Feed-Forward Air-Fuel Ratio Control during Transient Operation of an Alternative Fueled Engine
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
Andrew Michael Garcia, B.S.
Graduate Program in Mechanical Engineering
The Ohio State University
2013
Master’s Examination Committee:
Dr. Shawn Midlam-Mohler, Advisor Dr. Giorgio Rizzoni c Copyright by
Andrew Michael Garcia
2013 Abstract
With the increasing government regulations for higher vehicle fuel economy and lower tailpipe emissions, today’s automotive engineers are pushed to develop advanced vehicle architectures. Further, due to the high prices of oil, the consumer market is demanding for more fuel efficient vehicles. To adapt to the increasing demands, automotive manufacturers have been investing in the research of advanced vehicle technologies. The work described in this thesis details the development of a method- ology to improve the feed-forward air-fuel ratio control during transient operation of an alternative fueled engine.
Due to transport delays between the induction of the air-fuel mixture into the cylinder and the reading of the combustion exhaust gases from the oxygen sensor, conventional feedback control cannot be accurately used in transient operation. Since the engine used in this thesis is port-fuel injected, the fuel injection command is made a discrete amount of time before the intake valve opening. This gives the fuel time to vaporize in the intake runner before being inducted. Therefore, in order to achieve stoichiometric combustion, the amount of inducted air will have to be determined a discrete amount of time into the future.
This work outlines the development of a control algorithm that improves the tran- sient air-fuel ratio control by predicting the intake manifold air pressure forward in
ii time. Using model-based calibration techniques and engine dynamometer data, an in- take manifold model was created. Coupling this model with a Forward Euler approx- imation, a predictive intake manifold pressure algorithm was developed. Adaptive models were implemented into the control algorithm to account for day-to-day vari- ations in engine operation as well as calibration errors in the intake manifold model.
The algorithm was verified in software validation with a mean value engine model and hardware validation in the engine dynamometer test cell. With the implementation of the predictive control algorithm, there was a vast improvement in air-fuel ratio con- trol performance over the engine’s previous control strategy. Oxygen sensor results showed a significant reduction in deviations from stoichiometric combustion, allowing the three-way catalyst to operate in its most efficient range. The research detailed in this thesis shows the effectiveness of using a model-based approach to air-fuel ratio control and the importance of adaptive algorithms for day-to-day changes in engine operation.
iii This thesis is dedicated to my parents for their endless love, patience, and support.
iv Acknowledgments
I would like to thank the Center for Automotive Research for providing access to an unparalleled faculty and facilities to support my research. I would especially like to thank my advisor, Dr. Shawn Midlam-Mohler for his guidance and support throughout my graduate experience. His never-ending enthusiasm and dedication toward teaching has been paramount to success in my research. I would also like to thank Dr. Giorgio Rizzoni for his invaluable advice and support for the EcoCAR 2 program. I would like to thank my fellow graduate students, whom are always willing to share their knowledge and assistance.
I would also like to thank the entire EcoCAR 2 team, their efforts in the de- sign, build, and validation of our team’s parallel-series plug-in hybrid electric vehicle
(PHEV) has been nothing short of inspiring. I would especially like to thank my fellow team leaders Katherine Bovee, Jason Ward, Matthew Yard, Matthew Organis- cak, Eric Gallo, Amanda Hyde, and David Walters for their knowledge, enthusiasm, and support.
Finally, I would like to thank the U.S. DOE Graduate Automotive Technology
Education (GATE) Center of Excellence for providing the funds and resources for the research in this thesis.
v Vita
July 6, 1989 ...... Born - Cleveland, Ohio
December, 2011 ...... B.S. Mechanical Engineering, The Ohio State University December, 2011 ...... Graduate Research Associate, Department of Mechanical and Aerospace Engineering, The Ohio State University
Publications
Research Publications
K. Bovee, A. Hyde, M. Yard, T. Trippel, M. Organiscak, A. Garcia, E. Gallo, M. Hornak, A. Palmer, J. Hendricks, S. Midlam-Mohler and G. Rizzoni “Design of a Parallel-Series PHEV for the EcoCAR 2 Competition”. SAE, 2012-01-1762.
Fields of Study
Major Field: Mechanical Engineering
vi Table of Contents
Page
Abstract...... ii
Dedication...... iv
Acknowledgments...... v
Vita...... vi
List of Tables...... ix
List of Figures...... xi
Nomenclature...... xv
1. Introduction...... 1
1.1 Motivation...... 1 1.2 EcoCAR 2 Competition...... 2 1.2.1 Ohio State University EcoCAR 2 Vehicle Architecture...3 1.3 Thesis Overview...... 4
2. Literature Review...... 7
2.1 Introduction...... 7 2.2 Air Dynamics...... 7 2.2.1 Throttle Modeling...... 9 2.2.2 Volumetric Efficiency...... 12 2.2.3 Intake Manifold Modeling...... 15 2.2.4 Air-Fuel Ratio Control...... 22 2.3 Honda R18A3 Engine...... 30 2.4 Tailpipe Emissions...... 33
vii 3. Experimental Description...... 36
3.1 Engine Instrumentation...... 36 3.2 Data Acquisition System...... 37 3.3 GM LE5 Mean Value Engine Model...... 40
4. Control Algorithm Development...... 42
4.1 Introduction...... 42 4.2 Control Algorithm Description...... 42 4.3 Summary...... 47
5. Intake Manifold Modeling...... 50
5.1 Introduction...... 50 5.2 Throttle Model...... 50 5.3 Volumetric Efficiency Model...... 57 5.4 Intake Manifold Pressure Model...... 61 5.5 Summary...... 64
6. Control Algorithm Validation...... 66
6.1 Introduction...... 66 6.2 Software Validation...... 66 6.3 Hardware Validation...... 76
6.3.1 Recalibrating Ve Map...... 78 6.3.2 Implementation of Adaptive Control Strategies...... 83 6.3.3 AFR Results...... 101 6.4 Summary...... 115
7. Conclusions and Future Work...... 117
7.1 Conclusions...... 117 7.2 Future Work...... 118
Bibliography...... 120
Appendices 122
A. Intake Manifold Model Subsystems...... 122
viii B. Adaptive Volumetric Efficiency Table Subsysems...... 126
ix List of Tables
Table Page
2.1 Sensor specifications [1]...... 24
2.2 Engine specifications [15]...... 31
3.1 Relevant instrumented sensors on engine...... 37
4.1 Constant engine parameters...... 46
5.1 Model MAP Sensitivity Analysis...... 64
6.1 MAP prediction performance...... 77
6.2 Comparison among proposed 2-d lookup functions...... 80
6.3 Comparison between original and recalibrated Ve maps...... 83
6.4 Error improvement using PI control...... 91
6.5 Error improvement using Ve adaptive control...... 100
6.6 Closed-loop AFR results, area deviation...... 104
6.7 Closed-loop AFR results, maximum % deviation...... 104
6.8 Comparison of closed-loop AFR results for area deviation with steady- state algorithm recalibration...... 108
6.9 Comparison of closed-loop AFR results for maximum % deviation with steady-state algorithm recalibration...... 109
x 6.10 Open-loop AFR results, area deviation...... 112
6.11 Open-loop AFR results, maximum % deviation...... 112
6.12 Test operating points for open-loop AFR control performance comparison113
xi List of Figures
Figure Page
1.1 Ohio State University EcoCAR 2 vehicle architecture...... 4
2.1 Three-way catalyst conversion efficiency [12]...... 8
2.2 Variation in flow rate past a throttle [9]...... 9
2.3 Isenthalpic flow model of a throttle [12]...... 11
2.4 Affects of different flow phenomena on volumetric efficiency [8].... 14
2.5 Volumetric efficiency map of a 1.8L 4cyl E85 engine...... 16
2.6 Model classification for an intake manifold [8]...... 17
2.7 MAF and MAP reading from throttle transient at 1200 RPM..... 21
2.8 Injection and transport delays [1]...... 23
2.9 2006 Honda R18A3 engine [15]...... 31
2.10 Valve lift profiles of different cam settings [15]...... 32
2.11 Intake manifold variable length runner [15]...... 33
2.12 Emissions concentrations against air/fuel ratio [9]...... 34
3.1 Intake side of engine...... 38
3.2 Exhaust side of engine...... 38
xii 3.3 Engine test setup [6]...... 40
3.4 0-D Mean-value engine model for GM LE5 engine...... 41
4.1 Control algorithm timing...... 43
4.2 MAP prediction control algorithm...... 45
4.3 MAP prediction SIMULINK model...... 47
4.4 MAP prediction Stateflow diagram...... 48
5.1 Throttle affective area map, raw data...... 51
5.2 Throttle affective area map, function fit...... 52
5.3 Model and experimental CdA value comparison...... 54
5.4 Calculated and actual MAF value comparison...... 55
5.5 MAF during throttle transient event...... 56
5.6 Volumetric efficiency map, raw data...... 58
5.7 Model and experimental VE value comparison...... 60
5.8 Model and experimental MAF value comparison...... 60
5.9 SIMULINK diagram of intake manifold model...... 62
5.10 MAP during throttle transient event...... 63
6.1 MAP prediction SIMULINK implementation in MVEM...... 67
6.2 MVEM simulation results at varying engine operating points..... 69
6.3 MVEM simulation results for throttle transient...... 70
6.4 MVEM simulation results for throttle transient, with throttle rate limiter 72
6.5 MVEM normalized error vs. iteration number...... 74
xiii 6.6 MVEM simulation time vs. iteration number...... 74
6.7 MAP prediction performance results, 1200 RPM...... 77
6.8 CdA based Ve 2-d lookup function...... 81
6.9 MAF error between throttle and induction mass air flow...... 81
6.10 Comparison between original and recalibrated Ve maps at 1200 RPM 82
6.11 SIMULINK implementation of adaptive PI model...... 85
6.12 SIMULINK implementation of engine steady-state detection..... 87
6.13 Steady-state detection for random transients...... 88
6.14 MAP prediction SIMULINK diagram with adaptive PI model.... 89
6.15 Improvement using adaptive PI model at 1200 RPM...... 90
6.16 MAP prediction SIMULINK diagram with adaptive Ve table..... 93
6.17 Ve table correction...... 95
6.18 Layout of Ve adaptation zones...... 96
6.19 Improvement using adaptive Ve table at 1200 RPM...... 98
6.20 Day-to-day variability in Ve multiplier...... 101
6.21 AFR deviation from throttle tip-in, 1200 RPM, closed-loop...... 102
6.22 AFR deviation from throttle tip-out, 1200 RPM, closed-loop..... 102
6.23 Filter change comparison...... 106
6.24 Steady-state detection comparison...... 108
6.25 Open-loop AFR control performance comparison, 1200 RPM, 30-70 kPa transient...... 110
xiv 6.26 Method of calculating metrics for open-loop results...... 111
6.27 Open-loop AFR control performance comparison, area deviation... 114
6.28 Open-loop AFR control performance comparison, max % deviation. 114
A.1 Subsystem: throttle model...... 123
A.2 Subsystem: throttle model > flow restriction...... 123
A.3 Subsystem: throttle model > flow restriction > unchoked flow... 124
A.4 Subsystem: throttle model > flow restriction > choked flow..... 124
A.5 Subsystem: Ve model...... 125
A.6 Subsystem: Ve model > Ve to MAF...... 125
B.1 VE Lookup Table...... 127
B.2 VE Lookup Table > Zone Based Correction Control...... 128
B.3 VE Lookup Table > Zone Based Correction Control > Zone Deter- mination...... 129
B.4 VE Lookup Table > Zone Based Correction Control > Zone Deter- mination > X Zone Determination...... 130
xv Nomenclature
∆t time step
m˙ a,cyl mass air flow into cylinder
m˙ a,th mass air flow through throttle
ηv volumetric efficiency
γ specific heat ratio of air
λ relative air to fuel ratio
ρa density of air
Cd coefficient of discharge
CdA effective flow area
HC hydrocarbons
ma,IM mass of air in intake manifold
N engine speed
pr pressure ratio of intake manifold air pressure to the ambient air pressure
pa,IM intake manifold pressure
xvi pamb ambient air pressure
R universal gas constant
Ta,IM intake manifold temperature
Tamb ambient air temperature
Vd total engine cylinder displacement volume
Ve volumetric efficiency
VIM intake manifold volume
A throttle plate open area
AFR air to fuel ratio
APC air per cylinder
CAD crank angle degrees
CNG compressed natural gas
DOE Design of experiment
EGR exhaust gas recirculation
HEV hybrid electric vehicle
IAT intake air temperature
IVO intake valve opening
xvii MAF manifold air flow
MAP manifold absolute pressure
MRB multiquadratic radial basis
MVM mean value model
PFI port fuel injection
PHEV plug-in hybrid electric vehicle
RMSE root-mean-square error
RTD resistance temperature device
xviii Chapter 1: Introduction
1.1 Motivation
With the increasing government regulations for higher vehicle fuel economy and lower tailpipe emissions, today’s automotive engineers are pushed to develop advanced technology vehicles. Further, due to the high prices of oil, the consumer market is demanding for more fuel efficient vehicles.
To adapt to the increasing demands, automotive manufacturers have been in- vesting in the research of advanced technologies. These include engine technologies such as the use of variable valve timing or cylinder deactivation. Advances in vehi- cle aerodynamics have also been made with active grill shutters and improved body shapes to help reduce drag coefficients. Also, to help reduce oil dependence, the use of renewable sources such as ethanol and biodiesel has been utilized to fuel internal combustion engines.
With the introduction of hybrid vehicles in the late 1990s, the automotive in- dustry has since been able to dramatically increase the fuel economy and decrease tailpipe emissions. These vehicles include hybrid electric vehicles (HEV) and plug-in hybrid electric vehicles (PHEV). The vast improvement from hybrids comes from the combination of the high efficiencies of electric propulsion with the advanced technolo- gies of internal combustions engines. Today, these technologies are being researched
1 by every major automotive manufacturer. As advanced technology vehicles become more ubiquitous in today’s world, it is crucial to start educating future automotive engineers for the rigorous design process of these vehicles.
1.2 EcoCAR 2 Competition
EcoCAR 2 is a three-year competition designed to offer an unparalleled real- world experience aimed to educate the next generation of automotive engineers. This competition, headline-sponsored by the United States Department of Energy and
General Motors, is a continuation of a long series of Advanced Vehicle Technology
Competitions. The goal of EcoCAR 2 is to reduce the environmental impact of a
2013 Chevrolet Malibu without compromising the performance, safety, and consumer acceptability of the vehicle. This requires the 15 competing universities from across
North America to design, optimize, and build a new powertrain to create a fully functional prototype by the end of the third year.
The first year of the competition is geared towards the initial design and simula- tion of the future vehicle. Through the use of vehicle energy consumption simulations, hardware-in-the-loop and software-in-the-loop applications, and computer-aided de- sign, teams are able to begin the intense vehicle development process. The goal of year one is to develop vehicle technical specifications, select major powertrain components, complete the initial packaging strategies, and start designing the control strategies.
In the second year of the competition, the process of building a mule vehicle begins.
This involves a full teardown of the stock vehicle and integration of the powertrain components. By the end of year two, a fully functional mule vehicle is expected, which will be evaluated in a series of static and dynamic events. In year three, the teams
2 will refine the mechanical, electrical and control systems of their vehicle to produce
a near-production quality vehicle. The prototype vehicles will then be evaluated on
a multitude of metrics including: fuel economy, emissions, drivability, acceleration,
braking, and consumer acceptability.
1.2.1 Ohio State University EcoCAR 2 Vehicle Architecture
For the EcoCAR 2 competition, the Ohio State University team is designing a
parallel-series plug-in hybrid electric vehicle that is capable of 50 miles of all-electric
range. The vehicle is designed to drastically reduce fuel consumption with a projected
utility factor weighted fuel economy of 75 miles per gallon gasoline equivalent, while
meeting Tier II Bin 5 emissions standards. Several of the key features of the vehicle
include:
• Multi-mode operation to allow operation in series, parallel, or all-electric op-
eration. An on-board supervisory controller optimizes the switch among the
different modes in real-time.
