Disturbance Observer for Advanced Motion Control with MATLAB / Simulink

A fulsome and robust presentation of disturbance observers complete with MATLAB sample programs and simulation results

In Disturbance Observer for Advanced Motion Control with MATLAB/Simulink, distinguished electronics engineer Dr. Akira Shimada delivers a comprehensive exploration of the suppression of actual and unknown disturbances. In the book, you’ll find a systematic discussion of the basic theory and design methods of disturbance observers accompanied by instructive MATLAB and Simulink simulation examples.

Included appendices cover the mathematical background of classical, modern, and digital control and ground the reader’s understanding of the more advanced sections. The included material is ideal for students enrolled in courses in advanced motion control, mechatronics system control, electrical drives, motion control, robotics, and aeronautics.

In addition to topics like model predictive control, vibration systems, acceleration control, adaptive observers, and multi-rate sampling, readers will find:

• A thorough introduction to the various types of disturbance observers and the fundamentals of disturbance observers, including disturbance estimation and disturbance rejection
• Comprehensive explorations of stabilized control and coprime factorization, including the derivation of stabilizing controllers
• Practical discussions of disturbance observers in state space, including identity input disturbance observers and identity reaction force observers
• Fulsome treatments of the mathematical foundations of control theory, methods??for measuring and estimating velocities, and the disturbance estimation Kalman filter

Perfect for undergraduate and graduate students with existing knowledge of the fundamentals of control engineering who wish to learn how to design disturbance observers, Disturbance Observer for Advanced Motion Control with MATLAB/Simulink will also benefit professional engineers and researchers studying alternative control theories.

Akira Shimada, PhD, received his PhD. in Engineering from Keio University, Japan, in 1996. He is a Full Professor at Shibaura Institute of Technology, Japan, and has previously been a guest Professor at Chiba University and an Associate Professor at the Polytechnic University, Japan. His current interests include motion control, robotics, control engineering, and free climbing and he is a member of IEEE, SICE, RSJ, and a Senior Member of IEEJ.

