Gear shift strategies for automotive transmissions


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Gear shift strategies for automotive transmissions
Citation for published version (APA): Ngo, D. V. (2012). Gear shift strategies for automotive transmissions. [Phd Thesis 1 (Research TU/e / Graduation TU/e), Mechanical Engineering]. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR735458
DOI: 10.6100/IR735458
Document status and date: Published: 01/01/2012
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Download date: 13. Jul. 2022

Gear Shift Strategies for
Automotive Transmissions
Ngo Dac Viet

Doctoral committee: prof.dr. L.P.H. de Goey (chairman) prof.dr.ir. M. Steinbuch (supervisor) dr.ir. T. Hofman (co-supervisor) prof. Hyunsoo Kim, PhD (Sungkyunkwan University) prof. Huei Peng, PhD (University of Michigan) prof.dr.ir. P.P.J. van den Bosch (Eindhoven University of Technology) dr.ir. A.F.A. Serrarens (Drivetrain Innovations B.V.) dr.ir. P.A. Veenhuizen (HAN University of Applied Sciences)
The research leading to this dissertation is part of the project ‘Euro Hybrid’, which is a research project of Drivetrain Innovations B.V., together with Eindhoven University of Technology, The Netherlands. The project is financially supported by Dutch government through AgentschapNL.
Gear Shift Strategies for Automotive Transmissions / by Ngo Dac Viet – Eindhoven University of Technology, 2012 – PhD dissertation. A catalogue record is available from the Eindhoven University of Technology Library. ISBN: 978-90-386-3222-3 Copyright c 2012 by Ngo Dac Viet. All rights reserved. This dissertation was prepared with the PDFLATEX documentation system. Cover design: Oranje Vormgevers, Eindhoven, The Netherlands. Reproduction: Ipskamp Drukkers B.V., Enschede, The Netherlands.

Gear Shift Strategies for
Automotive Transmissions
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan de Technische Universiteit Eindhoven, op gezag van de rector magnificus, prof.dr.ir. C.J. van Duijn, voor een commissie aangewezen door het College voor Promoties
in het openbaar te verdedigen op woensdag 26 september 2012 om 16.00 uur
door
Ngo Dac Viet
geboren te Thua Thien Hue, Vietnam

Dit proefschrift is goedgekeurd door de promotor:
prof.dr.ir. M. Steinbuch
Copromotor: dr.ir. T. Hofman

Summary
Gear Shift Strategies for Automotive Transmissions
The development history of automotive engineering has shown the essential role of transmissions in road vehicles primarily powered by internal combustion engines. The engine with its physical constraints on the torque and speed requires a transmission to have its power converted to the drive power demand at the wheels. Under dynamic driving conditions, the transmission is required to shift in order to match the engine power with the changing drive power. Furthermore, a gear shift decision is expected to be consistent such that the vehicle can remain in the next gear for a period of time without deteriorating the acceleration capability. Therefore, an optimal conversion of the engine power plays a key role in improving the fuel economy and driveability. Moreover, the consequences of assumptions related to the discrete state variable-dependent losses, e.g. gear shift, clutch slippage and engine start, and their effect on the gear shift control strategies are necessary to be analyzed to yield insights into the fuel usage.
The first part of the dissertation deals with the design of gear shift strategies for electronically controlled discrete ratio transmissions used in both conventional vehicles and Hybrid Electric Vehicles (HEVs). For conventional vehicles, together with the fuel economy, the driveability is systematically addressed in a Dynamic Programming (DP) based optimal gear shift strategy by three methods: i) the weighted inverse of power reserve, ii) the constant power reserve, and iii) the variable power reserve. In addition, a Stochastic Dynamic Programming (SDP) algorithm is utilized to optimize the gear shift strategy, subject to a stochastic distribution of the power request, in order to minimize the expected fuel consumption over an infinite horizon. Hence, the SDP-based gear shift strategy intrinsically respects the driveability and is realtime implementable. By performing a comparative analysis of all proposed gear shift methods, it is shown that the variable power reserve method achieves the highest fuel economy without deteriorating the driveability. Moreover, for HEVs, a novel fuel-optimal control algorithm, consisting of the continuous power split and discrete gear shift, engine on-off problems, based on a combination of DP and Pontryagin’s Minimum Principle (PMP) is developed for the corresponding hybrid dynamical system. This so-called DP-PMP gear shift control approach benchmarks the development of an online implementable control strategy in
v

