Introduction to hybrid vehicle system modeling and control wei liu

INTRODUCTION TO HYBRID VEHICLE SYSTEM MODELING AND CONTROL INTRODUCTION TO HYBRID VEHICLE SYSTEM MODELING AND CONTROL WEI LIU A JOHN WILEY & SONS, INC., PUBLICATION Cover image: © Henrik Jonsson/iStockphoto Cover design: Michael Rutkowski Copyright © 2013 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic formats For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: Liu, Wei, 1960 Aug 30Introduction to hybrid vehicle system modeling & control / Wei Liu p cm Includes bibliographical references and index ISBN 978-1-118-30840-0 Hybrid electric vehicles–Simulation methods Hybrid electric vehicles–Mathematical models I Title TL221.15.L58 2012 629.22 93–dc23 2012009797 Printed in the United States of America 10 To my wife, Mei, and son, Oliver CONTENTS Preface xv Nomenclature xix Abbreviations xxv Introduction 1.1 1.2 1.3 1.4 General Architectures of Hybrid Electric Vehicle, 1.1.1 Series Hybrid, 1.1.2 Parallel Hybrid, 1.1.3 Series–Parallel Hybrid, Hybrid Vehicle System Components, Hybrid Vehicle System Analysis, 1.3.1 Power Flow of Hybrid Vehicles, 1.3.2 Typical Drive Cycles, 1.3.3 Vehicle Drivability, 1.3.4 Vehicle Fuel Economy and Emissions, Controls of Hybrid Vehicle, References, 10 Basic Components of Hybrid Vehicle 2.1 11 Prime Mover, 11 2.1.1 Gasoline Engine, 11 vii viii CONTENTS 2.2 2.3 2.4 Hybrid Vehicle System Modeling 3.1 3.2 3.3 3.4 3.5 3.6 3.7 2.1.2 Diesel Engine, 12 2.1.3 Fuel Cells, 14 Electric Motor with DC/DC Converter and DC/AC Inverter, 15 Energy Storage System, 17 2.3.1 Energy Storage System Requirements for Hybrid Vehicles, 17 2.3.2 Basic Types of Batteries for Hybrid Vehicle System Application, 19 Transmission System in Hybrid Vehicle, 24 References, 24 Modeling of Internal Combustion Engine, 25 Modeling of Electric Motor, 32 Modeling of Battery System, 37 Modeling of Transmission System, 42 3.4.1 Modeling of Clutch and Power Split Device, 42 3.4.2 Modeling of Torque Converter, 50 3.4.3 Modeling of Gear Box, 52 3.4.4 Modeling of Transmission Controller, 53 Modeling of Final Drive and Wheel, 56 Modeling of Vehicle Body, 58 PID-Based Driver Model, 59 References, 61 Power Electronics and Electric Motor Drives of Hybrid Vehicle 4.1 4.2 25 Basic Power Electronic Devices, 63 4.1.1 Diodes, 64 4.1.2 Thyristors, 65 4.1.3 Bipolar Junction Transistors, 67 4.1.4 Metal–Oxide–Semiconductor Field Effect Transistors, 69 4.1.5 Insulated Gate Bipolar Transistors, 71 DC/DC Converter, 72 4.2.1 Basic Principle of DC–DC Converter, 72 4.2.2 Step-Down (Buck) Converter, 74 4.2.2.1 Steady-State Operation, 76 4.2.2.2 Output Voltage Ripple, 80 4.2.3 Step-Up (Boost) Converter, 83 4.2.4 Step-Down/Up (Buck–Boost) Converter, 86 4.2.5 DC–DC Converters Applied in Hybrid Vehicle Systems, 90 4.2.5.1 Isolated Buck DC–DC Converter, 90 4.2.5.2 Four-Quadrant DC–DC Converter, 94 63 CONTENTS 4.3 4.4 4.5 DC–AC Inverter, 94 4.3.1 Basic Concepts of DC–AC Inverters, 95 4.3.2 Single-Phase DC–AC Inverter, 99 4.3.3 Three-Phase DC–AC Inverter, 102 Electric Motor Drives, 106 4.4.1 BLDC Motor and Control, 106 4.4.1.1 Operation of BLDC Motor, 106 4.4.1.2 Torque and Rotating Field Production, 107 4.4.1.3 BLDC Motor Control, 108 4.4.1.4 BLDC Motor Torque–Speed Characteristics and Typical Technical Parameters, 113 4.4.1.5 Sensorless BLDC Motor Control, 113 4.4.2 AC Induction Motor and Control, 115 4.4.2.1 Basic Principle of AC Induction Motor Operation, 115 4.4.2.2 Controls of AC Induction Motor, 118 Plug-In Battery Charger Design, 124 4.5.1 Basic Configuration of PHEV/BEV Battery Charger, 124 4.5.2 Power Factor and Correcting Techniques, 125 4.5.3 Controls of Plug-In Charger, 127 References, 129 Energy Storage System Modeling and Control 5.1 5.2 5.3 5.4 ix Introduction, 131 Methods of Determining State of Charge, 133 5.2.1 Current-Based SOC Determination, 133 5.2.2 Voltage-Based SOC Determination, 136 5.2.3 Extended Kalman Filter–Based SOC Determination, 145 5.2.4 SOC Determination Based on Transient Response Characteristics, 147 5.2.5 Fuzzy Logic–Based