• A high-efficiency E85 internal combustion engine, that is able to operate with
greater than 40% brake thermal efficiency.
• An automated manual transmission, developed completely by the team.
• Aggressive electric operation which includes high all-electric range and high
all-electric performance.
The overall architecture of the vehicle is shown in Figure 1.1. The front powertrain is consists of a Honda 1.8L E85 engine coupled to a Parker Hannifin electric machine.
The power is sent to the wheels through a 6-speed automated manual transmission.
3 Figure 1.1: Ohio State University EcoCAR 2 vehicle architecture
The rear powertrain includes a Parker Hannifin electric machine coupled to a Borg-
Warner single speed gearbox. The battery pack is an A123 Systems 18.9 kW-hr, 340V battery pack.
1.3 Thesis Overview
The research conducted in thesis will help improve the emissions and overall per- formance of the 1.8L alternative fueled engine used in the Ohio State EcoCAR 2 vehicle. This work outlines the development of a control algorithm that improves the transient air-fuel ratio control by predicting the intake manifold pressure forward in time. Using model-based calibration techniques and design of experiment engine dynamometer data, an intake manifold model was created and implemented into the
4 control algorithm. The algorithm was verified using both software and hardware val-
idation. A mean value engine model was used in the early stages of the development
process, and an engine dynamometer test cell was used as the control algorithm ma-
tured. The effectiveness of the intake manifold prediction software was determined
through simulation and engine dynamometer testing.
The organization of this thesis is as follows:
Chapter 2: Literature Review
Chapter 2 provides background information on the modeling an engine’s intake
manifold dynamics, common solutions to air-fuel ratio control, and tailpipe
emissions. The specifications for the engine used in this research are also in-
cluded.
Chapter 3: Experimental Description
Chapter 3 discusses the engine instrumentation, data acquisition systems, and
mean value engine model used in this thesis.
Chapter 4: Control Algorithm Development
Chapter 4 outlines the control algorithm for predicting the intake manifold
pressure.
Chapter 5: Intake Manifold Modeling
Chapter 5 discusses the process of calibrating the intake manifold dynamics
model. This includes modeling the throttle air flow and pumping efficiency of
the engine.
5 Chapter 6: Control Algorithm Validation
Chapter 6 details the process of validating the intake manifold pressure pre-
diction control algorithm; this includes both software validation and hardware
validation. Additionally, adaptive methods to improve the control algorithm
performance are described.
Chapter 7: Conclusions and Future Work
Chapter 7 summarizes the work presented in this thesis and outlines work that
can be completed in the future.
6 Chapter 2: Literature Review
2.1 Introduction
The following sections provide background information regarding air flow modeling of an engine’s intake system as well as control strategies used in this thesis.
2.2 Air Dynamics
In order to minimize emissions in the tailpipe exhaust gasses, an engine typically must achieve a stoichiometric air to fuel ratio (AFR). This is because the three-way catalyst operates at its best efficiency within a narrow band around the stoichiometric
AFR (λ = 1), as seen in Figure 2.1. If the engine runs under lean conditions (λ
>1), then the reduction of nitrogen oxides is reduced. If the engine runs under rich conditions (λ <1), then the reduction of hydrocarbons and carbon monoxide begins to decrease. These conversion efficiencies hold true only if a three-way catalyst is used. There exists other types of catalysts such as the NOx trap catalyst, which is used on lean-burn gasoline engines. This type of catalyst is employed to provide the same efficiencies as the three-way catalyst but at a slightly leaner operating point than stoichiometric combustion [11].
The importance of maintaining the correct AFR results in the need for electronic control systems coupled with the appropriate sensors to obtain information needed to
7 Figure 2.1: Three-way catalyst conversion efficiency [12]
make the correct control actions. Under steady-state conditions, the engine’s control algorithm can achieve stoichiometric AFR with high accuracy through the use of the lambda sensor and feedback control. A lambda sensor is a sensor that can measure the net oxygen content of the exhaust gas which can be used to determine the current
AFR. But, due to transport delays between the lambda sensor and the ECU as well as sensor response delays, feedback control cannot be accurately used in transient operation.
Under transient conditions, a stoichiometric AFR is difficult to achieve as a fuel request typically must be made before the intake stroke begins; for the engine dis- cussed in this paper, the fuel request must be made 700 crank angle degrees (CAD) before the intake stroke. This is to ensure that the fuel has maximum time to va- porize in the intake runner before it enters the combustion chamber. If the fuel is not vaporized, an emissions spike will occur. In order to achieve stoichiometric AFR during transient conditions, a feed forward control algorithm that is able to predict
8 Figure 2.2: Variation in flow rate past a throttle [9]
the amount of air mass entering the combustion chamber a short amount of time in the future is required.
2.2.1 Throttle Modeling
In an engine’s air induction system, the throttle is responsible for metering the amount of air that enters into the intake manifold. By metering the air, the throttle is able to control the torque output of an engine in relation to the demand from the driver’s accelerator pedal input. When the vehicle is under typical road-load conditions, the total pressure loss across the throttle plate can exceed 90 percent [9].
9 Figure 2.2 shows the relationship among air flow rate, throttle angle, intake man- ifold pressure, and engine speed of a typical production engine. It can be seen that at a given engine speed, an increase in throttle position will result in a higher intake manifold pressure and air flow rate (assuming the cam shaft timing is fixed and EGR is held constant). This figure also shows the non-linear relationship among all the pa- rameters. At lower throttle positions, a small increase in throttle position will result in a significant increase in air flow rate. At higher throttle positions, a small increase in throttle position will result in a relatively insignificant increase in air flow rate.
When the engine is in transient operation, the mass air flow rate into the cylinders cannot be measured using a mass air flow (MAF) sensor because the sensor is typically located upstream of the throttle body. In this location, the intake manifold dynamics are completely neglected, resulting in errors for the mass flow rate into the cylinders.
Instead, the mass air flow is calculated using information from the engine’s throttle position sensor, manifold absolute pressure (MAP) sensor, and intake air temperature sensor.
The air mass flow rate through the throttle valve can be calculated using standard orifice equations for compressible fluid flow [9]. These equations make two important assumptions. One assumption is that no losses occur in the accelerating portion of flow up to the narrowest point; all the potential energy stored in the flow is converted to kinetic energy, isentropically [12]. The second assumption is that after the narrowest point, the flow is fully turbulent and all the kinetic energy is dissipated into thermal energy [12]. Figure 2.3 shows the isenthalpic flow through the throttle valve.
Based on the thermodynamic relationships of isentropic expansion, the following equations can be derived to calculate mass air flow through the throttle valve:
10 Figure 2.3: Isenthalpic flow model of a throttle [12]
v 1 " γ−1 # γ u γ CdApamb pa,IM u 2γ pa,IM m˙ a,th = √ · · t 1 − (2.1) RTamb pamb γ − 1 pamb
s γ+1 CdApamb √ 2 γ−1 m˙ a,th = √ · γ · (2.2) RTamb γ + 1
γ 2 γ−1 p = = 0.528 (for γ = 1.4) (2.3) cr γ + 1 where Cd is the coefficient of discharge which indicates the losses due to turbulent friction and flow contraction, A is the throttle plate open area, pamb and Tamb are the upstream pressure and temperature, pa,IM is the downstream pressure in the intake manifold, R is the gas constant, and γ is the specific heat ratio. For convenience, the coefficient of discharge and throttle plate open area variables can be lumped into one variable parameter called the effective flow area (CdA). The effective flow area can be calculated using steady-state experimental data and Eq. 2.1 and 2.2.
11 Equation 2.1 is used for pressure ratios across the throttle (pa,IM /pamb) greater than or equal to the critical pressure value which indicates unchoked flow. Equation
2.2 is used for pressure ratios across the throttle less than the critical pressure value which indicates choked flow. Equation 2.3 shows how to calculate the critical pressure value. When the flow is choked, the flow is no longer dependent on the intake manifold pressure or engine speed. Looking at Figure 2.2, it can be seen that below the critical pressure value (40.1 cmHg) the air flow rate is constant.
2.2.2 Volumetric Efficiency
The volumetric efficiency (Ve) is a parameter that measures the overall effective- ness of a four-stroke engine’s induction process. It is defined as the ratio of the actual mass of the inducted charge to the ideal mass of air that would fill the capacity of the cylinder based on either ambient or intake manifold conditions. The equation for volumetric efficiency is shown in Eq. 2.4.
ma,inducted ηv = (2.4) ma,ideal where:
ma,ideal = ρaVd (2.5)
The ideal mass of air can be calculated by multiplying the density of air, ρa, and the cylinder displacement volume, shown in Eq. 2.5. This mass can be defined in two different ways: with respect to ambient conditions or with respect to intake manifold conditions [9]. If the atmospheric air density is used, then the calculated volumetric efficiency represents the pumping performance across the entire inlet system. The
12 inlet system includes the air filter, airbox, throttle, manifold, runners, ports, and valves. If the air density of the intake manifold is used, then the calculated volumetric efficiency represents the pumping performance of the inlet ports, runners, and valves only. The typical maximum values of volumetric efficiency for naturally aspirated engines are between 80 and 90 percent [9].
An alternate equation can be used to calculate volumetric efficiency. It is defined as the ratio of the volume flow rate of air into the engine’s intake system to the rate in which volume is displaced by the piston, shown in Eq. 2.6. This equation can be rewritten via the ideal gas law, shown in Eq. 2.7. Equation 2.7 is also known as the volumetric efficiency equation.
2m ˙ a ηv = (2.6) ρaVdN
2m ˙ aRT ηv = (2.7) pa,IM VdN
Conditions that Affect Volumetric Efficiency
Volumetric efficiency is dependent on the complex interactions of many factors inherent to the fuel, engine design, and engine operating conditions. Several of the factors are listed below [9]:
• Fuel type, fuel/air ratio, fraction of fuel vaporized in the intake system, and
fuel heat of vaporization
• Mixture temperature as influenced by heat transfer
• Ratio of exhaust to inlet manifold pressures
13 Figure 2.4: Affects of different flow phenomena on volumetric efficiency [8]
• Engine speed
• Intake and exhaust manifold and port design
• Intake and exhaust valve geometry, size, lift, and timings
These factors can be examined as quasi-steady affects. Therefore, they can be consid- ered either independent of engine speed or can be described in terms of mean engine speed. Figure 2.4 shows how these factors affect volumetric efficiency as a function of engine speed.
14 Model Calibration
As described previously, the volumetric efficiency of an engine is the result of many complex interactions within the system. Due to this complexity, the most practical way of determining the volumetric efficiency is through calibration data. This can be achieved by using the volumetric efficiency equation, Eq. 2.7, coupled with engine steady-state dynamometer data.
To create a complete map that characterizes the volumetric efficiency of an engine, a wide range of operating points is tested. At each operating point, steady-state data is collected, including the MAF, intake air temperature (IAT), and engine speed data.
Since the data is collected in steady-state, the MAF sensor provides a relatively accurate reading of the flowrate of inducted air. Using this data, the volumetric efficiency at each operating point can be calculated. Combining all the operating points will form a volumetric efficiency map that can be used to calculate the amount of air entering the engine’s cylinders. Figure 2.5 shows the volumetric efficiency map of the engine utilized in this paper, the map was created using the procedure described above.
2.2.3 Intake Manifold Modeling
The role of an intake manifold is to supply a fresh mixture of fuel and air to the engine cylinders. An intake manifold usually consists of a main plenum with individual runners that lead to each cylinder. The inlet of the plenum is bolted to the throttle body. The intake manifold geometry is designed to be able to ensure a proper charge delivery to all cylinders, maximize the amount of charge, and optimize the charge mixing and combustion. Due to the suction of the pistons during the intake
15 100
80
60
40
20
Volumetric Efficiency [%] 0 100 5000 50 4000 3000 2000 0 1000 MAP [kPa] Engine Speed [RPM]
Figure 2.5: Volumetric efficiency map of a 1.8L 4cyl E85 engine
stroke of an engine cycle and the presence of a throttle plate, the intake manifold is typically in partial vacuum. At wide open throttle (WOT) the plenum usually experiences a pressure of about 95 kPa, while at idling conditions the pressure is about 30 kPa [8].
In order to keep the engine operating at stoichiometric conditions, the air being inducted into the engine cylinders must be accurately represented. With a known amount of inducted air, the correct amount of fuel can be injected. To achieve this, a model of the intake manifold can be created to understand the dynamics of how air enters and exits the plenum and runners.
16 Figure 2.6: Model classification for an intake manifold [8]
Levels of Modeling
When modeling an engine component, such as the intake manifold, the fundamen- tal choice has to be made for what kind of model accuracy and fidelity is needed. Thus, the desired balance of both accuracy and fidelity versus computation time governs the appropriate model structure [7]. The different levels of modeling an intake manifold can generally be classified into three types: three-dimensional, one-dimensional, and zero-dimensional. In general, as the model fidelity increases, the required compu- tation time increases [2]. Further, these different levels of modeling require varying amounts of empirical data and model calibration effort to be able to build the model
[3].
17 Thee-dimensional models, often associated with computational fluid dynamics models, are studied not only in the three spatial dimensions but also in the time dimension. As a result of analyzing the system in four dimensions, a very high reso- lution study of the system dynamics can be studied. This fidelity allows the analysis of the 3D charge motion in the intake system including turbulent flow, dissipation, and
flow across each runner. While this level of modeling results in the greatest accuracy and bandwidth, it is the most computationally intensive method. Thus, this method is not practical in real-time applications and is reserved for design optimization [8].
The one-dimensional model simplifies the previous method by removing two spa- tial dimensions. Therefore, it is assumed that the state variables of the system only vary in respect to one spatial dimension and time. The reduction in analyzed dimen- sions reduces the computational intensity, but keeps a relatively high bandwidth and small discretization length. This level of modeling allows the analysis of wave propa- gation which can facilitate in the tuning of an intake manifold. The zero-dimensional model further simplifies the previously described methods by not considering any spa- tial variation in the system’s state variables. It is assumed that the thermodynamic properties are uniformly distributed. These models are also referred to as mean value models (MVM). This method can provide a lumped-parameter model that accurately describes the filling and emptying of a system [8].
The comparison of the different levels of modeling and their associated bandwidths and discretization lengths can be seen in Figure 2.6. For applications that require high fidelity such as flow junction design, multi-dimensional models are the most appropriate. But, for control system design and optimization, the one and zero- dimensional models are more often used. This generalization can be attributed to the
18 lower order models exhibiting a more simplified model structure and lower required
computational effort [7].
Filling and Emptying Model
Using the filling and emptying model, a simple manifold model can be created that
can portray the complex phenomena within an actual intake manifold with relatively
high accuracy. Since the intake manifold dynamics are a large contribution to the
overall engine dynamics, it will be considered as a mass and energy accumulator to
capture the filling and emptying dynamics [8]. Several assumptions are made in this
model:
• At any given time, the pressure and temperature inside the intake manifold is
uniform
• The flow through the engine is constant
• All gaseous fluids follow the ideal gas law
Using the continuity equation for the air flow in and out of the intake manifold the following dynamic equation can be derived:
dm a,IM =m ˙ − Σm ˙ (2.8) dt a,th a,cyl where ma,IM is the mass of air in the intake manifold,m ˙ a,th andm ˙ a,cyl are the mass air flows through the throttle and into the cylinders. Using the ideal gas law and the mass of air in the intake manifold the following equation can be derived:
VIM ma,IM = pa,IM (2.9) RairTa,IM 19 By taking the derivative of Eq. 2.9 and combining it with Eq. 2.8 gives:
dpa,IM RairTa,IM = [m ˙ a,th − Σm ˙ a,cyl] (2.10) dt VIM This equation assumes that there is no rapid change in the intake manifold temper- ature (dTa,IM /dt = 0). The total air flow into each of the engine’s cylinders can be analyzed by a quasi-steady approximation using the speed density equation shown in
Eq. 2.11.
p V N m˙ = η a,IM d (2.11) a v 2RT
Substituting the speed density equation into Eq. 2.10 gives:
dpa,IM ηvVdN RairTa,IM + pa,IM =m ˙ a,th (2.12) dt 2VIM VIM where the mass air flow through the throttle can be determined using either Eq. 2.1
or 2.2, depending on whether the air flow is choked or not. It can be seen that Eq.