vi

Summary

terms of the optimal tradeoff between calculation accuracy and computational efficiency. Driven by an ultimate goal of realizing an online gear shift strategy, a gear shift map design methodology for discrete ratio transmissions is developed, which is applied for both conventional vehicles and HEVs. The design methodology uses an optimal gear shift algorithm as a basis to derive the optimal gear shift patterns. Accordingly, statistical theory is applied to analyze the optimal gear shift patterns in order to extract the time-invariant shift rules. This alternative two-step design procedure makes the gear shift map: i) improve the fuel economy and driveability, ii) be consistent and robust with respect to shift busyness, and iii) be realtime implementable. The design process is flexible and time efficient such that an applicability to various powertrain systems configured with discrete ratio transmissions is possible. Furthermore, the study in this dissertation addresses the trend of utilizing route information in the powertrain control system by proposing an integrated predictive gear shift strategy concept, consisting of a velocity algorithm and a predictive algorithm. The velocity algorithm improves the fuel economy considerably (in simulation) by proposing a fuel-optimal velocity trajectory over a certain driving horizon for the vehicle to follow. The predictive algorithm successfully utilizes a predefined velocity profile over a certain horizon in order to realize a fuel economy improvement very close to that of the globally optimal algorithm (DP).
In the second part of the dissertation, the energetic losses, involved with the gear shift and engine start events in automated manual transmission-based HEVs, are modeled. The effect of these losses on the control strategies and fuel consumption for (non)powershift transmission technologies is investigated. Regarding the gear shift loss, the study discloses a perception of a fuel-efficient advantage of the powershift transmissions over the non-powershift ones applied for passenger HEVs. It is also shown that the engine start loss can not be ignored in seeking a fair evaluation of the fuel economy. Moreover, the sensitivity study of the fuel consumption with respect to the prediction horizon reveals that a predictive energy management strategy can realize the highest achievable fuel economy with a horizon of a few seconds ahead. The last part of the dissertation focuses on investigating the sensitivity of an optimal gear shift strategy to the relevant control design objectives, i.e. fuel economy, driveability and comfort. A singular value decomposition based method is introduced to analyze the possible correlations and interdependencies among the design objectives. This allows that some of the possible dependent design objective(s) can be removed from the objective function of the corresponding optimal control problem, hence thereby reducing the design complexity.

Contents

Summary

v

1 Introduction

1

1.1 Automotive Transmissions . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 Technology Trends . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4 Objectives and Contributions . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 Outline of The Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Optimal Gear Shift Strategies for Conventional Vehicles

17

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.1.1 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Fuel-Optimal Gear Shift Strategy . . . . . . . . . . . . . . . . . . . . . . 20

2.2.1 Powertrain Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2.2 Powertrain System Dynamics . . . . . . . . . . . . . . . . . . . . 22

2.2.3 Optimal Gear Shift Control Problem . . . . . . . . . . . . . . . . 23

2.2.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Driveability-Optimal Gear Shift Strategy . . . . . . . . . . . . . . . . . . 26

2.3.1 Driveability Definition . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.2 Method 1: The Weighted Inverse of Power Reserve . . . . . . . . 27

2.3.3 Method 2: The Constant Power Reserve . . . . . . . . . . . . . . 28

2.3.4 Method 3: The Variable Power Reserve . . . . . . . . . . . . . . . 29

2.3.5 Comparison of Three Methods . . . . . . . . . . . . . . . . . . . . 35

2.4 Stochastic Gear Shift Strategy . . . . . . . . . . . . . . . . . . . . . . . . 37

2.4.1 Stochastic Modeling of Power Request . . . . . . . . . . . . . . . 37

2.4.2 Stochastic Gear Shift Algorithm . . . . . . . . . . . . . . . . . . . 40

2.4.3 Simulation Results and Discussions . . . . . . . . . . . . . . . . . 41

2.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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Summary

3 Optimal Gear Shift Strategies for Hybrid Electric Vehicles

45

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Powertrain Modeling and Dynamics . . . . . . . . . . . . . . . . . . . . . 47

3.2.1 Powertrain Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.2.2 Powertrain System Dynamics . . . . . . . . . . . . . . . . . . . . 50

3.3 Optimal Gear Shift Strategy without Start-Stop Functionality . . . . . . 51

3.3.1 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . 52

3.3.2 Dynamic Programming-Pontryagin’s Minimum Principle . . . . . 53

3.4 Optimal Gear Shift Strategy with Start-Stop Functionality . . . . . . . . 57

3.4.1 Dynamic Programming . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4.2 Dynamic Programming-Pontryagin’s Minimum Principle . . . . . 58

3.5 Simulation Results and Discussions . . . . . . . . . . . . . . . . . . . . . 60

3.5.1 Baseline Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5.2 HEV without the Start-Stop Functionality . . . . . . . . . . . . . 63

