecture and used for TMS control devel- opment. The control objective was to use a dual-mode coolant pump, electrically heated thermostat, and electric radiator fan to maintain an engine coolant tempera- ture of 105◦ during the FTP drive cycle. A baseline, rule-based, TMS controller was established which represented the current rule-based control strategy of the produc- tion vehicle. This controller was able to maintain acceptable fluid temperatures, but there was room for improvement.
Significant system analysis was conducted to determine the control authority of each
TMS actuator at different engine operating conditons. It was discovered that ener- gizing the thermostat allows for more flow of coolant to the radiator, thus increasing radiator performance at very little cost. This improved performance allows for down- speeding of the coolant pump and radiator fan, thus conserving energy. For this reason, it was discovered that it was beneficial to operate the thermostat and coolant pump in electrical mode, which was not done using the baseline TMS fluid condition- ing controller. Additionally, it was observed that in certain engine operating ranges, different actuators have much greater control authority than others. The findings of this analysis were used to conduct a Design of Experiments, to find the optimum steady-state open-loop actuator positions for the coolant pump, radiator fan, and thermostat. An open-loop controller comprised of these maps as well as rule-based architecture was developed and its performance was compared to that of the baseline
TMS controller. The open-loop controller was able to reduce coolant temperature tracking error and actuator energy consumption, slightly.
A preliminary closed-loop controller was added to the previously developed controller in the form of PI controllers. These controllers correct the open-loop coolant pump
145 and radiator fan speed, based on coolant temperature tracking error. PI control was selected because the goal was to establish a simple TMS controller that could be easily implemented in the vehicle’s ECU. This controller was able to further reduce the RMS coolant temperature tracking error by a total of 0.35◦C, compared with the baseline controller. The open-loop and closed-loop controllers developed also reduced the energy consumption of the TMS actuators. This was done by electrically heating the thermostat, thereby increasing its opening and letting more coolant flow to the radiator. However, since the TMS actuators consume very little energy during the FTP when compared to the powertrain itself, these energy savings amounted to less than 0.3% in fuel savings during the entire FTP drive cycle. In creating this controller, it was discovered that tuning separate PI controllers for different engine operating conditions allows for optimal feedback control gains to be tuned for the entire range of engine operation. These gains are then scheduled based on engine- operation. However, a significant amount of time must be spent tuning the PI control gains for each engine operating conditon. For this reason, a multivariable control design method will be applied to this system. The work to implement multivariable control is ongoing and will allow the feedback gains for each engine operating range to be generated more quickly. This will reduce controller calibration time.
5.2 Future Work
This section of the Thesis details TMS control structures that will be investigated in the future. The control strategies of interest will be able to make more efficient use of the available actuators. However, a significant amount of time must be invested in
146 developing control-oriented TMS models. This section explains the control-oriented models that have been developed for future control design.
5.2.1 Future Control Development Methodology
In order to maintain the engine fluids at elevated temperatures and alleviate any temperature oscillations, a robust TMS controller shall be designed according to the procedures detailed in [16]. This methodology is shown in Figure 5.1 and involves utilizing both open-loop and closed-loop control. The open-loop controller is still designed as shown in Chapter 4 of this Thesis. The TMS model is then linearized around a specific set of conditons and model order reduction techniques are used to eliminate states which do not make significant contributions to the system dynamics when the engine fluids are fully warmed-up. The resulting linearized control-oriented
TMS model is used to develop a state space feedback control law. It is desirable to develop this multi-variable control law because it will allow for harmonious operation of all actuators, with minimal interference between them.
