Modeling, Design, Testing and Control of a Two-Stage Actuation Mechanism using Piezoelectric

230 Pages·2005·3.09 MB·English

by  Vijay Neelakantan

MODELING, DESIGN, TESTING AND CONTROL OF A TWO-STAGE
ACTUATION MECHANISM USING PIEZOELECTRIC ACTUATORS
FOR AUTOMOTIVE APPLICATIONS

DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University

By
Vijay Anand Neelakantan, B.Tech., M.S.
* * * * *

The Ohio State University
2005

Approved by

Dissertation Committee:

Dr. Gregory Washington, Adviser
Adviser
Dr. Giorgio Rizzoni
Mechanical Engineering Graduate Program
Dr. Krishnaswamy Srinivasan

Dr. Vadim Utkin
ABSTRACT

High bandwidth actuation systems capable of simultaneously producing relatively
large forces and displacements are required for use in automobiles and other industrial
applications. Conventional hydraulic actuation mechanisms used in automotive brakes
and clutches are complex, inefficient and have poor control robustness. For instance, the
hydraulic clutch actuation mechanism used in automatic transmissions requires pumping
hardware that derives power from the engine. Along with inefficient torque converters
these systems lead to reduced fuel economy, controllability issues and other
disadvantages. Therefore, using advanced technologies to develop and implement novel
devices, as replacements for the conventional hydraulic actuation mechanisms will
improve the vehicle fuel economy significantly. This thesis presents the concept, design,
development, modeling, testing and control of a novel two-stage hybrid actuation
mechanism by combining classical actuators like DC motors and advanced smart material
actuators like piezoelectric stack actuators. This two-stage mechanism takes advantage of
the unique stiffness (force-stroke) characteristic of a typical clutch or a brake engagement
process. This two-stage mechanism is modeled and designed by splitting the system into
two operating regimes, namely the stroke phase and the force phase. Importance is placed
on modeling the nonlinearities like the hysteresis property of piezoelectric actuators and
techniques to overcome it using appropriate analysis and control methodologies. Also a
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technique to estimate force based on the charge stored in the piezoactuator is discussed,
which leads to the elimination of the mechanical force sensor. A simple laboratory
prototype experimental setup is built to demonstrate the system functioning and to test
the different control strategies. A major part of this research includes the development of
robust control methodologies using advanced concepts like Internal Model Control
(IMC), Model Predictive Control (MPC) and a new strategy called Model Predictive
Sliding Mode Control (MPSMC). The different control strategies are used to guide the
two-stage actuation system to track time-varying reference force inputs. The IMC
concept is used to develop a robust controller based on the uncertainty-bound on the
system model. MPC is used to produce a sub-optimal controller that uses a receding-
horizon window for future prediction of system behavior. The new concept MPSMC is
developed to overcome the limitations of the conventional discrete-time sliding mode
control. In this method, the system is forced to reach the sliding mode in a smooth sub-
optimal trajectory. This optimization is carried out using MPC. Experimental results are
highlighted in each case comparing the effectiveness of the different methods.

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Dedicated to

my beloved grandfather Shri V. Natarajan
for his love, encouragement and support

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ACKNOWLEDGMENTS

I express my sincere thanks to my advisor Prof. Gregory Washington, for all his
guidance, support and encouragement throughout my graduate studies. His expertise,
knowledge, advice and comments were priceless. I admire his vision and ability to look at
things in a bigger perspective.
I express my sincere gratitude to the personnel in the Powertrain Systems
Research Lab at General Motors R&D for offering me a great opportunity to work with
them. This research would not have been possible without their financial and technical
support. I especially would like to thank Dr. Patrick Usoro, Dr. Norman Bucknor, Dr.
Chi-Kuan Kao and Dr. Hazem Ezzat for all the confidence they had in me to carry out the
research for this thesis. I express my gratitude to Prof Giorgio Rizzoni, Prof
Krishnaswamy Srinivasan and Prof Vadim Utkin for participating in my doctoral
dissertation committee in spite of their busy schedules.
In addition, I thank Amitesh, Farzad, Jun-Kyu, LeAnn, Leon, Dr. Yoon and all
other past members of the Intelligent Structures and Systems Lab for their invaluable
help and comradeship during graduate school.
I thank my family in India for their wonderful support throughout my life, and I
thank the Almighty for his blessings.
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VITA
May 06, 1979……………………………… Born – Nagapattinam, Tamil Nadu, India
July 2000…………………………………... B.Tech, Mechanical Engineering
Indian Institute of Technology, Madras
Chennai, India
March 2003………………………………… M.S., Mechanical Engineering
The Ohio State University, Columbus
Ohio, USA
Sep 2000 – Present………………………… Graduate Research Associate
Department of Mechanical Engineering
The Ohio State University

FIELDS OF STUDY
Major Field: Mechanical Engineering
Major Areas of Specialization: Dynamic Systems, Smart Materials and Control Systems

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TABLE OF CONTENTS
Page
Abstract...............................................................................................................................ii
Dedication..........................................................................................................................iv
Acknowledgments................................................................................................................v
Vita.....................................................................................................................................vi
List of Figures....................................................................................................................xi
List of Tables..................................................................................................................xvii