2.12 is a first order equation for pa,IM with a time constant that is reliant on the
engine speed and volumetric efficiency. The equation for the time constant is shown
in Eq. 2.13. It can be seen that as either the engine speed or volumetric efficiency
increase, the intake manifold pressure state response time decreases. A more in-
depth derivation of this first-order equation can be found in [8]. Figure 2.7 shows the
response from the MAF and MAP sensors to a throttle transient. The MAF sensor
reading represents the change of air flow into the intake manifold due to the sudden
change in throttle position. It can be seen that the sudden fluctuations in the mass
air flow are damped out in the manifold air pressure reading. The data in Figure 2.7
20 120 120 MAF*10 [g/s] 110 110 MAP [kPa]
100 100 90 90 80 80 70 70 Amplitude 60 Amplitude 60 50
40 50
30 MAF*10 [g/s] 40 MAP [kPa] 20 30 13 14 15 16 17 18 29 30 31 32 33 34 Time [s] Time [s] (a) Tip in (b) Tip out
Figure 2.7: MAF and MAP reading from throttle transient at 1200 RPM
was taken at an engine speed of 1200 RPM; with a relatively low engine speed, the
time constant is longer.
2V τ = IM (2.13) ηvVdN The filling and emptying model is very useful in analyzing the pressure variations due to changing load conditions. While this model can portray the complex interac- tions concerning the intake manifold with relatively high accuracy, there are several limitations. The model requires very accurate representations of empirical parameters such as volumetric efficiency (Ve) and the throttle effective flow area (CdA). Also, due to the relatively low bandwidth, the equation provides no insight into the pressure
fluctuations due to individual cylinder induction events. Other events that are not
21 factored into the model include manifold temperature, backflow of exhaust gases into
the intake manifold, and the presence of exhaust gas recirculation (EGR) [9], [8].
2.2.4 Air-Fuel Ratio Control
With the ever-tightening standards for vehicle exhaust emissions, the AFR control
problem has been a topic of high interest. The invention of the three-way catalyst
has been able to significantly reduce tailpipe emissions. But, in order for the catalyst
to operate at its best efficiency the engine must operate within a very narrow band
around the fuel’s stoichiometric AFR as seen in Figure 2.1. The AFR can be described
as the relative air-fuel ratio, λ:
(A/F ) λ = actual (2.14) (A/F )stoich
where (A/F )stoich is the ratio of air to fuel which achieves stoichiometric combustion.
When (λ = 1), the mixture is at stoichiometric proportions. For (λ > 1), the mix-
ture is fuel-lean, meaning that there is more air than needed in the mixture. For
(λ < 1), the mixture is fuel-rich, or the mixture contains more fuel than needed for stoichiometric combustion [9].
Conventional AFR control consists of static look-up tables to determine fueling decisions, with feedback control from a lambda sensor. A lambda sensor measures the net oxygen content of the exhaust gas which can be used to determine the current relative AFR. With feedback control, conventional AFR control can achieve high accuracy under steady-state conditions. But, due to the time delays inherent to engine operation, the response time of conventional AFR control is too long for transient engine operation. These delays are due to the dynamic nature of the air and fuel flows,
22 Figure 2.8: Injection and transport delays [1]
low-pass characteristics of sensors, and the transport delay for the charge mixture to cross the engine and be measured by the lambda sensors [1]. For engines that use a three-way catalyst, high bandwidth transient AFR control is necessary in order to achieve the highest conversion efficiency and to remain compliant with the industry’s emissions standards [14].
Figure 2.8 shows a graphical representation of the injection delay and lambda sensor feedback transport delay. The injection delay is time from when the engine electronic control unit (ECU) receives sensor data and when the air-fuel mixture is inducted into the cylinder. This includes the computation duration for one step of the AFR control strategy, injection duration, and injection timing and in the case of port fuel injected (PFI) engines, fuel dynamics. For PFI engines, the fuel is injected
23 Table 2.1: Sensor specifications [1]
Sensor type Accuracy Response time Manifold absolute pressure (MAP) ±1% 1 ms Mass air flow (MAF) ±2% 1 - 10 sec Throttle position ±3% in stationary flows 50 ms - 0.5 sec Exhaust gas oxygen 1 - 6% 50 ms Universal exhaust gas oxygen 1 - 6% > 50 ms
into the take port a short amount of time before the intake valve is opened. This is done to give the fuel the maximum amount of time to vaporize before being inducted into the cylinder. After the fuel is injected into the intake port, a fraction of that fuel evaporates while the rest of the fuel forms a liquid film on the intake manifold wall. A certain amount of the fuel in the film will evaporate in time. This mass flux into and out of the film creates fueling dynamics that add delays in the injection commands.
This delay is especially prevalent when in the engine block is cold. The transport delay is the time between the induction of the air-fuel mixture and the reading of the lambda sensor signal by the engine ECU. With conventional AFR control strategies, no control action can be taken until both the injection and transport delay have elapsed, significantly lowering the control system bandwidth [1].
There are several sensors that can be utilized the obtain information about the real-time air flow properties of the engine. Each sensor has its own characteristics for accuracy and response time. An AFR strategy should take into account these prop- erties and structure the control algorithm with appropriate sensors. Table 2.1 shows common sensors used in AFR control strategies and their characteristics. Clearly,
24 the MAF sensor’s response timing is significantly higher than any other sensor de- scribed. Despite the poor response time, this sensor still remains a popular method of determining the flow of air into the cylinders. In comparison, the MAP sensor and throttle position sensor are significantly faster. Using these two sensors, an accurate prediction of the mass air flow into the engine can be determined using the modeling methods described previously.
While using the MAP and throttle position sensor to calculate mass air flow into the cylinders is significatly more accurate than using a MAF sensor in transient operation, the injection delay is still not accounted for. The engine used in the research discussed in this paper utilizes port fuel injection. This signifies that the fuel is injected into the intake port a small amount of time prior to the intake valve opening (IVO). For this engine, the fuel is injected 700 CAD before IVO. So, in order to achieve stoichiometric combustion, the fuel injected has to be in stochiometric proportion to the air entering the cylinder 700 degrees after it was injected.
Forward Euler Scheme
To solve this issue, the intake manifold pressure can be predicted a discrete amount of time into the future using Eq. 2.12 and a Forward Euler scheme [1]. Since the engine’s ECU is a digital controller, a discrete form of the Forward Euler method is used. A general form is shown in Eq. 2.15,
dy y (t + ∆t) − y(t) (t) ≈ (2.15) dt ∆t
25 where ∆t is the time step; no information can be derived on a time scale smaller than the time step. The time step must be chosen wisely as accuracy of the approxima- tion worsens as the time step increases. Also, errors compound as each iteration is calculated. To reduce calculation error, the time step must be minimized without compromising the ECU’s throughput. But, there will be a point of diminishing re- turns where the time step is so small that there is no increase in the scheme’s accuracy due to computer round off errors [10]. Rearranging Eq. 2.15 to solve for the future value of the variable gives:
dy(n) y(n + 1) ≈ y(n) + ∆t (2.16) dt
For this application, the intake manifold pressure is of interest. Adapting Eq. 2.16 for the intake manifold pressure gives:
dp (n) p (n + 1) ≈ p (n) + ∆t a,IM (2.17) a,IM a,IM dt
This equation can be solved by using Eq. 2.12 and the current pressure reading from the MAP sensor. It is assumed that the engine speed, manifold temperature, and throttle position remain constant. If the intake manifold pressure is known a discrete amount of time in the future, the mass air flow into the cylinder can be calculated using the speed density equation. With the future mass air flow known, the correct amount of fuel can be injected to achieve stoichiometric combustion.
Linearizing Filling and Emptying Model
Another method of determining the intake manifold pressure a small amount of time into the future is to linearize the intake manifold filling and emptying model,
26 shown in Eq. 2.10. With a linearized version of this equation, an analytical solution to the estimated future value of MAP can be determined [16]. As mentioned previously, the engine speed, intake manifold temperature, and throttle position remain constant throughout the prediction.
The intake manifold filling and emptying model is linearized by expanding the air
flow through the throttle as a function of the current intake manifold pressure.
∂m˙ a,thr m˙ a,thr = (m ˙ a,thr)0 + (pa,IM − pa,IM,0) (2.18) ∂pa,IM 0 The terms subscripted with 0 denote current measured sensor readings. Taking the partial derivative of the air flow through the throttle in respect to the current intake manifold pressure gives:
m˙ a,thr 1 γ−1 ∂m˙ a,thr − 1 unchoked = γ pr γ (2.19) ∂p 2(pr −pr) a,IM 0 choked where pr is the ratio of the intake manifold air pressure to the ambient air pressure.
Equation 2.18 is then subsituted back into the filling and emptying model along with the speed density equation:
dpa,IM RairTa,IM ∂m˙ a,thr ηvVdN = (m ˙ a,thr)0 + (pa,IM − pa,IM,0) − pa,IM dt VIM ∂pa,IM 0 2Vim (2.20)
An analytical solution for the estimated value of intake manifold pressure in the future can be solved as:
−∆t pˆ = (p − p )exp + p (2.21) a,IM a,IM,0 a,IM,1 τ a,IM,1
27 where pa,IM,1 is the steady-state solution for the projected intake manifold pressure.
This can be solved by setting the left hand side of Eq. 2.21 to zero. ∆t is the amount of time into the future the intake manifold pressure is being predicted. The time constant is given as:
RT ∂m˙ η NV −1 τ = a,IM a,thr − v d (2.22) VIM ∂pa,IM 0 30RTa,IM A more detailed description of the derivation can be seen in [16].
Correcting Model Errors
Due to the assumptions made in developing the intake manifold model and the heavy reliance on empirically derived parameters, the models above will inevitably exhibit errors in practice. Methods to reduce these errors will be described in this section.
One of the main assumptions in the models mentioned previously is that the throttle position remains constant throughout the time that prediction is made. This assumption remains true in steady-state operation (with constant engine speed and spark timing). But, in transient events the throttle position a small amount forward in time will be slightly greater or less than the current position. This error in throttle position will cause the model to predict either a higher or lower manifold air flow through the throttle than the actual value, creating errors in the final MAP prediction.
A solution to this assumption is to create a lead filter to predict the throttle position one discrete time step ahead in time [13]. The equation for the filter is shown below:
28 θ+1(k) = (1 − a)θ+1(k − 1) + a(2θ(k) − θ(k − 1)), 0 < a < 1 (2.23) where a is the filter constant, θ is the current throttle position, and θ+1 is the one step ahead throttle prediction.
Another solution to correcting the throttle position is to delay the desired throttle position [1]. This is only viable in vehicles equipped with electronic throttle control.
With electronic throttle control, the driver’s throttle command can be stored in a memory buffer and a delayed command will be sent to the throttle actuator. Since the driver’s command is stored in a memory buffer, the throttle position trace is known a small amount of time in the future allowing a more accurate MAP prediction [1].
Along with the assumptions made, the model also relies on accurate values of the the throttle effective area and volumetric efficiency. While using conventional techniques of obtaining these values through steady-state engine dynamometer tests can provide very accurate values of these parameters, they cannot account for day- to-day changes in ambient temperature, pressure, and humidity and engine aging.
These changes can produce steady-state and dynamic errors in MAP prediction.
To help correct the drift in these parameters, an on-line calibration method of adjusting the parameters can be created [16]. The example below shows a procedure to adapt volumetric efficiency in real-time. By rearranging Eq. 2.12 at steady-state the following equation can be derived:
2RTa,IM m˙ a,th pa,IM = (2.24) ηvNVd Taking the partial derivative of 2.24 with respect to volumetric efficiency and solving
for the change in ηv gives:
29 2 ηv NVd ∆ηv = − ∆pa,IM (2.25) 2RTa,IM m˙ a,th where: ∆pa,IM is the error between the measured MAP and predicted MAP. With
Eq. 2.25, an integral compensator can be made:
Σ∆η η = η + L v (2.26) v v,0 p K where: ηv,0 is the original mapped value, Lp is the compensator gain, and Σ∆ηv is a running cumulative sum of ∆ηv and K is a large number to average out the cumulative sum. A low value of Lp would give good noise rejection while a higher value will give faster convergence.
2.3 Honda R18A3 Engine
The engine used for the research contained in this paper is the R18A3 engine developed by Honda. The engine was originally designed to use compressed natural gas (CNG) as the fuel. To improve power and efficiency, the engine contains actuators to allow variable valve timing (VVT), and a variable length intake manifold. The basic engine specifications are listed in Table 2.2 and a model of the engine is shown in
Figure 2.9.
The engine has two cam profile settings: high output and delayed closure. The high output cam settings allows the valve timing to be synchronous with the engine cycle events [6]. The intake cam opens the intake valve at the beginning of the intake stroke and then closes the intake valve at the beginning of the compression stroke. This setting is used when maximum power output is demanded from the engine. The delayed valve closure setting allows the intake valve to remain open for
30 Table 2.2: Engine specifications [15]
Property Value Unit Cylinder configuration In-line 4 - Bore × stroke 81 × 87.3 mm Displacement 1799 cm3 Compression ratio 12.5:1 - Valve train SOHC VVT, inlet delayed close - Number of valves 4 per cylinder - Cylinder offset 12 mm Intake manifold Variable intake system -
Figure 2.9: 2006 Honda R18A3 engine [15]
31 Figure 2.10: Valve lift profiles of different cam settings [15]
a discrete amount of time during the compression stroke before eventually closing.
This setting is used for when the required power output is low, such as maintaining a cruising speed. The delayed valve closure leads to better fuel economy by allowing a reduction in pumping losses due to the reduction in the effective compression ratio
[15]. The valve lift profiles for each setting can be seen in Figure 2.10.
A variable-length intake manifold is also installed on this engine. Inside the intake manifold is a bypass valve that changes the effective intake manifold length when opened or closed, shown in Figure 2.11. When the bypass valve is opened, the effective length is shorter. This setting is used primarily at high engine speeds. When the bypass valve is closed, the effective length is longer. This setting is used at lower engine speeds. By changing the effective intake manifold lengths at certain engine speeds, the wave dynamics inside the runners can be used to the engine’s advantage, leading to a higher torque output. For this engine, the lengths are designed where the bypass valve should opened only at engine speeds above 5000 RPM [4]. For more
32 Figure 2.11: Intake manifold variable length runner [15]
information about the engine and its performance and fuel economy improvement
strategies, refer to [15].
2.4 Tailpipe Emissions
Pollutant formation and control has been a major concern in the past few decades,
and spark-ignition and diesel engines are a major source of air pollution. The emis-
sions species from spark-ignition engines include: oxides of nitrogen (nitric oxide, NO
and NO2), carbon monoxide (CO), and unburned or partially burned hydrocarbons
(HC).
Nitrogen oxides (NOx) are formed in the high-temperature burned gases behind the combustion flame front. As the burned gas temperature increases, the rate of
NOx formation increases. As the burned gas temperatures cool, the NOx reactions
freeze and leave NOx concentrations in the tailpipe emissions. CO emissions can form
when the fuel-air mixture is rich due to an insufficient amount of oxygen presence
33 Figure 2.12: Emissions concentrations against air/fuel ratio [9]
34 to completely burn all the carbon in the fuel. Also, CO emissions are produced in
higher temperature burned gases, where dissociation occurs. HC emissions can be a
result of several processes. The large in-cylinder pressures can force some of the gas
mixture in the crevice volumes within the cylinder, which can be released later in the
cycle. A quench layer of unburned hydrocarbons can form on the cylinder wall due to
heat transfer and the flame burn zone not propagating throughout the entire cylinder.
Another source of HC emissions may come from oil layers from piston lubrication
that can absorb and desorb during combustion [9].