147 Figure 5.1: TMS Controller Design Methodology [16]
Model Linearization
To develop a state space feedback control law, a state space representation of the
TMS model must be found. Equation 5.1 shows the general form of a state space model. Since this form separates all state variables and control inputs into seperate terms, it cannot represent a set of nonlinear differential equations. In order to elimi- nate all terms in the nonlinear TMS model that are the product of one or more state variables and control inputs, the equations must be linearized. Linearization must be done about a particular equilibrium point. Since the linearized model is only an ap- proximation of the full model at the equilibrium point, exercising the linearized model at conditions that display different dynamics than those at the equilibrium point may
148 cause unexpected model behavior. For this reason, the model must be linearized at
a range of equilibrium points that cover the range of operating conditions it needs to
model. For a model that must simulate a wide range of operating conditions, this can
easily result in hundreds of equilibrium points. However, since the linearized TMS
model is only used for controller design during fully-warmed up vehicle operation, an
appropriate compromise between number of linearization points and model accuracy
can be achieved.
x˙ = Ax + Bu (5.1a)
y = CT x + Du (5.1b)
Let Equation 5.2 represent a system of nonlinear differential equations. For this set
of equations, an equilibrium point can be found such that all derivatives are equal
to zero, as shown in Equation 5.3. Each state variable and control input is then
expressed as a sum of its equilibrium value and a small perturbation term, as shown
in Equation 5.4. In order to find the value of the state varible, the state variable
perturbation, δx, must be found. To accomplish this, the control input peturbation,
δu is supplied to the linearized state space model. The coefficients of the A,B,C, and
D matrices of the linearized state space representation are found by taking the partial derivatives of each state variable and control input for each differential equation, as shown in Equation 5.5.
f1(X, u) ˙ . X = F (X, u) = . (5.2) fn(X, u)
149 F (X0, u0) = 0 (5.3)
x = x0 + δx (5.4a)
u = u0 + δu (5.4b)
df ∂f(X, u) ∂f(X, u) ∂f(X, u) ∂f(X, u) = +... + +... dδX ∂X1 Xi=Xi0 ∂Xn Xi=Xi0 ∂u1 Xi=Xi0 ∂un Xi=Xi0 ui=ui0 ui=ui0 ui=ui0 ui=ui0 (5.5)
Each partial derivative is then added to the matrices of the state space representation, shown in Equation 5.6. The solution of this state space matrix, calculated from the perturbed control inputs, is added to the equilibrium solution. This sum represents the final solution of the linearized system, as shown in Equation 5.7.
∂f1 ··· ∂f1 ∂X1 ∂Xn ∂F . . . AL = = . .. . (5.6a) ∂X Xi=Xi u =u 0 ∂fn ∂fn i i0 ··· ∂X1 ∂Xn ∂f1 ··· ∂f1 ∂u1 ∂un ∂F . . . BL = = . .. . (5.6b) ∂u Xi=Xi u =u 0 ∂fn ∂fn i i0 ··· ∂u1 ∂un
˙ X = F (X0, u0) + ALδX + BLδu (5.7)
Model Order Reduction
All thermal models are comibined to create a single TMS model. Although simple models are used to create each component, the entire system becomes very complex.
This TMS model is ideal for energy analysis, however, model-based control design is
150 more difficult with more complex models. For this reason, it is desirable to perform
Model Order Reduction (MOR) on the TMS model. This will reduce the TMS to a simplified model that will still retain the same system dynamics, such that it can be used for controller design.
The teachings of [44] illustrate the MOR method of truncation. The premise behind this system is to obtain a linearized set of differential equations to express the dy- namics of the system of study. Considering the state-space representation of a linear system, shown by Equation 5.1, the eigenvalues (representd by variable λ) of each eigen vector of the ”A” matrix are calculated according to Equation 5.8.
(A − λI)v = 0 (5.8)
In Equation 5.8, v is the eigenvector of the state matrix A, and I is the identity matrix.
The eigenvalues are analyzed and compared to one another. Large negative eigenval- ues correspond to fast system dynamics. After determining the state variable whose dynamics are most important to the controller design, its corresponding eigenvalue is compared to that of the other states. A eigenvalue which is significantly smaller in absolute value than that of the eigenvalue of the state variable of interest indicates that this state can be eliminated and replaced with a constant value for that state variable. This is because its dynamics are slow enough that they will not affect the system dynamics of the variable of interest. On the other hand, an eigenvalue which is significantly larger in absolute value than that of the variable of interest indicates that this state variable can be eliminated and replaced by an algebraic equation. In this case, the faster dynamics are approximated as being instantaneous, as they are
151 fast enough that they do not have a large impact on the dynamics of the variable of interest. This MOR process eliminates only those states that do not make significant contributions to the system dynamics important for the particular controller.