SOC Determination, 149 5.2.6 Combination of Estimated SOCs by Different Approaches, 151 5.2.7 Further Discussion of SOC Calculations in Hybrid Vehicle Applications, 152 Estimation of Battery Power Availability, 154 5.3.1 PNGV HPPC Power Availability Estimation, 156 5.3.2 Revised PNGV HPPC Power Availability Estimation, 158 5.3.3 Power Availability Estimation Based on Electrical Circuit Equivalent Model, 159 Battery Life Prediction, 165 5.4.1 Aging Behavior and Mechanisms, 165 5.4.2 Definition of State of Life, 167 131 385 STOCHASTIC AND ADAPTIVE CONTROL Solving the following Diophantine equation, we can obtain the quotient and remainder as + c1 q −1 C(q −1 ) a (a − c1 ) = = [1 + (c1 − a1 )q −1 ] + q −2 1 −1 −1 −1 A(q ) + a1 q + a1 q G(q −1 ) = a1 (a1 − c1 ) (B.93) Equating the coefficients of (B.92) and (B.93), we have ⇒ e1 = c1 − a1 E(q −1 ) = + (c1 − a1 )q −1 g0 = a1 (a1 − c1 ) f1 = b0 (c1 − a1 ) (B.94) Thus, the minimum-variance prediction and the variance of the prediction error are yˆ ∗ (k + 2|k) = f0 = b0 and g0 y(k) + (f0 + f1 q −1 )u(k) + c1 q −1 E{[y˜ ∗ (k + 2|k)]} = (1 + e12 )σ (B.95) Taking parameters a1 = −0.9, b0 = 0.5, c1 = 0.7 into the (B.94), we get e1 = −1.6, g0 = 1.44, f0 = 0.5, and f1 = 0.8 The variance of solved prediction error E{[y˜ ∗ (k + 2|k)]} = (1 + e12 )σ = (1 + 1.62 )σ = 3.56σ B.3.1.2 Minimum-Variance Control To derive the minimum-variance control law, we assume that system (B.78) is a minimum-phase system where all zeros are located inside the unit disc The objective of minimum-variance control is to determine a control law which has the following minimum objective function: J = E{[y(k + d) − ydesired (k + d)]2 } = (B.96) Based on minimum-variance prediction, system (B.78) can be expressed as y(k + d) = E(q −1 )ξ(k + d) + G(q −1 )y(k) B(q −1 )E(q −1 ) + u(k) C(q −1 ) C(q −1 ) (B.97) Substituting (B.97) into the objective function (B.96), we have J = E{[y(k + d) − ydesired (k + d)]2 } = E + B(q −1 )E(q −1 ) u(k) − ydesired (k + d) C(q −1 ) E(q −1 )ξ(k + d) + G(q −1 )y(k) C(q −1 ) (B.98) 386 ADVANCED DYNAMIC SYSTEM CONTROL TECHNIQUES Since the term E(q −1 )ξ(k + d) = ξ(k) + e1 ξ(k + 1) + · · · + ed−1 ξ(k + d) in the equation is a random sequence and independent with observed input and output data at time k, k − 1, k − 2, , equation (B.98) is equal to J = E{[E(q −1 )ξ(k + d)]2 } + E + G(q −1 )y(k) C(q −1 ) B(q −1 )E(q −1 ) u(k) − ydesired (k + d) C(q −1 ) (B.99) Without losing generality, we can set ydesired (k + d) = 0, so the minimumvariance control u∗ (k) can be obtained from the equation E G(q −1 )y(k) B(q −1 )E(q −1 ) + u(k) C(q −1 ) C(q −1 ) =0 (B.100) that is, B(q −1 )E(q −1 )u(k) = −G(q −1 )y(k) (B.101) Since the considered system is a minimum-phase system, the polynomial B(q −1 ) has a stable inverse, and the optimal control to have the variance of the control error minimized is G(q −1 )y(k) (B.102) u∗ (k) = − B(q −1 )E(q −1 ) The minimum-variance control law has a feedback form A control system diagram with minimum-variance controller is shown in Fig B-6 Example B-7 Consider a system given by y(k) = 1 + 0.7q −1 u(k − 1) + ξ(k) + 0.5q −1 + 0.2q −1 (B.103) where {ξ(k)} is a sequence of independent random variables with zero mean Determine the minimum-variance control law u∗ (k) Solution: From the system input–output equation, we have the polynomials A q −1 = + 0.5q −1 + 0.2q −1 = + 0.7q −1 + 0.1q −2 C q −1 = (1 + 0.5q −1 ) + 0.7q −1 = + 1.2q −1 + 0.35q −2 B q −1 = + 0.2q −1 d=1 (B.104) 387 STOCHASTIC AND ADAPTIVE CONTROL x(k) Plant C(q –1) A(q –1) y(k) q –d B(q –1) A(q –1) G(q –1) E(q –1) B(q –1) Control law Fig B-6 Minimum-variance control system Solving the following Diophantine equation, we can get the quotient and remainder: + 1.2q −1 + 0.35q −2 C(q −1 ) 0.5 + 0.25q −1 −1 = = + q A(q −1 ) + 0.7q −1 + 0.1q −2 + 0.7q −1 + 0.1q −2 ⇒ E(q −1 )=1 G(q −1 ) = 0.5 + 0.25q (B.105) −1 Thus, the minimum-variance control law is given as u∗ (k) = − B.3.2 0.5(1 + 0.5q −1 )y(k) + 0.2q −1 (B.106) Self-Tuning Control Minimum-variance control provides an effective control