The air-fuel ratio plays a major role in determining the amount of engine emis-
sions. Figure 2.12 shows the relationships among NOx, CO, and HC emissions and
the air-fuel ratio. As the charge mixture goes rich, HC and CO emissions will increase while NOx decreases. As the charge mixture goes lean, the HC, CO, and NOx emis- sions decrease. But, HC emissions will start to increase at very lean mixtures due to cylinder misfires. At stoichiometric mixtures, NOx emissions are the highest. When the engine is operating in a narrow region around stoichiometric combustion, the three-way catalyst exhibits its highest conversion efficiency (see Fig. 2.1). Any devi- ation from stoichiometric combustion will significantly increase the vehicle’s tailpipe emissions.
35 Chapter 3: Experimental Description
The Center for Automotive Research at The Ohio State University provided the facilities for the research described in this thesis. All the tests were completed in an engine dynamometer test cell containing a 200 horsepower, four-quadrant DC motor connected to a Honda 1.8L four cylinder engine. A dynamometer controller was utilized to maintain the engine speed to allow testing at different engine operating points. The engine was originally designed to run on compressed natural gas as a fuel, but has been converted to run on E85 fuel. To control the engine, a rapid prototyping, 128-pin Woodward engine control unit coupled with a variety of sensors mounted to the engine hardware were used. The engine control algorithms were designed in MATLAB and SIMULINK with the default SIMULINK block set as well as a proprietary Woodward Motohawk block set that allowed communication with the engine control hardware. Communication to the engine was conducted using a
CAN Calibration Protocol (CCP) network and ETAS INCA software.
3.1 Engine Instrumentation
The Honda engine used in this research is equipped with a variety of sensors to enable proper control of the engine. The sensors relevant to the research in this thesis are listed in Table 3.1. The locations of several of these sensors are shown in Figures
36 Table 3.1: Relevant instrumented sensors on engine
Number Sensor name 1 Crankshaft position sensor 2 Engine coolant temperature 3 Engine knock indicator 4 Engine oil temperature 5 Fuel level 6 Fuel rail pressure 7 Intake air temperature 8 Manifold absolute pressure 9 Mass air flow 10 Pre-catalyst RTD 11 Pre-catalyst UEGO 12 Throttle position
3.1 and 3.2 where the numbered labels correspond to Table 3.1. The engine knock indicator listed in the table is a custom made copper tube that is rigidly attached to the original knock port on the engine block. The tube is routed into the dynamometer control room where it is attached to a funnel to allow knock events to be heard by the test operator.
A cooling tower is attached to the engine’s coolant ports to maintain the engine block temperature. The cooling tower uses an external water source and a thermostat to regulate the engine temperature to about 80 degrees celsius.
3.2 Data Acquisition System
The engine test setup is instrumented with multiple devices to allow sensor signals and actuator commands to be transferred between the operator’s computer and the engine. To communicate with the sensors and actuators that were attached to the
37 Figure 3.1: Intake side of engine
Figure 3.2: Exhaust side of engine
38 original Honda engine wiring harness, a Woodward 128-pin ECU is used. The engine control code contained on the ECU is built using MATLAB and SIMULINK with the Motohawk development library. The Motohawk development library is a set of proprietary blocks which create an interface layer between the control code and the input/output pins of the ECU. The latest engine control codes are built using MAT-
LAB’s Real Time Workshop. Mototune, another software package from Woodward, allows the engine operator to flash new control builds onto the ECU as well as load the latest calibrations.
For sensors that were not originally on the Honda engine’s wiring harness, a series of ETAS modules are used to collect data signals. Four ETAS modules are used: the
ES410, ES411, ES420, and LA4 Lambda Meter. The ES410 provides eight analog channels, while the ES411 provides eight analog channels with sensor supply voltages.
The ES420 contains eight channels for thermocouples and the LA4 Lambda Meter allows data acquisition of the post-catalyst UEGO sensor. The four ETAS modules are daisy-chained together and connect to the operator’s computer via a proprietary
ETAS Ethernet cable [6].
INCA, data acquisition software provided by ETAS, is used for calibrating, mon- itoring, and recording engine data in real-time. The software allows the operator to send commands to the engine such as throttle position or spark timing. Simultane- ously, sensor data such as engine coolant temperature or oil pressure can be monitored and recorded. Communication between the operator’s computer and the Woodward
ECU and ETAS daisy-chain is accomplished through the CCP. The computer is in- strumented with a PCMCIA card that allows the interface between INCA and the
39 Figure 3.3: Engine test setup [6]
data acquisition hardware. A block diagram of the test setup can be seen in Figure
3.3.
3.3 GM LE5 Mean Value Engine Model
To assist in developing the throttle and intake manifold models and air prediction control, a mean-value engine model was utilized to simulate results. This model is a zero-dimensional model developed by Dr. Kenneth Follen. It simulates dynamics from a GM LE5 Eco-Tec, 2.4 liter, inline-4, gasoline engine. The model was created using mathematical models of several main subsystems in the engine coupled with experimental data obtained in a dynamometer cell. The subsystems modeled include: throttle, intake manifold, volumetric efficiency, fuel transport, and torque production dynamics. The model structure can be seen in Figure 3.4. The MVEM could easily
40 Figure 3.4: 0-D Mean-value engine model for GM LE5 engine
be run at different operating conditions, allowing for a wide range of validation tests for the air prediction control model. While the engine specifications in this model are not the same as the Honda engine used in this research, the ability to simulate and validate the various parts of the air prediction algorithm was very useful in the control development.
41 Chapter 4: Control Algorithm Development
4.1 Introduction
A control algorithm that more accurately injects the correct amount of fuel to achieve stoichiometric combustion during transient engine operation will be discussed in this chapter. Since the engine is port fuel injected, the fuel injection is made 700 degrees before the intake valve opening. This allows the fuel to vaporize in the intake manifold runner before being inducted into the cylinder. Therefore, in order to achieve stoichiometric combustion, the intake manifold air pressure will be determined up to
700 degrees into the future. To be able to predict the intake manifold air pressure, the dynamic model of the intake manifold pressure and the Forward Euler approximation will be used. This algorithm will be implemented using SIMULINK and Stateflow.
4.2 Control Algorithm Description
In order to allow enough time for the fuel to vaporize inside the intake manifold, a fuel request must be made up to 700 degrees before the intake valve opening. This causes the controller to need to predict the cylinder air mass 700 degrees forward in time to maintain stoichiometric combustion. With the total amount of air inducted in the intake stroke estimated, the correct amount of fuel can be injected. The air per
42 Figure 4.1: Control algorithm timing
cylinder can be calculated using Eq. 4.1; wherem ˙ a is the mass air flow rate in g/s and AP C is the air per cylinder in mg/stroke. This section will outline the control algorithm to approximate the mass air flow exiting the intake manifold a discrete amount of time in the future. A diagram outlining the air prediction timing is shown in Figure 4.1.
120000m ˙ AP C = a (4.1) N
This control algorithm combines the models that will be developed in later chap- ters to create a dynamic intake manifold model and the Forward Euler approximation.
Several assumptions are made when using this proposed control algorithm. The in- take manifold temperature and engine speed are considered to change at a slower rate relative to the change intake manifold pressure. Thus, both values are assumed to be constant over the prediction horizon. Throughout this thesis the prediction horizon will be defined as the total time in the future the algorithm is approximating.
Since the throttle trajectory in the future is unknown, the throttle percentage is also assumed to be constant. The pressure and temperature inside the intake manifold
43 are assumed to be constant as well as the air flow throughout the engine. And, all
gaseous fluids are assumed to follow the ideal gas law.
A flow diagram outlining the control algorithm is shown in Figure 4.2. The al-
gorithm begins by collecting current readings from multiple sensors on the engine.
These include: intake air temperature, manifold absolute air pressure, throttle po-
sition, and engine speed. These values are assumed to be constant throughout the
entire algorithm. Next, the total time for the engine crankshaft to rotate 700 degrees,
or the prediction horizon, is calculated. Equation 4.2 shows how to determine the
prediction horizon using engine speed as an input.
1 min 1rev 60sec · 700 deg · · = prediction horizon (sec) (4.2) N rev 360deg 1min
With the prediction horizon determined, the total time will be divided into time increments determined by the number of iterations desired. These time increments will be referred to as the time step, ∆t, in this algorithm. As mentioned in Section
2.2.4, to reduce calculation error, the time step must be minimized without compro- mising the ECU’s throughput. The calculation of the time step is shown in Eq. 4.3.
In the following sections, the number of iterations will be optimized to allow minimal error without overly taxing the ECU resources. The throttle effective area for the current engine operating point is also determined.
prediction horizon = ∆t (4.3) number of iterations
With the time step and throttle effective area calculated, the algorithm will start an iteration loop which implements the intake manifold air pressure dynamic equation and the Forward Euler approximation. Using the aforementioned sensor data along
44 Figure 4.2: MAP prediction control algorithm
45 Table 4.1: Constant engine parameters
Variable Description Value Units γ Specific heat ratio 1.4 - pcrit Critical pressure ratio 0.5283 - pbaro Barometric pressure 101325 P a R Universal gas constant 287.05 J/kg · K 3 VIM Intake manifold volume 0.005145 m 3 Vd Engine total displacement volume 0.001799 m
with the engine parameters shown in Table 4.1, the rate of change of intake manifold
pressure can be determined. Then, using the current MAP reading, the predicted
intake manifold pressure ∆t seconds in the future can be calculated using Eq. 4.4.
This process is repeated until the number of desired iterations is completed. Note,
each time the algorithm runs through an iteration, the value for the manifold air
pressure is updated from the Forward Euler approximation. When all the iterations
are completed, the final MAP value will be an approximated value for the intake
manifold air pressure 700 degrees into the future.
dp (n) p (n + 1) ≈ p (n) + ∆t a,IM (4.4) a,IM a,IM dt
Once the control algorithm was determined, it was implemented in SIMULINK so the code could be transferred to run on the engine’s ECU. Figure 4.3 shows the
SIMULINK model. The model accepts inputs of IAT, MAP, throttle percentage, and engine speed. Equation 4.3 and 4.1 are implemented in a subsystem called “Determine
Time Step”, while the throttle effective flow area is determined by a 2-d lookup table that will be derived in later sections. All these values are sent to a Stateflow diagram.
46 Figure 4.3: MAP prediction SIMULINK model
Within this diagram, the intake manifold air pressure dynamic equation is solved and the Forward Euler approximation is implemented. The Stateflow repeats this calculation until the number of iterations reaches the desired iteration number. The
Stateflow diagram then outputs the final value of the intake manifold air pressure, which represents the approximate MAP value 700 degrees in the future. Figure 4.4 shows the Stateflow diagram. Note that this whole algorithm is executed within one time step of the engine’s ECU, which is 7 milliseconds for the ECU used in this research.
4.3 Summary
A control algorithm was created that combines the intake manifold model dis- cussed in an earlier chapter with a Forward Euler approximation to allow the intake manifold air pressure to be predicted forward in time. This algorithm allows the engine control system to more accurately predict the inducted air flow, thus leading
47 Figure 4.4: MAP prediction Stateflow diagram
48 to better emissions and performance. The control algorithm was adapted to run in
SIMULINK so it can be easily implemented into the engine hardware. As mentioned previously, the control algorithm relies heavily on an accurate calibration of the CdA and Ve parameters. The process of calibrating these parameters will be discussed in later chapters. Validation of the performance of this algorithm will also be conducted in later chapters both in simulation and on engine hardware.
49 Chapter 5: Intake Manifold Modeling
5.1 Introduction
In order to be able to successfully predict the mass air flow into the engine’s cylinders, an accurate model of the intake manifold pressure must be created. If a dynamic relationship of the intake manifold pressure is known, then the inducted air
flow rate can be predicted a discrete amount of time into the future using Eq. 2.17.
A zero-order model was chosen, described in Section 2.2.3, because the model will be implemented to run in real-time on the engine’s ECU. The model requires an accurate representation of air flow through the throttle plate and the engine’s efficiency as a pumping device.
5.2 Throttle Model
To be able to accurately model the mass air flow into the intake manifold, a model of flow through the throttle plate is necessary. The methods described in 2.2.1 will be used to create the model. To calculate the mass air flow through the throttle, several parameters need to be known including the throttle’s effective flow area, current intake manifold pressure, and the ambient pressure and temperature. The effective
flow area is a highly non-linear term and must be determined experimentally.
50 −3 x 10
1
0.8 ] 2 0.6
0.4 CdA [m 0.2
0 5000 4000 100 80 3000 60 2000 40 20 1000 0 Engine Speed [RPM] Throttle [%]
Figure 5.1: Throttle affective area map, raw data
The standard orifice equations for compressible flow shown in Eq. 2.1 and 2.2 are used to determine the effective flow area values at various engine operating points.
At each operating point, steady-state engine data is recorded. Since the engine is in steady-state, the intake manifold dynamics are no longer present and the MAF sensor readings will be valid. Thus, the compressible flow equations can be solved for the effective flow area using the MAF sensor reading for the mass air flow along with the sensor readings from the MAP and IAT sensors.
Using the CdA values at the different engine operating points, a 2-d lookup func- tion was created to relate the throttle effective area to throttle position and engine speed. Previously, a DOE was conducted on the engine used in this thesis; the data from this DOE was used in the creation of throttle effective area and volumetric effi- ciency maps [6]. The number test points used to create the full map was determined using an iterative DOE process described in [6]. After the number of test points was
51 −3 x 10
1
0.8 ] 2 0.6
0.4 CdA [m 0.2
0 5000 4000 100 80 3000 60 2000 40 20 1000 0 Engine Speed [RPM] Throttle [%]
Figure 5.2: Throttle affective area map, function fit
determined a Halton sequence was used to determine which operating points to test
[6]. For this DOE, a set of 151 operating points were recorded with throttle positions ranging from 0 to 100% and engine speeds ranging from 1000 to 4200 RPM. At each operating point, engine data was taken at steady-state for several important variables including MAP, MAF, IAT, brake torque, and exhaust temperature. The effective
flow area was calculated for each of the 151 operating points and is shown in Figure
5.1.
Using these test points, a 2-d function was created to relate the effective flow area to the throttle percentage and engine speed. From previous research, it was found that a multiquadratic radial basis (MRB) fit is the most accurate and provides the lowest root-mean-square error (RMSE). The MRB fit is a curve fit used offline to create a look-up table that is to be implemented on the engine’s ECU. The resulting surface plot using the radial basis fit is shown in Figure 5.2.
52 To validate the accuracy of the 2-d function, a set of 25 validation test points were taken at various engine operating points within the same ranges as the DOE. For each operating point, the throttle effective area was calculated in the same manner as the data points in the DOE. Since these points were not used in the initial creation of the lookup table, they will provide insight into how accurate the created 2-d function is in modeling the throttle’s effective area.
A comparison between the model CdA values and the calculated CdA values from the validation data are shown in Figure 5.3. For each validation operating point, the engine speed and throttle position were used in the model function to determine the model’s CdA prediction. The calculated CdA values from the validation data set are on the x-axis while the predicted CdA values from the model are on the y-axis. If the model contained no prediction errors, then the slope of all the validation points would be one. Looking at 5.3, it can be seen that all the points are very close to the unity slope, indicating high accuracy in the CdA model.
The next validation test is to determine how well the mass air flow can be predicted using the CdA model and the compressible flow equations. For each of the operating points in the validation data set, the steady-state data was sent to a SIMULINK model to determine the calculated MAF values. The engine speed and throttle position allows the throttle effective area to be calculated. The CdA value coupled with the ambient pressures and temperatures and intake manifold pressure allow the MAF to be calculated using either Eq. 2.1 or 2.2. The equation used is dependent on whether the flow is choked or not. The calculated MAF values are then compared to the actual MAF sensor values. Since the validation data was taken in steady-state the
53 −4 x 10 4.5
4
3.5 ]
2 3
2.5
2
CdA Model [m 1.5
1
0.5 Validation points Unity slope 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 2 −4 CdA Calculated [m ] x 10
Figure 5.3: Model and experimental CdA value comparison
MAF sensor provides readings of high accuracy, allowing the use of its readings to validate the model.