Additionally, a physics-based model order reduction procedure can be adopted, if it is obvious that the system dynamics are characterized by significantly different time constants. For example, if for a particular operating condition of interest, it is observed that the dynamics of some states will not have a significant impact on the variables of interest, then these states can be replaced with constant values. The modal truncation process is performed on each subsystem of the TMS. Combining all of the reduced order subsystems yields a reduced model of the entire TMS. This model is ready for use in the linear controller design process.
EGRC Thermal Model Linearization and Model Order Reduction
Linearization techniques are applied to the EGRC thermal model. State variables from the differential equations describing the EGRC temperature dynamics (Equa- tions 3.24, 3.25, and 3.26) are selected, as shown in Table 5.1. The control inputs for the state space representation of the EGRC model are shown in Table 5.2. All other values in Equations 3.24, 3.25, and 3.26 are thermal properties which are left as constants in the linearized model.
Table 5.1: EGRC Thermal Model State Variables
State Output Variable
X1 Tclnt X2 Twall X3 Texh
152 Table 5.2: EGRC Thermal Model Control Inputs
Control Input Input Variable
u1 Tclntin u2 qclnt
u3 Texhin u4 m˙ exh u5 Tamb
The state equations representing the EGRC thermal model are obtained by replac- ing the variable names in Equations 3.24, 3.25, and 3.26, with the state variables and control inputs. Equations 5.9, 5.10, and 5.11 are the state equations for each respective node of the EGRC thermal model.
1 h X − X X˙ = 0 = 2 1 − ((X + u )/2)h A + 1 m c + m c R + R 1 1 amb shell clnt vclnt shell vshell clnt wall (5.9) i +u2ρclntcvclnt (u1 − X1)
˙ 1 h X1 − X2 u1 − X2 i X2 = 0 = + (5.10) mwallcvwall Rclnt + Rwall Rexh + Rwall
˙ 1 h X2 − X3 i X3 = 0 = + u4cpexh (u3 − X3) (5.11) mexhcvexh Rexh + Rwall Control inputs that are representative of typical EGRC operation are selected as the equilibrium inputs shown in Table 5.3. The equilibrium states are determined by inserting the equilibrium inputs into the state equations and settining all derivatives to zero and then solving for the state variables. The equilibrium states are shown in
Table 5.4.
153 Table 5.3: Equilibrium EGRC Thermal Model Control Inputs
Control Input Input Variable Value Units
u1 Tclntin 378.15 K 3 u2 qclnt 2.4e-4 m /s
u3 Texhin 480 K u4 m˙ exh 0.004 kg/s u5 Tamb 300 K
Table 5.4: Equilibrium EGRC Thermal Model State Variables
State Output Variable Value Units
X1 Tclnt 378.63 K X2 Twall 378.70 K X3 Texh 378.77 K
The partial derivatives of each state variable and control input in the state equations are taken, in order to construct the linearized state matrices. The partial derivatives for each node are not shown in symbolic form in this document, as they are very lengthy. However, Equation 5.12 shows the numerical value of each derivative. These partial derivatives are now used with the equilibrium inputs and states to construct the linearized EGRC thermal model. A block diagram for this model is shown in
Figure 5.2.