Chapters:
1. INTRODUCTION..................................................................................................1
1.1 Motivation......................................................................................................1
1.2 Introduction to Smart Material Systems and Structures................................6
1.3 Literature Review...........................................................................................9
1.3.1 Existing Controllable Clutch and Brake Actuation Technologies.....9
1.3.2 Piezoelectric Actuator System Modeling.........................................12
1.3.3 Advanced Control Strategies...........................................................16
1.4 Research Objectives.....................................................................................23
1.5 Outline of Subsequent Chapters...................................................................24

2. TWO-STAGE CLUTCH AND BRAKE ACTUATION MECHANISM............25
2.1 Clutch/Brake Actuation Requirements........................................................25
2.2 Alternative Clutch/Brake Actuation Mechanisms.......................................29
2.2.1 MRF (Magneto-Rheological Fluid) Clutch.....................................30
2.2.2 Magnetic Particle Clutch..................................................................31
2.2.3 Electromagnetic Clutch....................................................................31
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2.2.4 Magnetic Hysteresis and Eddy Current Clutch................................32
2.2.5 Electrical Clutching and Braking System........................................32
2.2.6 Smart Material Clutches and Brakes................................................34
2.2.7 Pneumatic Clutches..........................................................................36
2.3 Two Stage Clutch and Brake Actuation System..........................................36
2.3.1 Two-Stage Actuation Concept.........................................................36
2.3.2 Two Stage Clutch/Brake Actuator - System Description.................40

3. DYNAMIC MODELING AND DESIGN OF TWO-STAGE ACTUATION
SYSTEM...............................................................................................................46
3.1 Dynamic Model Development.....................................................................46
3.1.1 Analysis of Stroke Phase Dynamics................................................48
3.1.2 Analysis of Force Phase Dynamics..................................................55
3.2 Piezoelectric Actuator Modeling.................................................................59
3.2.1 Domain-Wall Model........................................................................59
3.2.2 Preisach Model.................................................................................64
3.2.3 Variable Delay and Gain Model......................................................69
3.3 Experimental Setup......................................................................................73
3.3.1 Model Verification...........................................................................75
3.4 Force Measurement/Estimation without Load Cell.....................................79

4. ROBUST INTERNAL MODEL CONTROL OF SYSTEM................................88
4.1 Introduction..................................................................................................88
4.2 Limitations of Classical Controller Structure..............................................91
4.3 IMC Analysis...............................................................................................95
4.4 IMC Design Procedure................................................................................97
4.4.1 IMC Design Example 1.................................................................102
4.4.2 IMC Design Example 2.................................................................104
4.5 PID Tuning using IMC..............................................................................106
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4.5.1 IMC-based PID tuning Example 1.................................................109
4.6 Variable Delay and Gain Model for the Piezoactuator System.................110
4.7 Internal Model Control of Force Phase of the System...............................113
4.7.1 PID Gains.......................................................................................116
4.8 Experimental results and Discussion.........................................................118

5. MODEL PREDICTIVE CONTROL OF SYSTEM...........................................125
5.1 Introduction................................................................................................125
5.2 Math Background and Notations for MPC................................................129
5.2.1 Discrete Time Systems..................................................................129
5.2.1.1 Z-Transform....................................................................130
5.2.1.2 Transfer Function Model................................................130
5.2.1.3 State Space Models.........................................................132
5.2.2 State Vectors of Past, Present and Future Values..........................133
5.2.3 Toeplitz and Hankel Matrices........................................................134
5.2.3.1 Multiplication of polynomials.........................................135
5.2.3.2 Inversion of Toeplitz Matrix...........................................137
5.3 Model Predictive Control Formulation......................................................138
5.3.1 Transfer Function Model...............................................................138
5.3.1.1 MPC of Systems with Transfer Function Model............140
5.3.2 State Space Model..........................................................................141
5.3.2.1 MPC Algorithm for Systems with State Space Model...142
5.4 Stability Analysis of MPC.........................................................................144
5.5 Model Predictive Control of Dual Stage Actuation System......................145
5.6 Experimental Results.................................................................................152
5.6.1 Control Law Implementation and Testing.....................................152
5.7 Concluding Remarks..................................................................................154

6. MODEL PREDICTIVE SLIDING MODE CONTROL OF SYSTEM.............159
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6.1 Introduction................................................................................................160
6.2 Conventional Discrete-Time Sliding Mode Control..................................165
6.2.1 Limitations of Conventional DSMC..............................................168
6.3 Model Predictive Sliding Mode Control – Method 1................................169
6.3.1 Simulation Example 1....................................................................174
6.3.2 Experimental Result.......................................................................178
6.4 Model Predictive Sliding Mode Control – Method 2................................185
6.4.1 Equivalent Control Augmentation.................................................187
6.4.2 Simulation Example 2....................................................................189
6.4.3 Experimental Result.......................................................................192
6.5 Concluding Remarks..................................................................................197

7. CONCLUSIONS.................................................................................................199
7.1 Summary....................................................................................................199
7.2 Scope for Future Work................................................................................204

REFERENCES................................................................................................................206
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