method for the system in process and measurement noise presence, while adaptive control techniques are used to deal with the variations of the model parameter and operating environment The fundamental principle of adaptive control is to assess such variations online and then change the control strategy correspondingly to maintain satisfactory control performance Self-tuning control is one of the most applied adaptive control methods, in which the parameters of the system model are estimated online by a recursive parameter estimation method introduced in Appendix A The self-tuning control system shown in Fig B-7 is a feedback control system which consists of three main functions: parameter estimation, control law modification, and control decision Since such an adaptive control strategy requires preforming considerable 388 ADVANCED DYNAMIC SYSTEM CONTROL TECHNIQUES ydesired (k) Reference input – u(k) Controller Plant Output y (k) Parameter Estimation Controller parameter modification Fig B-7 Self-tuning control system online computations and may also include various aspects of stochastic analysis, the controller must adapt faster than the parameter change rates of the plant and/or environment In addition, since the shown adaptive control system is an actual feedback control system, the entire system has to be subject to the stability consideration which usually results in complex analysis of system stability, convergence, and performance This section briefly outlines the widely used minimum-variance self-tuning control Assuming the system described by (B.79), the minimum-variance self-tuning adaptive controller can be designed based on the following procedure: (a) Set up a prediction model of the system as y(k ˆ + d) = G(q −1 )y(k) + F (q −1 )u(k) + E(q −1 )ξ(k + d) (B.107) (b) The corresponding minimum-variance prediction of the system is yˆ ∗ (k + d) = G(q −1 )y(k) + F (q −1 )u(k) = g0 y(k) + g1 y(k − 1) + · · · + gn−1 y(k − n + 1) + f0 u(k) + f1 u(k − 1) + · · · + fm+d−1 u(k − m − d + 1) (B.108) (c) Predetermine f0 = b0 based on the tests or knowledge on the system and establish the relationship between inputs and outputs as y(k) − b0 u(k − d) = φ(k − d)θ (B.109) where θ = [g0 φ(k) = [y(k) · · · gn−1 g1 y(k − 1) u(k − 2) ··· ··· f1 f2 · · · fm+d−1 ]T y(k − n + 1) u(k − 1) u(k − m − d + 1)] (d) Carry out the parameter estimation by a recursive estimation method based on the observed input and output data; the recursive least squares is the commonly used method to perform this task 389 STOCHASTIC AND ADAPTIVE CONTROL (e) Establish the minimum-variance controller based on the estimated parameter θˆ as (B.110) u(k) = − φ(k)θ(k) f0 B.3.3 Model Reference Adaptive Control Model reference adaptive control (MRAC) is another method to adapt the controller to maintain satisfactory system performance according to the changes in the plant or environment The model reference adaptive control system was originally developed at the Massachusetts Institute of Technology (MIT) for aerospace applications, and the parameter adjustment method is called the MIT rule, where the parameter adjustment mechanism is to minimize the error between model output and actual plant output The control action u(k) needs to be within the admissible boundary, and normally it is a linear combination of the model output ym (k), reference input r(k), and system output yp (k) The MIT rule-based MRAC design technique is introduced in this section with the control system diagram shown in Fig B-8 A model reference adaptive controller can be designed based on the following procedure: (a) Consider a single-input, single-output linear system described by yp (s) = G(s)u(s) (B.111) and a reference model of the form ym (s) = Gm (s)r(s) (B.112) (b) Set up the error function between system output and reference model output as e(t) = yp (t) − ym (t) (B.113) ym(t) Reference model Parameter adjustment rule r(t) Reference input u(t) Controller Plant Fig B-8 Adaptive control system yp(t) 390 ADVANCED DYNAMIC SYSTEM CONTROL TECHNIQUES (c) Define