∂X˙1 ∂X˙1 ∂X˙1 ∂X˙1 ∂X˙1 ∂X˙1 ∂X˙1 ∂X˙1 ∂X1 ∂X2 ∂X3 ∂u1 ∂u2 ∂u3 ∂u4 ∂u5 ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ δX˙ = ∂X2 ∂X2 ∂X2 δX + ∂X2 ∂X2 ∂X2 ∂X2 ∂X2 δu (5.12a) ∂X1 ∂X2 ∂X3 ∂u1 ∂u2 ∂u3 ∂u4 ∂u5 ∂X˙3 ∂X˙3 ∂X˙3 ∂X˙3 ∂X˙3 ∂X˙3 ∂X˙3 ∂X˙3 ∂X1 ∂X2 ∂X3 ∂u1 ∂u2 ∂u3 ∂u4 ∂u5
154 −1.67 1.51 0 0.17 −768.13 0 0 0 δX˙ = 11.01 −20.55 9.55 δX + 0.01 3.15e3 0 −90.11 0 δu 0 5.13e3 −5.13e3 0 0 3.22 1.43e5 0 (5.12b)
Figure 5.2: Block Diagram of Linearized EGRC Model
It is desirable to remove uneccessary state dynamics from the control-oriented model.
Since the control-oriented model will be used to design a controller to maintain a target coolant temperature, analysis was performed to eliminate state variables from the EGRC thermal model which do not have a significant impact on the dynamics of the coolant temperature. The main purpose of including the EGRC wall temperature node in the EGRC thermal model is because the heat exchanger wall is a significant heat sink during a cold-start. During cold-start conditions, the heat exchanger walls and coolant start from ambient conditions, but the exhaust flowing through the cooler is very hot. Since the heat from the exhaust must first be transferred through the heat exchanger walls, and then to the coolant, the heat exchanger walls have a sig- nificant impact on the coolant temperature dynamics. However, at fully warmed-up conditions, it can be observed that the wall temperature changes almost instanteously with the coolant temperature. Due to the relatively low thermal capacitance of the
155 exhaust gasses passing through the EGRC, the EGR outlet temperature also changes almost instantaneously with coolant temperature. These observations mean that the states X2 and X3 can be removed from the control-oriented EGRC thermal model and replaced with algebraic expressions.
The derivatives of states X2 and X3 are set to zero and the state equations are manipulated to find expressions for X2 and X3 in terms of the control inputs and X1 only. The algebraic expressions found for X2 and X3 are shown in Equations 5.13 and 5.14.
(u3 − X1)(cpexhaust u4(Rconvexhaust + Rcondwall ) + 1) X2 = u3 − (5.13) cpexhaust u4(Rconvcoolant + 2Rcondwall + Rconvexhaust ) + 1
u3 − X1 X3 = u3 − (5.14) cpexhaust u4(Rconvcoolant + 2Rcondwall + Rconvexhaust ) + 1 Equations 5.13 and 5.14 are substituted into Equation 5.9 to find a new expression ˙ for X1. The result is simplified and yields Equation 5.15.
(u −X )(c u (R +R )+1) 3 1 pexhaust 4 convexhaust condwall u3 − − X1 1 h cp u4(Rconv +2R +Rconv )+1 ˙ exhaust coolant condwall exhaust X1 = mclntcvclnt + mshellcvshell Rclnt + Rwall i −((X1 + u1)/2)hambAshell + u2ρclntcvclnt (u1 − X1) (5.15) The partial derivatives of equation 5.15 are taken, with respect to the single remaining state variable and the control inputs. The resulting state matrices for the reduced order EGRC thermal model are shown in Equation 5.16. A block diagram of the reduced order model is shown in 5.3. This shows the new model, which contains only a single state variables, with the two eliminated state variables being represented by algebraic equations.
156 ˙ ˙ ˙ ˙ ˙ ˙ δX˙ = ∂X1 δX + ∂X1 ∂X1 ∂X1 ∂X1 ∂X1 δu (5.16a) ∂X1 ∂u1 ∂u2 ∂u3 ∂u4 ∂u5
δX˙ = −0.17 δX + 0.17 −335.8 0+ 24.18 0+ δu (5.16b)
Figure 5.3: Block Diagram of Reduced Order and Linearized EGRC Model
The model described by 5.3 is used to simulate a step response, which is then com- pared to the step response obtained from the original nonlinear EGRC thermal model.
The step input in exhaust temperature at the EGRC inlet is 110% of the equilibrium value and is shown in Figure 5.4. All other control inputs remain at their equilib- rium conditions for both models. The step response of both the orignal and reduced order model are shown in Figure 5.5. The step responses of each model are nearly identical. Small differences in temperature predictions do exist betwen the models, but the maximum of this error is less than 0.02◦. Additionally, the trends in the step responses of the two models are identical.