The results of this test are shown in Figure 5.4. It can be seen that almost all of the test points are within ± 5% of the values of the MAF sensor. The two outlying data points (tests 1 and 2) were taken at operating points at low RPM and low throttle. This operating region in the CdA model is highly non-linear and is difficult to measure and model. Despite the two outlying points, the validation results show that the CdA map created coupled with the compressible flow equations provides an accurate representation of mass air flow.
Since this paper focuses on transient events in engine operation, a comparison between the MAF sensor reading and the calculated MAF using the created model
54 20
15
10
5
0
−5 MAF error [%]
−10
−15
−20 0 5 10 15 20 25 Test
Figure 5.4: Calculated and actual MAF value comparison
during a throttle transient was conducted. Tests at 1200, 1400, 1600, and 2000 RPM were evaluated. At each engine speed, a throttle transient was conducted to change the engine load from approximately 30 kPa to 70 kPa. For each transient event, the
MAF sensor reading was recorded along with throttle position, RPM, IAT, and MAP.
Using SIMULINK, post-processing was conducted to calculate the MAF based off of the throttle model. The results of these tests are shown in Figure 5.5.
It can be seen that the dynamic response of the throttle model is slightly quicker than that of the MAF sensor. As mentioned in Section 2.2.4, the MAF sensor has a response time on the order of 1 to 10 seconds. Since the throttle model uses the throttle position and MAP sensors (response times of about 1-50 milliseconds), the throttle model is able to capture the throttle change much quicker. The overshoot in
55 (a) 1200 RPM (b) 1400 RPM
14 24
22 12 20
18 10 16
8 14
MAF [g/s] MAF [g/s] 12 6 10
8 4 MAF sensor 6 MAF sensor Calculated MAF Calculated MAF 2 4 14.5 15 15.5 16 16.5 17 17.5 14.5 15 15.5 16 16.5 17 17.5 Time [s] Time [s] (c) 1600 RPM (d) 2000 RPM
Figure 5.5: MAF during throttle transient event
56 air flow is due to the sudden increase in throttle position, which creates a high pressure differential across the throttle plate. This differential causes a sudden increase in air
flow for a short period of time. With a faster response time, the throttle model can characterize higher frequency fluctuations in the mass air flow.
It can be seen that there exists an appreciable amount of steady-state error be- tween the calculated MAF and MAF sensor readings. These errors are due to in- accuracies of the CdA map in the throttle model. At 1200 RPM (Figure 5.5a), the steady-state errors are the most severe because of the high non-linearity in the lower
RPM and throttle ranges for the CdA map. Also, the data taken from these transient tests were taken on different testing days in the engine dynamometer cell, which can have significant effects on the results. The changing ambient conditions and engine aging can cause the previously obtained calibration data to become invalid.
5.3 Volumetric Efficiency Model
To be able to accurately model the mass air flow exiting the intake manifold into the engine’s cylinders, an accurate model of the volumetric efficiency is required.
The volumetric efficiency can then be used in the volumetric efficiency equation to calculate the mass air flow rate. Since volumetric efficiency is the result of many complex interactions within an engine’s air system, the parameter was determined empirically.
As outlined in Section 2.2.2, the volumetric efficiency was determined at multiple engine operating points during steady state operation. In the volumetric efficiency equation, if mass air flow rate, temperature, intake manifold pressure, and engine speed are known, then the volumetric efficiency can be solved for at that specific
57 100
80
60
40
20
Volumetric Efficiency [%] 0 150 100 5000 4000 50 3000 2000 0 1000 MAP [kPa] Engine Speed [RPM]
Figure 5.6: Volumetric efficiency map, raw data
operating point. Since the engine is in steady-state operation, the MAF sensor reading provides an accurate value for the mass air flow rate. The other parameters needed may be easily recorded during engine operation.
Using the volumetric efficiency values at the different operating conditions, a 2-d lookup function was created to relate the volumetric efficiency to manifold absolute air pressure and engine speed. The same DOE data used to create the throttle effective area, mentioned in the previous section, will be used to create the Ve plot. For each of the 151 test points, the volumetric efficiency was determined; Figure 5.6 shows all the points plotted in 3-d space. Using these test points, a 2-d function was created to determine the volumetric efficiency at certain operating points. From previous research, it was found that a cubic radial basis fit is the most accurate and provides the lowest RMSE [6]. The resulting surface plot using this function is shown in 2.5.
58 To validate the accuracy of the 2-d function, the same set of 25 validation points
used in the throttle modeling validation will be used. For each validation point, the
volumetric efficiency was determined in the same manner as described earlier. Since
the 2-d function was not derived from these points, the validation data can show the
accuracy of the volumetric efficiency model.
Figure 5.7 shows a comparison of Ve values between the model and experimental results using the validation data. The x-axis shows the calculated Ve value at each validation point using the speed density equation. The y-axis shows the Ve value at
each validation point evaluated from the 2-d function with the inputs of manifold
absolute air pressure and engine speed. Theoretically, if the model was in perfect
agreement with real-world testing, all of the validation points would be on the unity
slope. Looking at Figure 5.7, it can be seen that all the test points are very close to
the unity slope, which indicates the high accuracy of the model.
The next test involves comparing the calculated mass air flow rate using the
Ve model and speed density equation to the mass air flow reading from the MAF
sensor. For each validation operating point, the engine steady-state data was post-
processed in a SIMULINK model to determine the mass air flow. Using the mean
values of MAP, IAT and RPM, the mass air flow could be calculated. These values
are compared to the MAF sensor reading at each operating points and are shown in
Figure 5.8. It can be seen that every test point is well within ± 5% error with respect
to the MAF sensor. These validation results further indicate the high accuracy of the
experimentally determined Ve model and use of the volumetric efficiency equation.
59 85
80
75
70
65
VE Model [%] 60
55
50 Validation points Unity slope 45 45 50 55 60 65 70 75 80 85 VE Calculated [%]
Figure 5.7: Model and experimental VE value comparison
20
15
10
5
0
−5 MAF error [%]
−10
−15
−20 0 5 10 15 20 25 Test
Figure 5.8: Model and experimental MAF value comparison
60 5.4 Intake Manifold Pressure Model
In order to predict the intake manifold air pressure a discrete amount of time into
the future, a dynamic model of the intake manifold is necessary. As described in
Section 2.2.3, a zero-order model of the intake manifold was derived, incorporating
Eq. 5.1. The model considers the mass air flow into and out of the intake manifold
using models of the throttle flow and volumetric efficiency, respectively. These models
were developed and validated in previous sections of this chapter. The throttle model
relies on compressible flow equations to determine the flow of air while the Ve model
relies on the empirically found parameter volumetric efficiency and the speed density
equation.
dpa,IM RairTa,IM ηvVdN =m ˙ a,th − pa,IM (5.1) dt VIM 2Vim The entire model was implemented into SIMULINK, as shown in Figure 5.9. The intputs into the system are throttle position, engine speed, and intake air temperature.
The integrator represents the intake manifold pressure. Both the throttle model and
Ve model are implemented into separate subsystems. The implementation of these models is shown in AppendixA.
To validate the model, a series of tests were run on the engine dynamometer test setup. At 1200, 1600, 2000, 2800, and 3500 RPM, a throttle transient command was sent to the engine. The throttle transient caused an intake manifold pressure transient from about 30 kPa to 70 kPa at each engine speed. Among many parameters recorded, the IAT, RPM, and throttle percentage were included. For each test, these parameters were loaded into the SIMULINK model. The SIMULINK model was run
61 Figure 5.9: SIMULINK diagram of intake manifold model
for the same duration as the dynamometer test and the simulated intake manifold
air pressure was calculated for each time step of the simulation. The simulated MAP
was compared to the measured MAP from the MAP sensor during the dynamometer
test.
It can be seen that during the steady-state parts of each test, the simulated MAP
exhibits a steady-state error. This steady-state error is the result of errors in the CdA
and Ve 2-d lookup functions used in the models. If at a certain operating point, the
throttle model and Ve model do not agree (in terms of mass air flow), the resulting
MAP will either be higher or lower than the actual value determined from the sensor.
A numerical uncertainty analysis was conducted on the intake manifold model to determine the sensitivity of the model in respect to the calculated manifold air pres- sure values. At engine speeds of 1200, 1400, 1600, 2000 RPM and manifold pressures of around 20 kPa, perturbations were applied to the CdA and Ve parameters. Each
parameter was changed by ±5% and the resulting change in MAP was determined.
62 (a) 1200 RPM (b) 1600 RPM
80 80
70 70
60 60 50 50
MAP [kPa] MAP [kPa] 40
40 30
Measured MAP Measured MAP 30 Simulated MAP 20 Simulated MAP
14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 Time [s] Time [s] (c) 2000 RPM (d) 2800 RPM
(e) 3500 RPM
Figure 5.10: MAP during throttle transient event
63 Table 5.1: Model MAP Sensitivity Analysis
Test Change in MAP [%]
Engine speed [RPM] +5% CdA −5% CdA +5% Ve −5% Ve 1200 3.63 -3.28 -3.12 3.84 1400 3.31 -3.39 -3.22 3.48 1600 2.95 -2.93 -2.79 3.10 2000 3.60 -3.68 -3.50 3.79
A table of the results is shown in Table 5.1. On average, a five percent deviation of either parameter would result in about a 3.4% change in MAP. These deviations from a small amount of error cause steady-state error in the simulated MAP. In the control algorithm, these errors will compound with each iteration of the control al- gorithm, creating significant steady-state errors in MAP. Methods of eliminating the steady-state error will be described in later sections of this paper.
The dynamic nature of the intake manifold is captured accurately in the model.
It can be seen that the measured MAP follows a first-order dynamic response that the model approximated. While there exists a steady-state error, the general shape of the changing intake manifold pressure is captured well in the model.
5.5 Summary
A dynamic model of the intake manifold pressure was created using models of the throttle air flow and volumetric efficiency of the engine. Both the throttle and volumetric efficiency models required calibration data from the engine dynamometer to create 2-d lookup functions to model the CdA and Ve parameters. These models were validated using validation data points from previously obtained DOE data. The
64 throttle and volumetric efficiency models were combined into the full intake manifold pressure model. Simulations utilizing engine dynamometer data allowed comparisons to be made between simulated and measured MAP. While the simulated MAP results showed steady-state errors, the dynamics were captured accurately. Solutions to the steady-state error will be addressed in later sections.
65 Chapter 6: Control Algorithm Validation
6.1 Introduction
To validate the control algorithm, the MVEM described in Section 3.3 will be used.
This model will provide a software-in-the-loop test bed for the control algorithm to allow errors to be corrected before the code is implemented on the engine’s ECU.
Although the engine in the MVEM is not the same one used for the research in this thesis, the model will provide excellent insight on validating if the code can predict the intake manifold air pressure successfully. Next, engine data from the dynamometer cell will be collected and post-processed in MATLAB. This will further the control development by using actual engine data to produce results from the algorithm.
6.2 Software Validation
The control algorithm described in Chapter4 was validated in simulation. A simulator was used to verify the functionality of the control algorithm before it is implemented on the engine hardware. Further, using a simulator speeds up the de- velopment and refinement of the control algorithm; algorithm changes can be imple- mented in a vastly shorter period of time compared to using actual hardware. Since the simulator can run faster than real-time, different engine operating points can be tested very quickly. The simulator also allows the measurement of variables that
66 Figure 6.1: MAP prediction SIMULINK implementation in MVEM
are difficult to measure in real-world testing. To validate the control algorithm, the
MVEM model described in Section 3.3 will be used as the plant model. Although this model is not calibrated to the engine used in this research, it will provide results necessary in validating the accuracy of the control algorithm.
The control algorithm was combined with the MVEM in a SIMULINK diagram, shown in Figure 6.1. The inputs into the MVEM were throttle position and engine speed. The ambient air pressure and temperature were assumed to be 101.325 kPa and 26.85 degrees C, respectively. The outputs of the plant model were intake air temperature and intake manifold air pressure. The outputs of the MVEM along with the throttle position and engine speed were fed into the MAP prediction con- trol algorithm, whose output was the predicted MAP 700 CAD in the future. The control algorithm used the same 2-d functions for throttle effective area and volu- metric efficiency as the MVEM used. Also, the engine constant parameters such as piston displacement and intake manifold volume were changed to match those of the modeled engine.
67 Figure 6.2 shows simulation results at different engine operating points. For each simulation, a transient throttle command was created and the resulting MAP and predicted MAP values were recorded. There are three different signals shown in each plot in Figure 6.2, the current MAP, predicted MAP, and correct MAP. The current
MAP corresponds to the manifold air pressure output from the plant model. The predicted MAP is the output of the MAP prediction control algorithm. And, the correct MAP is the signal that represents the correctly predicted intake manifold air pressure for a 700 CAD prediction horizon. The correct MAP was found by shifting the current MAP signal earlier in time by an amount equal to the prediction horizon.
The time duration of the prediction horizon can be calculated using Eq. 4.2.
In Figure 6.2, results are shown for engine operating points at 1200 and 1600
RPM. For each engine speed, throttle transients from 15 to 25 degrees and 25 to 15 degrees were commanded. It can be seen that up until the current MAP increases, the current and prediction MAPs are the same value. But, once the current MAP increases, the predicted MAP very closely matched that of the correct MAP signal trace. The transient dynamics are predicted well with the intake manifold model and the Euler approximation is able to accurately predict the intake manifold air pressure forward in time.
A more in-depth look at one of the simulations is shown in Figure 6.3. This figure shows results for a simulation run at an engine speed of 1200 RPM and throttle transient from 15 to 25 degrees. The top plot shows the same information as Figure
6.2. The middle plot shows the throttle position, while the bottom plot shows the
MAP error for both the current and predicted MAP traces. The MAP error is defined as the difference between a MAP value and the correct MAP value at a discrete point
68 80 80 Current Predicted 75 75 Correct
70 70
65 65
60 60
55 55 MAP [kPa] MAP [kPa]
50 50
45 45
Current 40 40 Predicted Correct 35 35 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 3.5 4 4.5 5 Time [s] Time [s] (a) 1200 RPM, tip in (b) 1200 RPM, tip out
70 70 Current Predicted 65 65 Correct
60 60
55 55
50 50
45 45 MAP [kPa] MAP [kPa]
40 40
35 35
Current 30 30 Predicted Correct 25 25 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 3.5 4 4.5 5 Time [s] Time [s] (c) 1600 RPM, tip in (d) 1600 RPM, tip out
Figure 6.2: MVEM simulation results at varying engine operating points
69 80 70
60
50 Current MAP [kPa] 40 Predicted Correct 30 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 Time [s]
30
25
20
Throttle [%] 15
10 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 Time [s]
30 Current Predicted 20
10 MAP error [kPa]
0 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 Time [s]
Figure 6.3: MVEM simulation results for throttle transient
70 in time. It can be seen that the predicted MAP is unable to successfully match the correct MAP trace until the throttle position starts its transient. This is because the intake manifold model relies on throttle position to be able to predict the mass air flow into the intake manifold. If there is no change in throttle, then the model will assume the engine is still in steady-state and the rate of change of the intake manifold air pressure will remain zero. But, once the throttle position changes, the control algorithm is able to successfully predict the MAP forward in time. Looking at the bottom plot, the MAP error goes to zero after the throttle increase, while the current MAP error remains until the engine returns to steady-state again.
It is apparent that the lack of knowledge of the throttle position ahead of time can cause significant errors. Before the throttle change, the predicted MAP trace accumulated as much error as the current MAP trace. In this case, the error reached about 30 kPa in a single point in time, which can cause a significant deviation in the resulting air-fuel ratio. Since the engine was running at 1200 RPM, this is one of the worst case scenarios because the lower the engine speed, the greater the prediction horizon.