the objective function as J (θ) = 12 e2 (t) (B.114) (d) Determine the adaptive control law If the objective function is defined as equation (B.114), the parameter of the controller can be updated in the direction of the negative gradient of J , that is, dθ ∂J ∂(e(t)) = −λ = −λ e(t) dt ∂θ ∂θ (B.115) where ∂e/∂θ is the sensitivity derivative of the system and λ is a parameter that determines the adaption rate Example B-8 Given a system described by yp (s) = kG(s)u(s) (B.116) where the transfer function G(s) is known but the gain k is unknown Assume that the desired system response is ym (s) = km G(s)r(s) and the controller is of the form u(t) = θ1 · r(t) + θ2 r(t), where r(t) is the reference input Determine an adaptive control law based on the MIT rule Solution: The error between the reference model and the actual output can be expressed as e(s) = yp (s) − ym (s) = kG(s)u(s) − km G(s)r(s) = kG(s) θ1 · r(s) + θ2 r(s) s − km G(s)r(s) (B.117) The sensitivity to the controller parameter is ∂(e) k = kG(s)r(s) = y ∂θ1 km m k ym kG(s)r(s) ∂(e) = = ∂θ2 s km s ⇒ ∂(e) k = ∂θ2 km (B.118) ym dt Based on the MIT rule, to make the system response follow the desired response, the controller’s parameter θ is adjusted as follows: ∂J ∂(e) k dθ1 = −λ1 = −λ1 e = −λ1 ym e = −β1 ym e dt ∂θ1 ∂θ1 km dθ2 ∂J ∂(e) k = −λ2 = −λ2 e = −λ2 dt ∂θ2 ∂θ2 km ym dt e = −β2 e ym dt (B.119) 391 STOCHASTIC AND ADAPTIVE CONTROL ym(s) Reference model kmG(s) β – s1 r (s) Π u(s) Π s Π s e(s) yp(s) Plant kG(s) β – s2 – Π Fig B-9 Adaptive control system based on MIT rule Thus, θ1 = −β1 ym e dt θ2 = −β2 ym dt e dt (B.120) The corresponding control system diagram is shown in Fig B-9 MRAC theory and methodologies have been extensively developed since it was successfully applied to solve aerospace control problems in 1950’s In order to improve the stability of a closed-loop control system, MARC design has been mainly based on Lyapunov’s stability theory and Popov’s hyper-stability theory since 1970’s The Lyapunov design approach is to find out the optimal control law that is subject to a Lyapunov function for a given plant so the stability of the closed-loop system is guaranteed; however, the drawback of this approach is that there is no a systematic way of finding a suitable Lyapunov function to specify the adaptive control law On the other hand, Popov’s hyper-stability is concerned with finding conditions that must be satisfied to have the feedback system be globally asymptotically stable These conditions are called Popov integral inequality According to Popov’s hyper-stability theory, the feedback control system is stable if the adaptive control has the closed-loop system satisfy Popov integral inequality Thus the approach from Popov hyper-stability is much more flexible than the Lyapunov approach to design adaptive control law For more detailed materials regarding these two approaches, the interested reader is referred ˚ to the literature (Astrom and Witternmark, 1995; Landau, 1979; Butler, 1992) B.3.4 Model Predictive Control Model predictive control (MPC), referred to as moving-horizon control or receding-horizon control, is an advanced control technology developed in 1980s which has been widely implemented in practical applications (Garcia et al., 1989) MPC can be formulized as follows 392 ADVANCED DYNAMIC SYSTEM CONTROL TECHNIQUES Assume that the system is described by a single-input, single-output model shown as equation (B.78) or the state space model x(k + 1) = Ax(k) + Bm u(k) + Bd w(k) y(k) = Cx(k) + v(k) (B.121) where y(k) is the measurable system output, u(k) is the manipulated system input, w(k) is the measurable disturbances, and v(k) is assumed to be white-noise sequences Model predictive control is to select the manipulated input variables u(k + i|k), i = 1, , p at time k which have the following minimum objective function: p J = m [y(k + i|k) − ysp (k)]2 + u(k + i|k)2 = (B.122) umax ≥ u(k + i − 1|k) ≥ umin i = 1, , m (B.123) umax ≥ i = 1, , m (B.124) i = 1, , p (B.125) i=1 ri i=1 subject to u(k + i − 1|k) ≥ − umax ymax ≥ y(k + i|k) ≥ ymin where p and m < p are the lengths of the system output prediction and the manipulated input horizons, u(k + i|k), i = 1, , p is the set of future manipulated input values which make the objective function minimum, ysp (k) is the setpoint, and is the differencing operator, that is, u(k + i|k) = u(k + i|k) − u(k + i − 1|k) It needs to be emphasized that although the manipulated variables are determined by optimizing the objective function (B.122) over the horizons m, the control action only takes the first step Therefore, the optimization of MPC is a rolling optimization, and the amount of computation is one of concern when the MPC strategy is implemented in practical applications The MPC control scheme is shown in Fig B-10 B.4 FAULT-TOLERANT CONTROL Fault-tolerant control is a set of advanced control methodologies which admit that one or more key components of a physical feedback system will fail and such failures can have a significant impact on system stability or other performance At the simplest level, sensor or actuator failure can be considered, while at a more complex level, subsystem failure needs to be tolerated In the same vein, engineers can also worry about computer hardware and software failure in the system The idea of fault-tolerant control design is to retain the stability and safety of the system while losing some performance of the system in a graceful 393 FAULT-TOLERANT CONTROL Start State-space model At time k Is the system described byinput/output or state-space model? Input/output model At time k Take system input, output measurements Are states measureable? Take system input, output measurements No Set the objective function and control constraints Yes Take the measured states Obtain the states by a state observer Determine the best current and future control actions by solving above optimization problem Set the objective function and control constraints Determine the best current and future control actions by solving above optimization problem Implement the best current control action At time k + Implement the best current control action At time k+1 Fig B-10 Schematic of model predictive control manner To implement this, it may be necessary to reconfigure the control system in real time following the detection of such failures The advancement of hybrid vehicle systems is leading to increasingly complex systems with ever more demanding performance goals Modern hybrid vehicle systems will require that fault detection, isolation, and control reconfiguration be completed in a short time, and the controller will allow the vehicle to maintain adequate levels of performance even with failures in one or more actuators or sensors; furthermore, the higher degrees of autonomous operation may be required to allow for health monitoring and fault tolerance over certain periods of time without human intervention Since a practical HEV/PHEV/EV must have the capability of fault accommodation in order to operate successfully over a period of time, fault-tolerant control strategies are necessary to fulfill the safety requirement Fault-tolerant control is also a topic of immense activity in which a number of different design and analysis approaches have been suggested Some mention of such control strategies is desirable, but it is important to realize the nature of 394 ADVANCED DYNAMIC SYSTEM CONTROL TECHNIQUES fault-tolerant control problems The briefest coverage is given here to illustrate two fault-tolerant control system architectures B.4.1 Hardware Redundant Control In principle, tolerance to control system failures can be improved if two or more strings of sensors, actuators, and microprocessors, each separately capable of satisfactory control, are implemented in parallel The characteristics of a hardware redundant control architecture are that the system consists of multiple information processing units each with the same functional objective The objective may include the generation of control signals and the prediction of system variables One example of hardware