157 Exhaust Temperature at EGRC Inlet 255
250
245 C] o 240
235
230
225
220 Exhaust Inlet Temperature [ 215
210
205 0 50 100 150 Time [s]
Figure 5.4: Inlet Exhaust Temperature Step Input
Control-Oriented TMS Model
The remaining TMS submodels are linearized and combined to create the control- oriented TMS model. The model order reduction procedure previously described is also performed on the radiator thermal model. This model is first reduced from three lumps to a single lump. This reduces the model from nine states to three, with a separate node for the liquid, wall, and surface thermal dynamics. The states representing the wall and surface nodes are then replaced with algebraic equations, as was done for the EGRC thermal model. This results in a linear radiator thermal model consisting of only one state, instead of the original nine state model. Since the transmission thermal model is not coupled to the coolant circuit by means of the TOH
158 Simulation Results from Reduced Order and Full EGRC Model 106
105.9
105.8 C] o
105.7
Coolant−full model
Temperature [ Wall−full model 105.6 Exhaust−full model Coolant−reduced & linearized model Wall−reduced & linearized model 105.5 Exhaust−reduced & linearized model
105.4 50 60 70 80 90 100 Time [s]
Figure 5.5: Step Response of EGRC Thermal Model
when the vehicle is fully warmed-up, the thermal models of the transmission, TOH, and TOC are omitted from the control-oriented model. The remaining thermal models for the ETM and EOC, along with the CFN model, are linearized and included in the control-oriented mode, but no model order reduction is performed. It should be noted that the CFN model contains no states, as it consists only of a static look-up table.
However, the Matlab command ”linmod” was still used to produce a set of linear algebraic equations from this look-up table, so that the CFN could be represented by a set of state-space equations with no actual states. The CHC model is also omitted from the control-oriented TMS model, as the cabin heater is not used during the FTP driving cycle. Table 5.5 shows a summary of the reduction in state variables to form the control-oriented TMS model.
159 Table 5.5: Summary of TMS Model Order Reduction
Submodel Original Number of States Number of States in Reduced Model ETM 6 6 Radiator 9 1 EGRC 3 1 EOC 2 2 CFN 0 0 TTM 3 N/A TOC 2 N/A TOC 9 N/A CHC 6 N/A Total 40 10
Using the control-oriented TMS model, a Linear Quadratic Regulator (LQR) will be developed for closed-loop TMS control. LQR controllers use a user specified cost function to find the ideal control gains for each actuator at any given time. This technique works well for multi-variable systems because if the cost function used is designed properly, it will penalize the use of certain actuators in conditions in which it is not beneficial to use them. This allows the controller to specify the optimal control gains for disturbance rejection in a given situation.
The next step in designing this controller is to combine the state equations for all of the linearized submodels into a single state-space representation. A cost function will be determined and a LQR controller will be designed for a single linearization point.
This controller will then be tested within the operating range that the linearized model is valid for. The model will be linearized for more data points, until it has been linearized for the entire vehicle operating range of interest. This will be done using an iterative method, as shown in Figure 5.6. Using this method, the model
160 is linearized at a single point, and then used to conduct simulations at different operating conditions around the point at which it was linearized. The simulation results are compared to results from the full model and when the results from the control oriented model are no longer comparable to the results from the full model, the model is linearized at additional points. This process repeats until there are no areas left that the linearized model is not valid in. If done correctly, this will lead to the smallest number of linearization points possible, which will reduce controller development time.
Figure 5.6: Linearization Point Selection
At each linearzation point, a LQR will be designed. The seperate feedback gains for each linearization point will be incorporated into the controller, with switching as the vehicle changes operating zones. Smoothing factors will be applied to the gains during switching. This will lead to smooth controller operation. Once the controller is designed with appropriate feedback gains for the entire engine operating range of
161 interest, it will be tested in simulation. The controller will be refined and further tested experimentally.