While the simulation run in Figure 6.3 shows a good representation of what would result in real-world testing, the throttle response is largely inaccurate. It assumes that the throttle can follow a step command instantaneously. This is inaccurate as the throttle plate has an inertia as well as a counteracting force from the throttle plate return spring. To more accurately model the throttle movement, a rate limiter was applied to the throttle command. A rate limiter applies a maximum and minimum slew rate to an incoming signal. Previous research was completed to determine what the correct slew rate for the throttle is. Using throttle position data from a vehicle
71 80 70
60
50 Current MAP [kPa] 40 Predicted Correct 30 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 Time [s]
30
25
20
Throttle [%] 15
10 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 Time [s]
30 Current Predicted 20
10 MAP error [kPa]
0 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 Time [s]
Figure 6.4: MVEM simulation results for throttle transient, with throttle rate limiter
72 drive cycle, the speed of the throttle at different points in time was determined. The resulting slew rate was 233 deg/s [5]. Using a rate limiter on the throttle, another simulation was run at an engine speed of 1200 RPM and a throttle transient of 15 to
25 degrees, and is shown in Figure 6.4.
It can be seen that the throttle trace no longer represents a step input; the trace ramps up to the final value. This is due to the rate limit of 233 deg/s set on the throttle command. The results are for the most part similar to those of Figure 6.3, except the predicted MAP does not match the correct MAP immediately after the throttle transient started. After the throttle starts to move, the predicted MAP moves towards the correct MAP, but it is not instantaneous. This is due to the throttle change not being instantaneous. Since the control algorithm assumes the throttle effective flow area is constant throughout the prediction horizon, the control algorithm will contain errors while the throttle is ramping into its final position. This is because the throttle position it is using to predict MAP forward in time is not the actual throttle position
700 CAD later. It can be seen that once the throttle reaches its desired set point, the predicted MAP error goes to zero because the throttle position remains constant from that point on.
With the control algorithm successfully predicting intake manifold air pressure, the number of iterations must be optimized. As the number of iterations increases, the time step in the Euler approximation will decrease. As mentioned previously, the accuracy of the approximation increases as the time step is reduced. But, an increasing amount of iterations will require more throughput from the engine’s ECU, which may cause operational problems if the ECU becomes overloaded. Figure 6.5 shows a graph of the MAP error versus the number of control algorithm iterations.
73 1.8
1.6
1.4
1.2
1
0.8
Normalized Error 0.6
0.4
0.2 Normalized Error No Prediction 0 10 12 14 16 18 20 22 24 26 28 30 Number of Iterations
Figure 6.5: MVEM normalized error vs. iteration number
4.2
4
3.8
3.6
3.4
3.2 Simulation Time [s] 3
2.8
2.6 10 12 14 16 18 20 22 24 26 28 30 Number of Iterations
Figure 6.6: MVEM simulation time vs. iteration number
74 The MAP error is the cumulative error from a 15-75-15 degree transient at 2000 RPM.
The number of iterations ranged from 10 to 30. The plot shows the cumulative error normalized against the cumulative error from using the current MAP reading without prediction. It can be seen that at lower iteration numbers, the control algorithm produces a larger amount of error than not using prediction at all. After thirteen iterations, the MAP prediction algorithm performs better than the current MAP. But, after sixteen iterations there is no increase in performance from the MAP prediction algorithm. At this point, the increases in accuracy from increasing the iteration number are smaller than the round off errors from the computer.
The computational time was also considered when optimizing the iteration num- ber. For each test, the simulation time was determined. This was done by inserting timers in the MATLAB code that recorded the computers clock time before and after the simulation. Figure 6.6 shows the simulation time versus the number of iterations.
As the number of iterations increased, the simulation time also increased. This is because the computer has to re-calculate another set of equations for each increase in iteration number. Thus, in terms of computational time, the number of iterations must be minimized. Considering the results from Figure 6.5, sixteen or more itera- tions would provide the most accurate results. This would lead to choosing sixteen iterations as the most optimal number. But, since the accuracy diminishes with iter- ations immediately under sixteen iterations, eighteen iterations will be chosen. This will give a small safety buffer as the control algorithm may perform differently for different test cases.
75 6.3 Hardware Validation
With the control algorithm validated in simulation using the MVEM, the next step is to use actual engine data from the dynamometer to further validate the per- formance. For the following tests, engine data at different operating points were recorded and post-processed in MATLAB and SIMULINK. In the SIMULINK dia- gram, the engine data were fed into the model as time varying traces that were used with the MAP prediction algorithm. The implementation into SIMULINK is shown in Figure 4.2.
To validate the algorithm, tests were conducted at engine speeds of 1200, 1400,
1600, and 2000 RPM. For each engine speed, a throttle transient was commanded to produce a MAP transient of about 20-70-20 kPa. Figure 6.7 shows the results for the tests run at 1200 RPM. The plots show the current, predicted, and correct
MAP traces as well as the MAP error for the current and predicted MAP traces.
It can be seen that there is exists about a 2 to 3 kPa error throughout the entire test for the predicted algorithm. This is due to the steady-state error present at the lower and higher intake manifold pressures. This error is to be expected from the results in Section 5.4 where it was determined that a small deviation from the true value of either the throttle effective area or volumetric efficiency parameters can produce appreciable errors in the resulting manifold air pressure. These errors are further worsened by the fact that the algorithm runs eighteen iterations in open-loop, meaning that the error will compound with each iteration.
The results of each test are listed in Table 6.1. For each test, the absolute value of the MAP error was integrated with respect to time for the current and predicted
MAP traces. The errors for each predicted MAP trace were then normalized against
76 80 75 Current 70 Predicted 70 Correct 65
60 60
50 55 MAP [kPa] MAP [kPa] 50 Current 40 Predicted 45 Correct 30 40 15 16 17 18 19 30 31 32 33 34 Time [s] Time [s]
8 5 Current Current Predicted Predicted 4 6
3 4 2
MAP Error [kPa] 2 MAP Error [kPa] 1
0 0 15 16 17 18 19 30 31 32 33 34 Time [s] Time [s] (a) Tip in (b) Tip out
Figure 6.7: MAP prediction performance results, 1200 RPM
Table 6.1: MAP prediction performance
Test Engine speed [RPM] MAP transient [kPa] Normalized MAP error 1200 20-70 3.18 1400 20-70 2.12 1600 20-70 2.01 2000 20-70 1.02 1200 70-20 3.56 1400 70-20 2.51 1600 70-20 3.83 2000 70-20 1.94
77 the current MAP trace’s errors. It can be seen that for every test the MAP predic- tion performance was worse than using the current MAP values. Again, these large amounts error in each test are due to a mismatch in calculated mass air flow between the throttle and volumetric efficiency models.
6.3.1 Recalibrating Ve Map
The steady-state errors that are persistant in the initial hardware tests are due to a disagreement between the throttle and volumetric efficiency model. At steady-state, the intake manifold dynamics are zero and both the throttle and volumetric efficiency models should be calculating the same value for mass air flow. If the calculated values are different, then an offset of MAP will occur since the model is incorrectly showing that there is a greater influx of outflux of air mass in the intake manifold causing a change in the manifold air pressure.
A proposed solution to this problem is to recalibrate the volumetric efficiency model so that it calculates the same mass air flow as the throttle model at every engine operating point. If the calculated mass air flow is matched for both models, dpa,IM /dt will be zero, thus creating no change in the current MAP in steady-state.
To recalibrate the volumetric efficiency model, the 2-d lookup function for the Ve parameter will need to be recalculated. This parameter was originally calculated using the volumetric efficiency equation (Eq. 2.7), with steady-state engine dynamometer data. For the mass air flow, the MAF sensor reading was used. To allow both the throttle and volumetric efficiency models to be in agreement, the volumetric efficiency parameter will need to be determined using the mass air flow calculated from the throttle model. This involves using throttle position and engine speed to determine
78 the throttle effective area, which is used in the flow restriction model. Since the
mass air flow calculated from the throttle model is used to determine the volumetric
efficiency 2-d lookup function at a certain engine operating point, the calculated
mass air flows from the throttle and volumetric efficiency model will be equivalent.
To recalibrate the volumetric efficiency 2-d lookup function, the same 151 test points
used to calibrate the model in Section5 were used. For each test point, the volumetric
efficiency parameter based on the throttle model’s mass air flow was calculated.
With the 151 CdA based volumetric efficiency points determined, another 2-d lookup function was created. The inputs to the function would remain the same as the original function, intake manifold pressure and engine speed. The MATLAB package sftool was used to create the 2-d lookup function. This package allows test points to be loaded into the graphical user interface and the user can apply different
fitting functions to determine the best fit.
Three different types of fits were considered for creating the 2-d lookup function: biharmonic interpolant with and without outliers and lowess. The biharmonic model is a radial basis function interpolant. The lowess model uses locally weighted linear regression to smooth data. For the biharmonic model, functions were created with and without points that were considered outliers from the calibration data.
To validate the function fits, the same 25 test points used to validate the model in Chapter5 were used. Using the resulting 2-d functions from each fit, the mass air flow from the volumetric efficiency model was calculated at a certain engine point and compared to the mass air flow calculated from the throttle model. The RMSE was calculated for all 25 validation test points for each 2-d function. The results are shown in Table 6.2. With the lowest RMSE, the biharmonic interpolant with outliers
79 Table 6.2: Comparison among proposed 2-d lookup functions
Interpolation Method RMSE [g/s] Biharmonic interpolant (w/o outliers) 0.00323 Biharmonic interpolant (w/ outliers) 0.00273 Lowess 0.00287 Original 0.0124
was chosen to be the new recalibrated Ve function. The percent MAF error for each of the validation points is shown in Figure 6.9. It can be seen that all but two test points are within 5 percent error, providing confidence of a good fit. The resulting surface plot of the function is shown in Figure 6.8. The general shape of the surface is similar to typical volumetric efficiency maps, except at lower engine speeds and manifold air pressures. In this area of the map, the throttle effective area parameter is highly non-linear.
With the new volumetric efficiency 2-d lookup function implemented in the SIMULINK diagram, the same tests in Table 6.1 were completed. Figure 6.10 plots a comparison between the original and recalibrated Ve maps for the test run at 1200 RPM for a throttle tip in. It can be seen that while steady-state error still exists, the magnitude of steady state-error has been decreased. The rest of the results are shown in Table
6.3. This table compares the normalized MAP error between both the original and recalibrated Ve maps. For every test except at an engine speed of 2000 RPM, the recalibrated map improved on the cumulative MAP error, but the results are still not an improvement over using the current reading from the MAP sensor. This is because the steady-state error in MAP still exists in all the tests. This steady-state error is a result of the sensitivity of the intake manifold model. As found in previous sections,
80 100
80
60
40
Volumetric Efficiency [%] 20 100 5000 50 4000 3000 2000 0 1000 MAP [kPa] Engine Speed [RPM]
Figure 6.8: CdA based Ve 2-d lookup function
20
15
10
5
0
−5 MAF Error [%]
−10
−15
−20 0 5 10 15 20 25 Test
Figure 6.9: MAF error between throttle and induction mass air flow
81 80 80
70 70
60 60
50 50 MAP [kPa] MAP [kPa]
Current Current 40 40 Predicted Predicted Correct Correct 30 30 15 16 17 18 19 15 16 17 18 19 Time [s] Time [s]
8 8 Current Current Predicted Predicted 6 6
4 4
MAP Error [kPa] 2 MAP Error [kPa] 2
0 0 15 16 17 18 19 15 16 17 18 19 Time [s] Time [s]
(a) Old Ve map (b) New Ve map
Figure 6.10: Comparison between original and recalibrated Ve maps at 1200 RPM
82 Table 6.3: Comparison between original and recalibrated Ve maps
Test Normalized MAP error Engine speed MAP transient Without V e With V re-cal % change [RPM] [kPa] re-cal e 1200 20-70 3.18 2.13 33 1400 20-70 2.22 1.68 24 1600 20-70 2.01 1.80 11 2000 20-70 1.02 1.31 -28 1200 70-20 3.56 2.35 34 1400 70-20 2.51 1.86 26 1600 70-20 3.83 3.09 19 2000 70-20 1.94 1.94 0
a five percent deviation in either the throttle effective area or volumetric efficiency parameters can cause about a 3.4% error in MAP. This error is further exacerbated by the fact that the control algorithm iterates the model 18 times, during which the error is compounded with each iteration. Even though the volumetric efficiency map was recalibrated using the throttle model mass air flow, the 2-d lookup function can- not perfectly match the throttle model mass air flow at every operating point. This is seen in Figure 6.9, where the majority of the validation tests showed lower than
five percent error in MAF calculation. And, with a small disagreement in air flow calculation, the steady-state MAP error can be significant.
6.3.2 Implementation of Adaptive Control Strategies
A major source of the error that is making the intake manifold pressure prediction model worse than using the current MAP sensor reading is the existence of steady- state error. When the engine is in steady-state, the current and predicted MAP values should be the same. One cause of the steady-state error are the imperfections
83 in the model calibration. Even though both the throttle and volumetric efficiency models were calibrated with relatively good accuracy, small errors still exist. One source of error is that the 2-d look-up function for the CdA parameter has a high rate of change with small deviations of either the throttle position or intake manifold pressure. Thus, small errors in the calibration will cause steady-state errors in the resulting calculated MAP. Another source of error comes from obtaining the correct intake manifold temperature reading which can affect the Ve model. Currently, the temperature is taken from the IAT sensor, which is integrated into the MAF sensor.
Since the IAT sensor is placed upstream of the intake manifold in the air system, the assumption that the IAT sensor temperature reading is equivalent to the temperature of the intake manifold is not correct. With the presence of an engine block that is at a much higher temperature than the ambient temperature, the intake manifold temperature will often be higher than the temperature at the IAT sensor. Also, with the intake valve closing after the compression stroke begins, there will be a finite amount of reverse flow into the intake manifold from the engine cylinders, causing higher intake manifold temperatures.
Another cause of steady-state error are the day-to-day changes in engine opera- tion. These include engine aging and changes in ambient conditions for temperature, pressure, and humidity. These changes cannot be accounted for in a model without adaptive control. As determined previously, any small error in the model can produce significant deviations in the predicted intake manifold pressure values. A solution to these problems of steady-state error would be to implement a control algorithm that uses feedback from sensors to correct the model. For this model, feedback from the
84 Figure 6.11: SIMULINK implementation of adaptive PI model
MAP sensor will be used to correct the error between the current and predicted MAP in steady-state.
Adaptive PI Model
To allow the use of feedback control to correct error in the model, an adaptive PI model was implemented into the control algorithm. The inputs are the current and predicted intake manifold pressure values, and the output is the adjusted predicted intake manifold pressure. An adaptive PI model was chosen instead of an adaptive
PID model because the derivative term is very sensitive to measurement noise.
The methodology of the model is shown in 6.11. The setpoint of the system is the current MAP. The error between the predicted and current MAP values is calculated.
This error is applied to the proportional and integral terms of the controller. The proportional term corrects using the present error, while the integral term corrects using a cumulative sum of past errors. The integral term allows the system to elimi- nate steady-state error. A weighted sum of both terms is calculated and the resulting
85 multiplying factor is applied to the predicted MAP value. A heuristic approach to tuning the controller gains was taken, which is similar to the Ziegler-Nichols method of gain tuning. The proportional gain was tuned first, with the integral following.
The desired settling time was under five seconds with less than five percent over- shoot. The gains were manually tuned until the desired response was achieved. The proportional and integral gains are 0.009 and 0.008 kP a−1, respectively.
The adaptive PI model should only be correcting MAP when the engine is oper- ating in steady-state. This is because during a transient, the adaptive PI model will try to correct the predicted MAP towards the current MAP. But, during transients the current MAP is incorrect. In steady-state the predicted and current MAP values should be equivalent. To allow the control algorithm to only be active during steady- state, the adaptive PI model was placed in an enabled subsystem in SIMULINK which is activated only in steady-state operation. To control the enabling and dis- abling of the adaptive PI model, an algorithm to determine if the engine is operating in steady-state will need to be created.