redundant control systems is multiple sensors measuring the same quantity, and the best estimate can be obtained by a majority vote A hardware redundant control system is illustrated in Fig B-11 A voting scheme is normally used for redundancy management by comparing control signals to detect and overcome failures in a hardware-redundant-based system With two identical channels, a comparator simply determines whether or not control signals are identical such that a failure can be detected; however, it cannot identify which string has failed In most cases, additional online logics are needed to select the unfailed channel to execute a control task The design tasks of a hardware-redundant-based fault-tolerant control system usually solve the following problems: selection logic, nuisance trips, generic failures, reliability of voting/selection units, control action contention, cross-strapping, increased cost of operation and maintenance, and number of operating channels required for dispatch Since the fault detection algorithm is the core functional algorithm, it has to meet higher standard requirements; it must be sensitive to failures yet insensitive to small operational error, including data lost or interrupted due to noncollocation of sensors or actuators In addition, false indications of failure must be minimized to assure that useful resources are kept online and missions are not aborted prematurely B.4.2 Software Redundant Control A hardware redundant control strategy can protect against control system component failures, but it will increase the cost, make maintenance more difficult, Voting scheme Actuators Redundant processor Interface Main processor Redundant actuators Inputs Section logic Sensors Redundant sensors Fig B-11 Hardware redundant control system Outputs Plant 395 REFERENCES Controller Controller Reference inputs Actuators Inputs Plant Sensors Outputs … … … – Controller n Fault diagnosis Section logic Candidate controller Performance prediction Control change decision Fig B-12 Software redundant control system and does not address failures on plant components such as a battery subsystem, transmission, and motors Furthermore, in the general case, this form of parallelism implies that fault tolerance can only be improved by physically isolating the processors from each other On the other hand, a software redundant control strategy provides the capability of improving the fault tolerance of the control system on the above three aspects with fewer additional components Although hardware redundancy is at the core of most solutions for reliability, uninterrupted operation can also be achieved in control systems through redistribution of the control authority between different functioning actuators rather than through duplication or triplication of those actuators The idea of a software redundant strategy is to utilize different subsets of measurements along with different system models and control algorithms In other words, if a variety of system fault patterns and corresponding fault situations are able to be characterized and some possible algorithms can be selected and simulated based on the particular fault pattern, a decision unit will determine the appropriate control algorithm or appropriate combination of algorithms When the correct algorithm is determined, the control system can be reconstructed against the failures over time If failures occur within the system, the control algorithm can be changed over time Software-based redundancy is also called functional redundancy, which mainly consists of a fault detection or diagnosis unit identifying the failed components, controller change, and selection logic units selecting the controller and control channels based on the performance prediction of the selected controller so that the system will adapt to the failure situation A software redundant control system is illustrated in Fig B-12 REFERENCES ˚ Astrom, K J., and B Witternmark Computer Controlled Systems—Theory and Design Prentice-Hall, Englewood Cliffs, NJ, 1984 ˚ Astrom, K