162 References
[1] U.S. Energy Information Administration. 2011 International Energy Outlook, 2011.
[2] U.S. Energy Information Administration. Annual Energy Outlook 2012, 2012.
[3] Davis, S., Boundy, R., Diegel, S. 2011 Vehicle Technologies Market Report. Technical report, Oak Ridge National Laboratory, 2012.
[4] “Internal Report”. Center for Automotive Rearch, The Ohio State University, Columbus, Ohio.
[5] Keller, P., Wenzel, W., Becker, M., Roby, J. “Hybrid Coolant Pump with Electric and Mechanical Drive”. ATZ autotechnology, 2010.
[6] Diehl, P., Haubner, F., Klopstein, S., Koch, F. “Exhaust Heat Recovery System for Modern Cars”. SAE Technical Paper 2001-01-1020, 2001.
[7] Mori, M., Yagami, T., Oda, N., Hattori, M., Sorazawa, M., Haraguchi, T. “Cur- rent Possibilities of Thermoelectric Technology Relative to Fuel Economy”. SAE Technical Paper 2009-01-0170, 2009.
[8] Kuze, Y., Kobayashi, H., Ichinose, H., Otsuka, T. “Development of New Gen- eration Hybrid System (THS II)- Development of Toyota Coolant Heat Storage System”. SAE Technical Paper 2004-01-0643, 2004.
[9] Wurms, R., Jung, M., Adam, S., Dengler, S., Heiduk, T., Eiser, A. “Innovative Technologies in Current and Future TFSI Engines from Audi”. 20th Aachen Colloquium Automobile an Engine Technology, 2011.
[10] Choukroun, A., Chanfreau, M. “Automatic Control of Electronic Actuators for an Optimized Engine Cooling Thermal Management”. SAE Technical Paper 2001-01-1758, 2001.
[11] “Report on Vehicle Energy Analysis and Definition of the Pathways for the Development of the VEM”. The Ohio State University, 2012.
163 [12] Wagner, J., Ghone, M., Dawson, D., Marotta, E. “Coolant Flow Control Strate- gies for Automotive Thermal Management Systems”. SAE Technical Paper 2002- 01-0713, 2002.
[13] Setlur, P., Wagner, J., Dawson, D., Marotta, E. “An Advanced Engine Thermal Management System: Nonlinear Control and Test”. IEEE/ASME Transactions on Mechatronics, Vol. 10, No. 2, 2005.
[14] Agarwal, N. “Modeling, Validation and Analysis of an Advanced Thermal Mangement System for Conventional Powertrains”. Master’s thesis, The Ohio State University, 2012.
[15] “Heat Transfer Basics”. Washington University, www.cheresources.com, 2011.
[16] Canova, M., Laboe, K. “Powertrain Waste Heat Recovery: A Systems Approach to Maximize Drivetrain Efficiency”. In Internal Combustion Engine Division Spring Technical Conference, 2012.
[17] Heywood, J. Internal Combustion Engine Fundamentals. McGraw-Hill Book Company, Second edition, 1988.
[18] Hosaka, T., Hamazaki, M. “Development of the Variable Valve Timing and Lift (VTEC) Engine for the Honda NSX”. SAE Technical Paper 910008, 1991.
[19] Stan, C. “Future Trends in Spark Ignition Engines”. SAE Technical Paper 2001-01-085, 2001.
[20] Shahed, S., Bauer, K. “Parametric Studies of the Impact of Turbocharging on Gasoline Engine Downsizing”. SAE Technical Paper 2009-01-1472, 2009.
[21] Bandel, W., Fraidl, G., Kapus, P., Sikinger, H., Cowland, C. “The Turbocharged GDI Engine: Boosted Synergies for High Fuel Economy Plus Ultra-low Emis- sion”. SAE Technical Paper 2006-01-1266, 2006.
[22] Dhand, A., Cho, B., Walker, A., Muncey, A., Kok, D., Karden, E., Hochkirchen, T. “Stop-Start Micro Hybrid: An Estimation of Automatic Engine Stop Duration in Real World Usage”. SAE Technical Paper 2009-01-1336, 2009.