3.5.3 HEV with the Start-Stop Functionality . . . . . . . . . . . . . . . 65

3.5.4 Simulation Results on FTP75 . . . . . . . . . . . . . . . . . . . . 66

3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4 Gear Shift Map Design Methodology

67

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.2 Powertrain Modeling and Dynamics . . . . . . . . . . . . . . . . . . . . . 70

4.2.1 Powertrain Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.2.2 Powertrain System Dynamics . . . . . . . . . . . . . . . . . . . . 72

4.3 Analysis of Gear Shift Contribution to Fuel Economy . . . . . . . . . . . 73

4.3.1 Conventional Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.3.2 Hybrid Electric Vehicle . . . . . . . . . . . . . . . . . . . . . . . . 74

4.4 Gear Shift Map Design for Conventional Vehicles . . . . . . . . . . . . . 77

4.4.1 Acquisition of Optimal Gear Shift Data . . . . . . . . . . . . . . 78

4.4.2 Analysis of Shift Data . . . . . . . . . . . . . . . . . . . . . . . . 79

4.4.3 Shift Map Verification . . . . . . . . . . . . . . . . . . . . . . . . 82

4.5 Gear Shift Map Design for Hybrid Electric Vehicles . . . . . . . . . . . . 83

4.5.1 Gear Shift Map for Hybrid Mode . . . . . . . . . . . . . . . . . . 84

4.5.2 Gear Shift Map for E Mode . . . . . . . . . . . . . . . . . . . . . 86

4.5.3 Gear Downshift Map for Regenerative Mode . . . . . . . . . . . . 87

4.5.4 Shift Map Verification . . . . . . . . . . . . . . . . . . . . . . . . 87

4.6 Experimental Validation on Conventional Vehicle . . . . . . . . . . . . . 89

4.6.1 Gear Shift Map Generation . . . . . . . . . . . . . . . . . . . . . 90

4.6.2 Description of Gear Shift Pattern . . . . . . . . . . . . . . . . . . 90

4.6.3 Validation in Simulation Environment . . . . . . . . . . . . . . . 92

4.6.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Contents

ix

5 Integrated Predictive Gear Shift Strategy

97

5.1 Benefits of The Preview Route Information . . . . . . . . . . . . . . . . . 97

5.2 Powertrain Modeling and Dynamics . . . . . . . . . . . . . . . . . . . . . 99

5.2.1 Powertrain Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.2.2 Powertrain System Dynamics . . . . . . . . . . . . . . . . . . . . 102

5.3 Predictive Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.3.1 Model Predictive Control . . . . . . . . . . . . . . . . . . . . . . . 102

5.3.2 Predictive Gear Shift Problem . . . . . . . . . . . . . . . . . . . . 103

5.3.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.4 Velocity Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.4.1 Travel Requirements on a Preview Route Segment . . . . . . . . . 107

5.4.2 Optimal Velocity Problem . . . . . . . . . . . . . . . . . . . . . . 107

5.5 Implementation of the Velocity Algorithm . . . . . . . . . . . . . . . . . 109

5.5.1 Discretization of Vehicle Longitudinal Dynamics . . . . . . . . . . 109

5.5.2 Decoupling of Velocity Algorithm . . . . . . . . . . . . . . . . . . 110

5.5.3 Driving Horizon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.5.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.6 Integrated Predictive Gear Shift Strategy . . . . . . . . . . . . . . . . . . 114

5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6 Effect of Gear Shift and Engine Start Losses

117

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6.2 Hybrid Powertrain Model . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.3 Hybrid Powertrain Control Algorithm . . . . . . . . . . . . . . . . . . . . 121

6.3.1 Optimal Control Problem Formulation . . . . . . . . . . . . . . . 121

6.3.2 Gear Shift Command Sensitivity . . . . . . . . . . . . . . . . . . 123

6.3.3 Gear Shift Hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . 123

6.4 Gear Shift Loss Model and Control Problem . . . . . . . . . . . . . . . . 125

6.4.1 Gear Shift Loss Model . . . . . . . . . . . . . . . . . . . . . . . . 125

6.4.2 Optimal Control Problem with Gear Shift Loss . . . . . . . . . . 128

6.4.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.5 Engine Start Loss Model and Control Problem . . . . . . . . . . . . . . . 131

6.5.1 Engine Start Loss Model . . . . . . . . . . . . . . . . . . . . . . . 131

6.5.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.6 Prediction Horizon Sensitivity Study . . . . . . . . . . . . . . . . . . . . 134

6.6.1 Predictive Control Algorithm . . . . . . . . . . . . . . . . . . . . 134

6.6.2 Simulation Results and Discussions . . . . . . . . . . . . . . . . . 135

6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

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Gear shift strategies for automotive transmissions