J., and Witternmark, B Adaptive Control , 2nd ed Addison-Wesley, Reading, MA, 1995 396 ADVANCED DYNAMIC SYSTEM CONTROL TECHNIQUES Bellman, R E Dynamic Programming Princeton University Press, Princeton, NJ, 1957 Butler, H Model-Reference Adaptive Control—From Theory to Practice, Prentice-Hall, Englewood Cliffs, NJ, 1992 Huo, B C Automatic Control System, 4th ed Prentic-Hall, Englewood Cliffs, NJ, 1982 Garcia, E C., Prett, M D., and Morari, M “Model Predictive Control: Theory and Practice—A Survey,” Automatic, 25(3), 335–348, 1989 Landau, Y D Adaptive Control: The Model Reference Approach Marcel Dekker, New York, 1979 Pontryagin, L S., et al The Mathematical Theory of Optimal Processes Interscience, New York, 1962 INDEX AC-120 plug-in charger, 280–281 AC-240 plug-in charger, 281 AC induction motor and control, 115 Acceleration, 8, 57–59, 60–61, 206–207, 307–308 Acceleration time calculation, 308 Active suspension control, 267–273 Adaptive control, 381, 387–391 Aerodynamic drag coefficient, 308, 315 Aerodrag factor, 308–309 Ahr capacity, 18, 40, 133–136, 145, 158, 165–168, 170–172, 176–177, 185, 190–192, 280, 296 Air density correction, 308 Anode, 14, 64–66 Anti rollback control, 266 ARX model, 339 ARMAX model, 340, 354 Base vehicle weight, 307 Battery core temperature, 192–196 Battery efficiency, 19–23, 196–197 Battery life, 165–180 Battery thermal control, 262–264 Battery thermal dynamic model, 41, 193 Bipolar junction transistor, 67 Brushless DC (BLDC) motor, 16–18, 32, 106–115 BLDC motor control, 108–115 BLDC motor torque-speed characteristics, 16, 113 Calendar life of battery, 167–172 Cell balancing, 132, 181–192 C-factor, 51 Charge depleting, 132, 280 Charge sustaining, 280 Controllability, 333, 365, 368, 380 Cost function-based optimal energy management strategy, 233–237 Coulombic efficiency, 40, 133–134, 145, 176 Curb Weight, 307 Cycle life of battery, 19–21, 177–180 DC-AC inverter, 65, 94–105 DC-DC converter, 65, 72–94 Delayed plug-in charging, 289 Diesel engine, 12–13, 26–32, 222, 237, 245–247 Diode, 64–65 Drivability, 8, 24, 201, 218, 234, 265, 306–308, 313–319 Introduction to Hybrid Vehicle System Modeling and Control, First Edition Wei Liu © 2013 John Wiley & Sons, Inc Published 2013 by John Wiley & Sons, Inc 397 398 Drive cycles, 7, 300–306 Driving cycle recognition (DCR), 239–240 Driving style recognition (DSR), 239–240 Dynamic programming, 220–223, 241, 294–297 Dynamic response 30–31 See also Response; Transient response Economic Commission for Europe Elementary Urban Cycle (ECE), 303, 305–306 Electrical circuit model of battery, 37, 39–41, 139–141, 145, 164, 193–194 Electric grid, 279, 286–290 Electromagnetic interfere, 32, 124–125 Electromotive force (EMF), 94, 101, 107–108, 115 Emissions, 29–31, 199, 229, 320–323 Engine idle, 28–29, 32–33 Engine torque fluctuation dumping control, 247–252 Energy management, 199–241, 280, 299–300 Energy storage system (ESS), 2, 11, 17–23, 131–197, 312 Extended Kalman filter, 145, 351–353 Extra urban driving cycle (EUDC), 303–305 Faraday constant, 41, 137 Fault-tolerant control, 392–394 Federal test procedures (FTP), 300–303 Final drive, 56–57, 309, 315, 322 Four quadrant DC-DC converter, 94 First-order hold, 338 Frontal area, 59, 308 Fuel cell, 14–15 Fuzzy logic, 149–151, 201–218 Fuzzy logic-based energy management strategy, 201–218 Fuzzy relation, 205–208 Fuzzy reasoning, 206–207, 218, 240 Fuzzy sets and membership functions, 202–203 Gasoline engine, 11–12, 320 Gearbox, 52–53, 309 Generalized least squares (GLS), 348–349 Golden section search, 220–221 Gradeability, 306–307, 309 Gradeability limit, 306 Highway fuel economy test schedule (HWEFT), 303 High-voltage bus spike control, 253–257 HEV/EV traction torque control, 265–266 Hybrid pulse power characterization test (HPPC), 39, 156–162 INDEX Insulated gate bipolar transistor (IGBT), 71–72, 86, 95 Isolated buck DC–DC converter, 90 Kalman filter, 145, 349–353 K-factor, 51 Lead-acid battery, 19–20 Least squares, 141–144, 149, 194, 341–348 Linear discrete system, 334–335 Linear quadratic control, 