[23] Vinodh, B. “Technology for Cylinder Deactivation”. SAE Technical Paper 2005- 01-0077, 2005.
[24] Pagerit, S., Sharer, P., Rousseau, A. “Fuel Economy Sensitivity to Vehicle Mass for Advanced Vehicle Powertrains”. SAE Technical Paper 2006-01-0665, 2006.
[25] Cuddy, M., Wipke, K. “Analysis of the Fuel Economy Benefit of Drivetrain Hybridization”. SAE Technical Paper 970289, 1997.
164 [26] “Secretary Chu Announces $187 Million to Improve Vehicle Efficiency for Heavy- Duty Trucks and Passenger Vehicles”, Jan 2010.
[27] Reese, R. II. “A MultiAir-MultiFuel Approach to Enhancing Engine System Efficiency”. 2011 DOE Vehicle Technologies Program Annual Merit Review and Peer Evaluation Meeting, 2011.
[28] Allen, D., Lasecki, M. “Thermal Management Evolution and Controlled Coolant Flow”. SAE Technical Paper 2001-01-1732, 2001.
[29] Burke, R., Brace, C. “The Effects of Engine Thermal Conditions on Performance, Emissions and Fuel Consumption”. SAE Technical Paper 2010-01-0802, 2010.
[30] Perset, D., Jouannet, B. “Simulation of a Cooling Loop for a Variable Speed Fan System”. SAE Technical Paper 1999-01-0576, 1999.
[31] Chanfreau, M., Gessier, B., Farkh, A., Geels, P. “The Need for an Electrical Water Valve in a THErmal Management Intelligent System (TMEMIS)”. SAE Technical Paper 2003-01-0274, 2003.
[32] El-Sharkawy, A., Kamrad, J., Lounsberry, T., Baker, G., Rahman, S. “Evalua- tion of Impact of Active Grille Shutter on Vehicle Thermal Management”. SAE Technical Paper 2011-01-1172, 2011.
[33] Wagner, J., Srinivasan, V., Dawson, D., Marotta, E. “Smart Thermostat and Coolant Pump Control for Engine Thermal Management Systems”. SAE Tech- nical Paper 2003-01-0272, 2003.
[34] Coggiola, E., Dessale, B., Moreau, S., Broberg, R., Bakir, F. “CFD Based Design for Automotive Engine Cooling Fan Systems”. SAE Technical Paper 980427, 1998.
[35] Incropera, F., Dewitt, D., Bergman, T., Lavine, A. Introduction to Heat Transfer. Number ISBN: 978-0-471-45727-5. John Wiley & Sons, Inc., fifth edition, 2007.
[36] Agarwal, N., Chiara, F., Canova, M. “Control-Oriented Modelling of an Auto- motive Thermal Management System”. International Federation for Automatic Control, 2012.
[37] Grimm, B. “Modeling and Analysis of Crankshaft Energy Harvesting for Vehicle Fuel Economy Improvement”. Master’s thesis, The Ohio State University, 2012.
[38] Owen, R. “Modelling, Analysis, and Open-Loop Control of an Exhaust Heat Recovery System for Automotive Internal Combustion Engine”. Master’s thesis, The Ohio State University, 2011.
165 [39] Scott, T. “Modeling Compact Heat Exchanger for HVAC Applications”. 2003.
[40] Scott, T. “Exhaust Gas Heater Modeling and Simulation”. Chrysler Group LLC, 2011.
[41] Couch, J. “An ECMS-Based Controller for the Electrical System of a Passenger Vehicle”. Master’s thesis, The Ohio State University, 2013.
[42] Zhang, Q., Canova, M. “Lumped-Parameter Modeling of an Automotive Air Conditioning System for Energy Optimization and Management”. In ASME Dynamic Systems and Control Conference, 2013.
[43] EPA. “Detailed Test Information”. www.fueleconomy.gov/feg/fe test schedules, 2013.
[44] Schilders, W. “Introduction to Model Order Reduction”. Eindhoven University of Technology.
166