In this thesis, engine steady-state operation will be defined as a state in operation in which transients of the engine speed and intake manifold air pressure values have ceased over a small period of time. A steady-state detection algorithm was created and implemented in SIMULINK. The algorithm structure is shown in 6.12. The inputs into the subsystem are the current engine speed and intake manifold pressure and the output is a binary value indicating if the engine is operating in steady-state.
For the engine to be in steady-state, both the engine speed and intake manifold air pressure cannot exhibit transients. To determine if a variable is exhibiting a transient, the present value of the variable is compared to a past value. If the difference between
86 Figure 6.12: SIMULINK implementation of engine steady-state detection
the two values is lower than a specified tolerance, then the variable is considered to
be in steady-state. Since the sensor data is susceptible to noise, a first-order filter is
applied to the input signals, shown in Eq. 6.1.
1 F (s) = (6.1) 0.25s + 1
To test the performance of the steady-state detection algorithm, a series of engine transients were input into the detection algorithm. Figure 6.13 shows the MAP trace and steady-state status. The shaded sections of the graph indicate portions of the trace the algorithm determined to be steady-state operation. Looking at the graph, it can be seen that the algorithm can successfully determine which portions of the trace the engine was in steady-state. The adaptive PI model and steady-state detection subsystems were implemented into the base algorithm, shown in Figure 6.14.
Eight validation tests were performed on the base algorithm with the adaptive
PI model. At 1200, 1400, 1600, and 2000 RPM, throttle transients producing MAP
87 Figure 6.13: Steady-state detection for random transients
transients of about 20-70 and 70-20 kPa were conducted. Similar to the analyses done previously in this chapter, the cumulative MAP error was recorded over a small period in time during the transient step and was compared to the performance without adaptive parameters.
In Figure 6.15, a comparison between the base control algorithm and the updated algorithm with adaptive parameters is shown. For the updated algorithm it can be seen that before the transient begins, the steady-state error is eliminated. This is because the adaptive PI model has driven the error to zero since the engine is in steady-state. After the transient is over, there is steady-state error. This is a result of the adaptive PI model resetting during the transient; the multiplier is set back to the default value of one. The error after the transient is ramping down as the engine returns to steady-state operation and the adaptive PI model is the changing
88 Figure 6.14: MAP prediction SIMULINK diagram with adaptive PI model
89 80 80
70 70
60 60
50 50
MAP [kPa] 40 MAP [kPa] 40 Current Current 30 Predicted 30 Predicted Correct Correct 20 20 15 16 17 18 19 15 16 17 18 19 Time [s] Time [s]
10 10 Current Current Predicted Predicted 8 8
6 6
4 4 MAP Error [kPa] MAP Error [kPa] 2 2
0 0 15 16 17 18 19 15 16 17 18 19 Time [s] Time [s] (a) Without adaptive PI model (b) With adaptive PI model
Figure 6.15: Improvement using adaptive PI model at 1200 RPM
90 Table 6.4: Error improvement using PI control
Test Normalized MAP error Engine speed MAP transient Without PI With PI model % change [RPM] [kPa] model 1200 20-70 2.13 1.60 25 1400 20-70 1.68 0.96 43 1600 20-70 1.80 1.18 35 2000 20-70 1.31 0.91 30 1200 70-20 2.35 1.50 36 1400 70-20 1.86 1.33 28 1600 70-20 3.09 2.28 26 2000 70-20 1.94 1.41 27
the multiplier accordingly. The same analysis was completed for each test and the normalized error against the base algorithm was calculated. The normalized MAP error between the algorithm with and without adaptive PI model is shown in Table
6.4. It can be seen for every test, there was a significant reduction in error. And, for the first time, the control algorithm performed better than using the current
MAP in terms of MAP error. The tests run at engine speed of 1400 and 2000 RPM produced 0.96 and 0.91 normalized error. The significant reduction in error is due to the adaptive PI model being able to successfully drive the steady-state error to zero.
Adaptive Ve Model
With the addition of the adaptive PI model, the steady-state error was able to be significantly reduced. But, the adaptive PI model is only active in steady-state, which causes the controller gain to be reset every time a transient occurs. This gives motivation to develop an algorithm that can adapt to changing engine operating conditions and learn in on-line operation of the engine’s ECU. If the algorithm can
91 remember the corrections, then the steady-state error can be eliminated after the transient engine events.
To correct for the steady-state error, an algorithm was created that adjusts a multiplier that is applied to the current volumetric efficiency. The steady-state error is the result of a mismatch in the mass flow rates of air into and out of the intake manifold. At steady-state, the mass air flow rates should be equivalent since there is no change in intake manifold pressure. By adjusting the volumetric efficiency, the mass air flow rate out of the intake manifold can be adjusted to match that of the mass of air flowing into the intake manifold.
The adapting volumetric efficiency table algorithm implemented into the base algorithm is shown in Figure 6.16, and the algorithm subsystems are shown in Ap- pendixB. The inputs into the algorithm are the current engine speed, intake manifold pressure, error between the current and predicted MAP values, and steady-state sta- tus. The output of the system is the adjusted volumetric efficiency parameter. As mentioned previously, the steady-state error in MAP will be corrected by adjusting a multiplier that is applied to the current volumetric efficiency. This multiplier is adjusted according to the error between the predicted and current MAP values.
The desired time for convergence of the predicted MAP to the current MAP for the algorithm was set to be about 60 seconds. This duration was chosen because this is a correction stored in memory and to ensure the validity of the correction, a longer duration was used. This prevents any short disturbances to be rejected in the on-line correction. For short disturbances, the adaptive PI model (with a settling time of
5 seconds) will be able to correct the errors in the short-term. In this algorithm,
0.01% of the MAP error is either added or subtracted to the multiplier, depending on
92 Figure 6.16: MAP prediction SIMULINK diagram with adaptive Ve table
93 whether the predicted MAP is higher or lower than the current MAP. To determine the percentage of error added to the multiplier, the average steady-state MAP error was found. The average steady-state among tests run at engine speeds of 1200, 1400,
1600, and 2000 RPM was about 2 kPa. In simulation, it was determined that with a 2 kPa MAP error, taking 0.01% of the MAP error and adding it to the multiplier will yield about a 60 second convergence rate.
The results of this simulation are shown in Figure 6.17. It can be seen that within the first five seconds, the steady-state error is driven to zero; this is because the adaptive PI model is active along with the adaptive volumetric efficiency table algorithm. After the adaptive PI model has converged, the MAP error is showing to be zero. But, since the adaptive volumetric efficiency table algorithm scopes the
MAP error prior to the adaptive PI model, the magnitude of actual MAP error can still be used to correct the volumetric efficiency parameter. During this time, the adaptive volumetric efficiency table algorithm is adjusting the volumetric efficiency multiplier from its default value of 1. About 60 seconds later, the multiplier converges to a value of about 0.7. On the way to the convergence of the volumetric efficiency multiplier, the adaptive PI model’s multiplier settles back down to 1. This is because the adaptive volumetric efficiency table algorithm is slowly correcting the volumetric efficiency parameter, and the adaptive PI model does not need to adjust the final predicted MAP as much. When the volumetric efficiency parameter settles to its
final value of 0.7, the PI multiplier settles back to a value of 1.
Since the volumetric efficiency multiplier may not be assumed to be constant throughout the entire engine operating range, the 2-d volumetric efficiency look-up table was split into sixteen different zones. The different zones are shown in Figure
94 45
40 Actual Future Correct MAP [kPa] Future Predicted 35 0 10 20 30 40 50 60 70 80
2 Experimental Predicted 1
MAP Error [kPa] 0 0 10 20 30 40 50 60 70 80
1
0.9
0.8 VE Multiplier 0.7 0 10 20 30 40 50 60 70 80
1.05
1 PI Multiplier 0.95 0 10 20 30 40 50 60 70 80 Time [s]
Figure 6.17: Ve table correction
95 Figure 6.18: Layout of Ve adaptation zones
6.18. While the most accurate method of adaptation would be to have a zone mul- tiplier for each operating point, it would not be practical. One reason is that the algorithm would be constantly adapting as the operating points changed, also the amount of memory required to store a multiplier for each point would be unreason- able. Sixteen zones were chosen in that it provides fine enough discretization of the volumetric efficiency table without overly taxing the ECU or having the algorithm constantly learning on-line. Further calibration of the appropriate amount of zones will be completed in-vehicle, where the algorithm will experience real-world drive traces. Hysteresis bands were also implemented into the zone-based control. This prevents the adaptation learning from chattering between zones when the operating point is close to the edge of a zone.
96 The methodology of the zone-based adaptation is shown in AppendixB. The in- puts into the system are the current volumetric efficiency, current MAP error, steady- state status, and engine speed and intake manifold pressure data. The output of the system is the corrected volumetric efficiency value. Within the zone-based adapta- tion subsystem, the characteristics of the zone-based control are set. These include the number of zones, minimum range value, incremental range value, and hysteresis threshold. The minimum range value is the smallest value the respective variable can be, while the incremental range value is the size of the zone with respect to the variable. The hysteresis threshold is the size of the hysteresis bands applied to all zones with respect to the variable. For the engine used in this research, the engine speed and intake manifold pressure variables were both split into four zones. The engine speed range is 1000 to 4200 RPM, while the MAP range is 0 to 112 kPa.
To test the performance of the adaptive volumetric efficiency table algorithm, the same eight validation tests as used previously in this thesis were performed. At 1200,
1400, 1600, and 2000 RPM, throttle transients producing MAP transient of about
20-70 and 70-20 kPa were conducted. The cumulative MAP error was recorded over a small period of time during the transient step and was compared to the performance without the additional adaptive parameters. For these tests, the adaptive volumetric efficiency table was given time to adapt and learn before the data was recorded.
In Figure 6.19, a comparison between the base algorithm with adaptive PI model versus the base algorithm with adaptive PI model and adaptive volumetric efficiency table is shown. The results are both from the tests run at an engine speed of 1200
RPM with a throttle tip-in. It can be seen that both algorithms are able to suc- cessfully drive steady-state error to zero before the throttle transient. As discussed
97 80 80
70 70
60 60
50 50 MAP [kPa] MAP [kPa] 40 40 Current Current 30 Predicted 30 Predicted Correct Correct 20 20 15 16 17 18 19 379 380 381 382 Time [s] Time [s]
10 10 Current Current Predicted Predicted 8 8
6 6
4 4 MAP Error [kPa] MAP Error [kPa] 2 2
0 0 15 16 17 18 19 379 380 381 382 Time [s] Time [s]
(a) With adaptive PI model (b) With Ve adaptation
Figure 6.19: Improvement using adaptive Ve table at 1200 RPM
98 previously, since the engine is in steady-state before the transient, the adaptive PI model is active and drives the predicted MAP towards the current MAP. Similarly, the adaptive volumetric efficiency table algorithm is able to adjust the Ve multiplier to create zero steady-state error. After the transient, the base algorithm with only adaptive PI model exhibits steady-state error. This is because the adaptive PI model resets during a transient, and the algorithm will have to re-adjust the PI multiplier to bring the steady-state error to zero. The MAP error is slowly decreasing, but a significant amount of MAP error is accumulating during the PI convergence. With the addition of the adaptive volumetric efficiency table algorithm, the steady-state error after the throttle tip-in was decreased greatly. This is because the algorithm was able to adapt and store the appropriate correction to the Ve parameter in memory.
And, since the steady-state values before and after the throttle transient are correct, the MAP value accuracy during the transient itself was increased.
The results shown in Figure 6.19b, are very similar to the simulation results shown in Figure 6.4. Looking at the simulation results, the only source of error in MAP values comes from the lack of knowledge forward in time of the throttle position.
This results in an inability to correctly predict MAP forward in time until the throttle position actual changes. Similar results are shown in the transient with the addition of the adaptive volumetric efficiency table algorithm.
The results from the rest of the eight validation tests are shown in Table 6.5. For every test, there was a significant reduction in the normalized MAP error with the addition of the adaptive volumetric efficiency table algorithm. On average, there was about a 70 percent reduction in normalized MAP error. This large reduction in error
99 Table 6.5: Error improvement using Ve adaptive control
Test Normalized MAP error Engine speed MAP transient Without V e With V adapt % change [RPM] [kPa] adapt e 1200 20-70 1.60 0.40 75 1400 20-70 0.96 0.37 61 1600 20-70 1.18 0.35 69 2000 20-70 0.91 0.47 48 1200 70-20 1.50 0.40 73 1400 70-20 1.33 0.39 70 1600 70-20 2.28 0.42 81 2000 70-20 1.41 0.38 73
is due to the algorithm successfully eliminating steady-state error before and after
the throttle transients.
One of the driving factors of creating an on-line adaptive volumetric efficiency
table is the effect of day-to-day changes in the engine operating conditions. These
changes can invalidate the empirically calibrated CdA and Ve tables, causing signif-
icant errors in MAP prediction. To see how much the day-to-day changes effect the
model, the Ve multiplier was tracked from different testing sessions throughout the course of a couple months. Figure 6.20 shows the results of the Ve multiplier from
Zone 5 of the zone-based adaptive algorithm throughout time. It can be seen that there is a great deal of variability on the multiplier, ranging from about 0.6 to 1. Dur- ing the November tests, it can be seen that there are drastic changes even between just a couple days of testing. On November 9, the multiplier was 1.01 and then on
November 10 it was 0.74. Two days later on November 12, the multiplier was back
100 1.3
1.2
1.1
1
0.9 Multiplier e
V 0.8
0.7
0.6
0.5 11/12 12/12 01/13 02/13 Date
Figure 6.20: Day-to-day variability in Ve multiplier
up to 0.98. This great amount of variability in the Ve parameter reinforces the need for adaptive algorithms in the control.
6.3.3 AFR Results
To further validate the control algorithm, oxygen sensor data was recorded in the engine dynamometer cell to analyze the AFR results from throttle transient. Looking at the AFR data will provide an excellent indication to the performance of the control algorithm. As discussed previously, any deviation from stoichiometric combustion will lead to increased emissions when a three-way catalyst is used. Thus, during transient engine events, it is desired that the AFR trace show minimal deviations from stoichiometric combustion (λ = 1).
101 1.15 No prediction 1.1 Prediction
1.05
1
0.95 Equivalence Ratio 0.9
0.85
0.8 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 Time [s]
Figure 6.21: AFR deviation from throttle tip-in, 1200 RPM, closed-loop
1.25 No prediction 1.2 Prediction
1.15
1.1
1.05 Equivalence Ratio 1
0.95
0.9 30 30.5 31 31.5 32 32.5 33 33.5 34 34.5 35 Time [s]
Figure 6.22: AFR deviation from throttle tip-out, 1200 RPM, closed-loop
102 Figures 6.21 and 6.22 show AFR results from the tests run at an engine speed of 1200 RPM with a throttle tip-in and tip-out, respectively. For these tests, the closed-loop AFR control algorithm was enabled, which means feedback control from the oxygen sensor was used to assist in adjusting the fueling to allow stoichiometric combustion. Figure 6.21 shows the results of a throttle tip-in event. Baseline results using the previous engine air mass estimation algorithm (simply the speed density equation) are compared to results using the control algorithm created in this thesis.
Looking at the results without prediction software, it can be seen that the beginning of the throttle transient causes a large deviation of almost 20% toward lean combustion.
Deviations of this magnitude can be dangerous in that engine knock events can occur along with increased tailpipe emissions. With the prediction software implemented, the initial deviation was reduced by about 50%. Also, the subsequent deviations were minimized compared to those in the results without prediction. Figure 6.22 shows the results of a throttle tip-out event. Similar results as the previous test occurred; not using the prediction software caused a large initial AFR deviation during the initial throttle change. The initial deviation spiked about 15% towards rich combustion.
Using the prediction software, the initial deviation was reduced by about 55%.