378–381 Linear time-invariant and time-continuous system, 326–328 Linear time-invariant discrete time stochastic system, 335–340 Lithium-ion battery (Li-ion), 21–22 Lithium-iron phosphate battery (LiFePO4 ), 22–23, 147 Maximum charge power capability, 132, 156–164 Maximum discharge power capability, 132, 156–164 Metal oxide semiconductor field effect transistor (MOSFET), 69–71 Miner’s rule, 178 Minimum variance control, 385 Minimum variance prediction, 382 Model reference adaptive control, 389–391 Model predictive control, 391–392 Nernst equation, 137 New York City driving cycle (NYCC), 302–303 Nickel-cadmium battery (NiCd), 20–21 Nickel-metal hydride battery (NiMH), 21 Numerical stability, 356–357 Observability, 333, 365 Open circuit voltage, 39–40, 136–144 Optimal battery thermal control strategy, 262–264 Optimal control, 9, 262–264, 371–381 Optimal operating points, 220–223 Optimal plug-in charging, 292–297 Output voltage ripple, 80–82, 85, 88 Palmgren–Miner linear damage hypothesis, 178 Parallel HEV, 2–3, 201, 311 Parameter estimation, 141–144, 194, 341–349, 356, 357, 388 Payload, 307 PID control, 28, 31, 59–60, 112–113, 255, 261–262, 266–267, 272 Plug-in charging characteristics, 280–284 Pole placement, 366–370 399 INDEX Pontryagin’s maximum principle, 264, 372–373 Power distribution system, 286 Power factor and the correcting techniques, 125–127 Power split transmission (PST), 24 Prime mover, 11 Proton exchange membrane fuel cell (PEMFC), 14–15 Pulse-width modulation (PWM), 73–74 PHEV/BEV battery charger, 124–128, 280–284 Rainflow cycle counting algorithm, 179 Rapid public charging, 284 Recursive least squares, 141–144, 193–194, 344–348 Regenerative braking, 2, 5–7, 18, 47, 94, 101, 234, 237, 265, 312, 321 Response, 272, 327–8, 390 See also Dynamic response; Transient response Road surface coefficient, 59, 308–309 Roadway recognition (RWR), 239–240 Rolling resistance, 58–59, 61, 307–310, 315 Rule-based energy management strategy, 200–201 Sampling frequency, 335–336 Self-discharge, 19–23, 37, 131, 134, 187, 189 Self-tuning control, 387–388 Series HEV, 2, 222 Series-parallel HEV, Single phase DC-AC inverter, 99 Singular pencil (SP) model, 353 Sizing prime mover, 310 Sizing transmission/gear ratio, 312 Sizing energy storage system, 312 Sliding mode control, 248–253 Solid electrolyte interface (SEI), 167 Solid oxide fuel cell (SOFC), 14 Square-root algorithm, 357–358 State estimation, 145, 349–351 State of charge (SOC), 9, 37, 133–154 State of health (SOH), 165 State of life (SOL), 167–180 Statistical property of least-squares, 342 Step-down (buck) converter, 74 Step-down/up (buck-boost) converter, 86 Step-up (boost) converter, 83 Stochastic and adaptive control, 381 Stochastic process, 326, 336–340 Supercapacitor, 23 See also Ultracapacitor Suspension system model, 269 System poles and zeros, 148–149 Three phase DC-AC inverter, 102 Thermal control of HEV battery system, 258 Thyristor, 65 Transfer function, 59, 149, 270–271, 327–328 Transient response, 119, 147–148 See also Dynamic response; Response UDU T covariance factorization estimation algorithm, 358 Ultracapacitor, 23 See also Supercapacitor United Nations Economic Commission for Europe (UN/ECE), 303, 305–306 See also ECE Urban dynamometer driving schedule (UDDS), 300, 303 Urban dynamometer driving schedule for heavy duty vehicles (HD-UDDS), 303 US06 supplemental federal test procedure (US06), 35–37, 189, 302 Viscous friction, 26–27, 34 Zero-order hold, 338–339 .. .INTRODUCTION TO HYBRID VEHICLE SYSTEM MODELING AND CONTROL INTRODUCTION TO HYBRID VEHICLE SYSTEM MODELING AND CONTROL WEI LIU A JOHN WILEY & SONS, INC., PUBLICATION... Data: Liu, Wei, 1960 Aug 3 0Introduction to hybrid vehicle system modeling & control / Wei Liu p cm Includes bibliographical references and index ISBN 978-1-118-30840-0 Hybrid electric vehicles–Simulation... and two appendices Chapter provides an introduction to hybrid vehicle system architecture, energy flow, and control of a hybrid vehicle system Chapter reviews the main components of a hybrid system