Contents

About the Author xv

Preface xvii

About the Companion Website

1 Introduction of Disturbance Observer 1

1.1 Types of Disturbance Observers 1

1.1.1 Introduction 1

1.1.2 Observer and Control System Design Concepts 3

1.2 Format of Example and Use of MATLAB 4

1.2.1 Format of the Example Problem 4

1.2.2 Using MATLAB/Simulink 5

1.3 How This Book Is Organized 5

1.3.1 The Structure of This Document 5

1.3.2 How to Read This Book 6

References 7

2 Basics of Disturbance Observer 9

2.1 What Is Disturbance 9

2.2 How Disturbance Estimation Works 11

2.3 Disturbance Rejection and Acceleration Control System 13

2.3.1 Concept of Disturbance Rejection and Acceleration 13

2.3.2 Different Disturbance Observers Depending on How the Disturbance Is Captured 15

2.3.3 Basic Control System Design 16

2.4 Reaction Force Observer (RFOB) 18

2.4.1 Reaction Force Observer Design 18

2.4.2 Combined Use of DOB and RFOB 20

2.5 Internal Model and Two-degrees-of-freedom Control 24

2.5.1 Internal Model Principle 24
Copyrighted Material xxi

2.5.2 Feedforward Control 28

2.5.3 Control System with Disturbance Observer and Feedforward 29

2.6 Effect of Observation Noise and Modeling Error 31

2.6.1 Effect of Observation Noise 31

2.6.2 Effect of Modeling Error 31

2.6.3 Effect of Viscous Friction 32

2.6.4 Effect of Varying Mass 33

2.7 Real System Modeling 37

2.7.1 dc Motor Torque Control Model 37

2.7.2 Without Current Feedback 38

2.7.3 Relationship Between the Cart Model and Rotary-type Motor 38

2.8 Idea of Robust Control 39

References 41

3 Stabilized Control and Coprime Factorization 45

3.1 Coprime Factorization and Derivation of Stabilizing Controller 45

3.1.1 Derivation of Parameters for Coprime Factorization 46

3.1.2 Stabilizing Controller and Free Parameters 50

3.1.3 Double Coprime Factorization Involving Q(s) 52

3.2 Relationship with Disturbance Observer 52

3.3 Coprime Factorization and Structure of Two-degrees-of-freedom Control System 53

References 56

4 Disturbance Observer in State Space 59

4.1 Identity Input Disturbance Observer 59

4.1.1 How to Design the Identity Input Disturbance Observer in Continuous System 59

4.1.2 Controllability and State Feedback 68

4.1.3 Continuous-time Servo System with Identity Disturbance Observer 69

4.2 Identity Reaction Force Observer 72

4.3 Identity Output Disturbance Observer 75

4.4 Identity Higher Order Disturbance Observer Design 79

4.5 Minimal Order Disturbance Observer 82

4.6 Design of Periodic Disturbance Observer 89

4.7 Observability and Noninput/Output Disturbances 94

4.7.1 Mathematical Model of a DC Motor 94

4.7.2 dc Motor Observable Matrix and Rank 95

4.7.3 Observability of Disturbance Estimation 97

4.7.4 Noninput/Output Disturbance Observer and Control 97

References 100

5 Digital Disturbance Observer Design 101

5.1 Identity Digital Disturbance Observer Design 101

5.2 Confirmation of Separation Theorem 108

5.3 Minimal Order Digital Disturbance Observer 109

5.4 Identity High-order Digital Disturbance Observer 119

References 122

6 Disturbance Observer of Vibrating Systems 123

6.1 Modeling of the Two-inertia System 123

6.2 Vibration Suppression Control in Transfer Function Representation 126

6.3 Disturbance Observer and Stabilization for Two-inertia Systems 129

6.3.1 Observer to Estimate Input Shaft Disturbance τ d 1 129

6.3.2 Observer to Estimate Output Shaft Disturbance τ d 2 132

6.4 Servo System with DOB for Two-inertia Systems 135

6.4.1 Input Shaft Servo System Considering Input Shaft Disturbance
τ d 1 136

6.4.2 Output Shaft Servo System Considering Output Shaft Disturbance
τ d 2 138

References 140

7 Communication Disturbance Observer 141

7.1 Smith Method Overview 141

7.2 Communication Disturbance Observer 142

7.3 Control with Communication DOB Under Disturbance 146

References 149

8 Multirate Disturbance Observer 151

8.1 Multirate System Modeling 151

8.2 Multirate Disturbance Observer (Method 1) 153

8.2.1 Disturbance Observer Design (Method 1) 153

8.2.2 Controller Design Using Multirate Observer (Method 1) 154

8.3 Multirate Disturbance Observer (Method 2) 158

References 161

9 Model Predictive Control with DOB 163

9.1 Model Predictive Control (MPC) 163

9.1.1 Overview of MPC 163

9.1.2 Formulation and Objective Function for the MPC Design 165

9.2 Constraint Descriptions 167

9.2.1 Treatment of Constraints on the Control Input û(k) 168

9.2.2 Constraints on the Control Variable ẑ(k) 169

9.2.3 Constraints on Δû(k) Change in the Control Input 169

9.2.4 Constraints on the Control Inputs and Quantities 170

9.3 MPC System Design 170

9.4 Design of Disturbance Observer-Merged MPC System 174

References 178

10 Kalman Filter with Disturbance Estimation (KFD) 179

10.1 Design of Kalman Filter with Disturbance Estimation 179

10.2 Design of Stationary Kalman Filter with Disturbance Estimation (skfd) 190

10.3 Design of Extended Kalman Filter with Disturbance Estimation (ekfd) 193

References 200

11 Adaptive Disturbance Observer 201

11.1 Structure of an Adaptive Observer 201

11.2 Derivation of Observable Canonical System for Adaptive DOB 202

11.3 Creating State Variable Filter 203

11.4 Design of Kreisselmeier-Type Adaptive Disturbance Observer 208

References 214

12 Methods for Measuring and Estimating Velocities 217

12.1 Importance of Velocity Measurement 217

12.2 Velocity Measurement and Estimation Methods 219

12.2.1 Pseudo-derivative 219

12.2.2 Counting and Timekeeping Methods 220

12.2.3 M∕T Method 222

12.2.4 Synchronous Counting Method 223

12.2.5 Instantaneous Velocity Observer 225

References 227

Appendix A Mathematical Foundations and Control Theory 229

A.1 Mathematics 229

A.1.1 Definition and Calculus of Matrix Exponential Functions 229

A.1.2 Positive Definite Matrix 229

A.1.3 Matrix Rank 230

A.2 Basic Classical Control Theory 230

A.2.1 Poles and Zeros 230

A.2.2 PI Velocity Control 231

A.2.3 PID Position Control System 232

A.2. 4 Final Value and Initial Value Theorems 232

A. 3 Basic Modern Control Theory 233

A.3. 1 State and Output Equations 233

A.3. 2 Solution of the State Equation for the Continuous System 234

A.. 3 Equation of State to Transfer Function 234

A.3. 4 Poles and Zeros of Continuous Systems 234

A.3. 5 Controllability and Observability of Continuous Systems 235

A.3. 6 Duality Theorem 236

A.3. 7 State Feedback Control of Continuous Systems 236

A.3. 8 Servo System Design 243

A. 4 Doyle’s Notation and Double Coprime Factorization 244

A.4. 1 Doyle’s Notation 244

A.4. 2 Confirmation of Double Coprime Factorization 245

A. 5 Foundations of Digital Control Theory 245

A.5. 1 Digital Control and State and Output Equations 245

A.5. 2 Poles and Zeros of Digital Systems 247

A.5. 3 Reachability and Observability of Digital Systems 247

A.5. 4 Digital State Feedback Control System Design 248

A.. 5 Digital Servo System Design 248

A. 6 Representation and Meaning of Optimal Programming 250

A.6. 1 What Is Optimal Programming? 250

A.6. 2 fmincon Function 250

A.6. 3 Example of a Drawing Program 252

References 254

Index 255

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