The same eight tests used previously in this thesis were conducted to analyze the
AFR results using the air-prediction control algorithm. At 1200, 1400, 1600, and
2000 RPM, throttle transient producing MAP transients of about 20-70 and 70-20 kPa were conducted. Two metrics of performance were measured, the area deviation from the setpoint equivalence ratio and the maximum deviation from the setpoint equivalence ratio. The area deviation was found by integrating the absolute value of the deviation from the control’s equivalence ratio setpoint value over time. Area
103 Table 6.6: Closed-loop AFR results, area deviation
Test Area deviation Engine speed MAP transient No prediction Prediction % change [RPM] [kPa] 1200 20-70 0.093 0.040 57 1400 20-70 0.080 0.043 46 1600 20-70 0.086 0.046 47 2000 20-70 0.089 0.034 62 1200 70-20 0.098 0.039 60 1400 70-20 0.069 0.040 42 1600 70-20 0.091 0.065 29 2000 70-20 0.093 0.073 22
Table 6.7: Closed-loop AFR results, maximum % deviation
Test Maximum % deviation Engine speed MAP transient No prediction Prediction % change [RPM] [kPa] 1200 20-70 18.80 10.07 46 1400 20-70 18.39 10.48 43 1600 20-70 25.27 13.32 47 2000 20-70 30.93 11.29 64 1200 70-20 13.88 6.35 54 1400 70-20 12.45 7.62 39 1600 70-20 19.78 13.22 33 2000 70-20 22.21 14.77 33
104 deviation is important to analyze as it is an indication of not only how far the AFR deviates from stoichiometric combustion, but for how long the deviation lasts. The results of the area deviation and maximum percent deviation are shown in Tables 6.6 and 6.7, respectively. It can be seen that for all tests shown, there were significant performance increases when the prediction software was implemented. The average percentage reduction in the area deviation and maximum percent deviation were both
45%.
Recalibration of Steady-State Algorithm
To further improve the performance of the MAP prediction control algorithm, the steady-state detection was recalibrated. One source of error in the results is the time delay between when an engine transient occurs and when the algorithm is able to detect the transient. Every moment the engine is in a transient state and the prediction algorithm is not active, air charge estimation error will occur and large
AFR deviations will result. Thus, the quicker the algorithm can detect a transient event, the less AFR deviations will occur and consequently less tailpipe emissions.
Currently the previous steady-state algorithm takes about 40 ms to respond to a transient event.
To improve the steady-state detection performance, the first-order filter constant was changed as well as the threshold tolerance. The methodology of the original steady-state algorithm is outlined in Section 6.3.2. The first-order filter was imple- mented into the algorithm to smooth out the sensor data from the MAP sensor. But, the addition of a first-order filter adds a delay to the system. To quicken the response, the filter constant was adjusted to accommodate a wider bandwidth. The new filter equation is shown in Eq. 6.2.
105 100
95
90
85
80 MAP [kPa]
75 MAP MAP old 70 filtered MAP new filtered 65 18 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 20 Time [s]
Figure 6.23: Filter change comparison
A simulation to compare the responses of both filters to a MAP transient was run, and the results are shown in Figure 6.23. The traces for the MAP sensor data, and the filtered MAP using both the old and recalibrated filters are shown. For the recalibrated filter, it can be seen that the response is much faster than that of the old filter. With a quicker filter response, the time delay for transient event detection will be shorter.
1 F (s) = (6.2) 0.10s + 1
Another change to the algorithm was adjusting the threshold value in which the algorithm considers the engine to be in steady-state. As mentioned in a previous chapter, the algorithm subtracts past MAP values from the current MAP values, and
106 if the result is less than the threshold value the engine is considered to be in steady- state. With a conservative threshold value, the algorithm will take longer to consider itself in transient operation, but will be more robust in rejecting sensor noise. A balance between a quick-responding threshold value and one that rejects noise data from being flagged as transient operation is needed. For the re-calibration of the algorithm, the MAP tolerance was changed from 0.60 kPa difference to a 0.30 kPa difference. A simulation was run to compare the steady-state detection performance between the old and recalibrated steady-state detection algorithms and the results are shown in Figure 6.24. The recalibrated algorithm takes about 20 ms to respond to a transient event, which is a 20 ms improvement over the previous algorithm. Also, the new steady-state algorithm is able to detect a return to steady-state operation after the transient is over much quicker than that of the old algorithm. There was about a 300 ms improvement in detection time.
To further test the performance of the new steady-state detection algorithm, the same eight validation tests performed previously were run again with the new algo- rithm implemented. The results for the area deviation and maximum percent devi- ation are shown in Tables 6.8 and 6.9. Each table outlines the percent improvement of the addition of the MAP prediction software before and after the recalibration of the steady-state algorithm. The percent improvement of the recalibrated steady-state algorithm over the old algorithm was also calculated.
Looking at Table 6.8, generally there was a significant improvement in area devi- ation; on average there was a 14% improvement over the old calibration. Two tests showed a worse performance. The tests run at engine speeds of 1200 and 2000 RPM for a throttle tip in showed a -13 and -2 % change. Similar results were shown for
107 105
100
95
90
85
80 MAP [kPa] 75
70 MAP S.S. *100 65 old S.S. *100 new 60 18 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 20 Time [s]
Figure 6.24: Steady-state detection comparison
Table 6.8: Comparison of closed-loop AFR results for area deviation with steady-state algorithm recalibration
New cal. [% Old cal. [% Test % change improve.] improve.] Engine speed MAP transient [RPM] [kPa] 1200 20-70 50 57 -13 1400 20-70 65 46 42 1600 20-70 53 47 14 2000 20-70 61 62 -2 1200 70-20 65 60 10 1400 70-20 54 42 29 1600 70-20 47 29 62 2000 70-20 25 22 14
108 Table 6.9: Comparison of closed-loop AFR results for maximum % deviation with steady-state algorithm recalibration
New cal. [% Old cal. [% Test % change improve.] improve.] Engine speed MAP transient [RPM] [kPa] 1200 20-70 46 46 0 1400 20-70 51 43 19 1600 20-70 57 47 20 2000 20-70 58 64 -8 1200 70-20 54 54 0 1400 70-20 45 39 16 1600 70-20 46 33 39 2000 70-20 42 33 27
the maximum percent deviation shown in Table 6.9, on average there was a 19% improvement over the old calibration. The only test to show worsened performance was a throttle tip-in at an engine speed of 2000 RPM with a -8% change. There were also two tests that showed no improvement.
Open Loop Performance
To further validate the air prediction control algorithm, tests were conducted with open-loop control only. This means that both feedback loops from the oxygen sensors were turned off. Open-loop AFR control performance was evaluated because the influence of the closed-loop feedback loops was removed. This provides a better insight on how the predictive feed-forward algorithm alone performs against the original algorithm.
109 1.1 No prediction 1.05 Prediction
1
0.95
0.9 Equivalence Ratio 0.85
0.8
0.75 10 12 14 16 18 20 22 24 26 Time [s]
Figure 6.25: Open-loop AFR control performance comparison, 1200 RPM, 30-70 kPa transient
The same eight validation tests as performed previously were conducted for the open-loop tests. Figure 6.25 shows the AFR results for both the original and pre- dictive algorithms for the test conducted at 1200 RPM with a throttle tip-in. Both algorithms showed a lean spike in engine operation, this is due to the throttle tip- in. The sudden increase in air flow is unable to be detected by the control software immediately so an inadequate amount of fuel is provided to have stoichiometric com- bustion. Similar to closed-loop results, there is a large decrease in both the maximum percent deviation and area deviation of the AFR trace with the addition of the new algorithm.
110 1.1
1.05
1
0.95
0.9 Maximum % deviation Area deviation Equivalence Ratio 0.85
0.8
0.75 10 12 14 16 18 20 22 24 26 Time [s]
Figure 6.26: Method of calculating metrics for open-loop results
When looking at Figure 6.25, it can be seen that the AFR traces do not settle down to the setpoint value in engine steady-state operation. This is because the control algorithm for air calculation is running in open-loop, which means that there is no feedback to correct for errors. Thus, the steady-state deviations from the setpoint are caused from errors in the calibration of engine maps such as volumetric efficiency or injector characterization. Since the steady-state AFR values are not necessarily at the same value, a method of calculating the same metrics used previously will have to be established. The reference value in which the maximum percent and area deviation will be calculated from will be the steady-state value after the engine transient is over. The calculation method of the metrics is shown in Figure 6.26.
111 Table 6.10: Open-loop AFR results, area deviation
Test Area deviation Engine speed MAP transient No prediction Prediction % change [RPM] [kPa] 1200 20-70 0.081 0.040 50 1400 20-70 0.082 0.029 65 1600 20-70 0.066 0.020 70 2000 20-70 0.091 0.023 75 1200 70-20 0.094 0.042 55 1400 70-20 0.071 0.039 45 1600 70-20 0.144 0.102 29 2000 70-20 0.189 0.096 49
Table 6.11: Open-loop AFR results, maximum % deviation
Test Maximum % deviation Engine speed MAP transient No prediction Prediction % change [RPM] [kPa] 1200 20-70 23.95 9.12 62 1400 20-70 18.30 6.29 66 1600 20-70 25.48 4.64 82 2000 20-70 31.16 12.92 59 1200 70-20 14.38 4.92 66 1400 70-20 10.26 4.69 54 1600 70-20 13.17 7.14 46 2000 70-20 30.68 16.52 46
112 Table 6.12: Test operating points for open-loop AFR control performance comparison
Test Engine Speed [RPM] MAP transient [kPa] 1 1200 30-70 2 1400 40-20 3 1500 50-35 4 1900 35-55
The rest of the validation tests are summarized in Tables 6.10 and 6.11. Table
6.10 shows the results for the amount of deviation area from the steady-state setpoint.
For every test case, there was an improvement with the addition of the prediction algorithm. On average, there was about a 55% improvement over the old control algorithm. Table 6.11 shows the results of the maximum percent deviation from the steady-state setpoint. Similar to the previous results, there was a significant improvement for every test case. On average, there was about a 60% improvement in maximum percent deviation with the addition of the prediction algorithm.
The prediction control algorithm was also benchmarked against a production com- petitor sedans control algorithm. The competitor sedan data from a FTP drive cycle was taken. With these results, portions of the cycle were analyzed, specifically look- ing at the current intake manifold pressure, engine speed, and resulting AFR traces.
From the FTP cycle, four engine transient test points were determined and the same tests were evaluated on the engine dynamometer for the prediction control algorithm.
These tests are summarized in Table 6.12.
The results are shown in Figures 6.27 and 6.28 for the area deviation and max- imum percent deviation, respectively. For each test, the results for the algorithm with and without prediction and the competitor algorithm are shown. Similar to
113 0.09 No prediction 0.08 Prediction Competitor algo 0.07
0.06
0.05
0.04
Area deviation 0.03
0.02
0.01
0 1 2 3 4 Test
Figure 6.27: Open-loop AFR control performance comparison, area deviation
25 No prediction Prediction 20 Competitor algo
15
10 Max % deviation
5
0 1 2 3 4 Test
Figure 6.28: Open-loop AFR control performance comparison, max % deviation
114 the previous results, the addition of the prediction algorithm significantly improved the performance over the original control algorithm. Compared to the competitors algorithm, the prediction algorithm was able to achieve a smaller area deviation for every test. For the maximum percent deviation, the prediction algorithm was able to significantly improve upon the original control algorithm for every test. For Tests 1,
2 and 3, the prediction software was an improvement over the competitor algorithm.
For Test 4, the competitor algorithm performed slightly better than the prediction algorithm.
6.4 Summary
The proposed control algorithm was validated in both software and hardware vali- dation. In the software validation, the prediction control algorithm was implemented with a mean value engine model to verify performance before the algorithm was imple- mented on engine hardware. The algorithm proved to successfully predict the MAP forward in time, and the simulations showed what the ideal results would like (Figure
6.1). Further, the simulations allowed the optimization of the number of iterations to run for the control algorithm. Next, the control algorithm was validated using data collected from the engine dynamometer cell. Initial results showed a significant amount of steady-state error, which gave motivation for the Ve map recalibration and implementation of adaptive control strategies. With these additions to the code, the hardware results matched closely with the software simulation results. The control algorithm was then evaluated using the AFR trace data in both open and closed-loop operation. The control algorithm was not only able to make significant improvements
115 over the original control algorithm, but over a competitive production sedan’s control algorithm.
116 Chapter 7: Conclusions and Future Work
7.1 Conclusions
In this thesis, a model-based design approach to air-fuel ratio control was suc- cessfully created and validated. The resulting control algorithm combines an intake manifold model with a Forward Euler approximation. To create the intake manifold model, steady-state engine dynamometer data from a 151 point DOE test was used to calibrate the throttle air flow and volumetric efficiency models. The intake manifold model was validated in simulation against engine dynamometer data. The results showed significant steady-state error, but an accurate representation of the dynamics of the intake manifold pressure variable was produced.
The validated intake manifold model was the combined with the Forward Euler approximation to create a predictive intake manifold air pressure algorithm. The control algorithm was validated in both software and hardware validation. In software validation, the control algorithm was combined with a mean value engine model.
From this, rapid control development of the control algorithm was completed. The software validation provided an insight on what the ideal results a successful algorithm would yield as well as an optimization of the number of iterations for the control algorithm to run. In hardware validation the control algorithm was validated in both offline post-processing of engine dynamometer data and in real-time implementation
117 on the engine ECU. The initial results showed a significant amount of steady-state error, which gave motivation to implement adaptive control strategies. An adaptive
PI model was created which allowed the elimination of steady-state error until an engine transient occurred. A zone-based adaptive volumetric efficiency table was also implemented which was able to significantly reduce steady-state error by storing the corrections in memory.
The oxygen sensor data also was analyzed to validate the performance of the con- trol algorithm. AFR traces from both closed and open-loop operation were collected.
For both cases, the control algorithm was proven to have a significant performance increase over the original control algorithm. And, in open-loop control, the predic- tive control algorithm was able to be competitive with a production sedan’s control algorithm.
7.2 Future Work
While the validation of the air prediction control algorithm showed positive results, there are several improvements that can be implemented to further its performance.
One improvement is the implementation of throttle command buffering. This involves storing the throttle command from the driver in the ECU’s memory. By delaying the driver’s throttle command, the control algorithm achieves a priori knowledge of the future throttle commands, which allows the MAP to be successfully predicted throughout the entire engine transient. In order to successfully implement throttle command buffering, a dynamic model of the throttle plate dynamics will need to be created.
118 Another possible addition to the control algorithm is intake manifold volume tun- ing. Since the filling and emptying process of the intake manifold may not utilize the entire volume of the manifold, the system response may have a different time constant than that of the model. Using parameter identification techniques, the actual used intake manifold volume can be found, which will correct the model’s time constant.
Additionally, the algorithm should undergo in-vehicle calibration. This is essential to complete before the control algorithm is permanently implemented into the ECU in the vehicle. During this validation process, further tuning and optimization of parameters such as number of control algorithm iterations and number of adaptation zones can be completed. Performing in-vehicle validation will allow further calibration of the control algorithm by creating drive cycles that cannot be easily replicated in the engine dynamometer cell.
119 Bibliography
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121 Appendix A: Intake Manifold Model Subsystems
This appendix shows the subsystems of the intake manifold SIMULINK model shown in Figure 5.9.
122 Figure A.1: Subsystem: throttle model
Figure A.2: Subsystem: throttle model > flow restriction
123 Figure A.3: Subsystem: throttle model > flow restriction > unchoked flow
Figure A.4: Subsystem: throttle model > flow restriction > choked flow
124 Figure A.5: Subsystem: Ve model
Figure A.6: Subsystem: Ve model > Ve to MAF
125 Appendix B: Adaptive Volumetric Efficiency Table Subsysems
This appendix shows the subsystems of the adaptive volumetric efficiency table
SIMULINK model.
126 Figure B.1: VE Lookup Table
127 Figure B.2: VE Lookup Table > Zone Based Correction Control
128 Figure B.3: VE Lookup Table > Zone Based Correction Control > Zone Determi- nation
129 Figure B.4: VE Lookup Table > Zone Based Correction Control > Zone Determi- nation > X Zone Determination
130