Disturbance Observer for Advanced Motion Control with MATLAB / Simulink

Akira Shimada, 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.

• About the Author xvPreface xviiAbout the Companion Website xxi1 Introduction of Disturbance Observer 11.1 Types of Disturbance Observers 11.1.1 Introduction 11.1.2 Observer and Control System Design Concepts 31.2 Format of Example and Use of MATLAB 41.2.1 Format of the Example Problem 41.2.2 Using MATLAB/Simulink 51.3 How This Book Is Organized 51.3.1 The Structure of This Document 51.3.2 How to Read This Book 6References 72 Basics of Disturbance Observer 92.1 What Is Disturbance 92.2 How Disturbance Estimation Works 112.3 Disturbance Rejection and Acceleration Control System 132.3.1 Concept of Disturbance Rejection and Acceleration 132.3.2 Different Disturbance Observers Depending on How the Disturbance Is Captured 152.3.3 Basic Control System Design 162.4 Reaction Force Observer (RFOB) 182.4.1 Reaction Force Observer Design 182.4.2 Combined Use of DOB and RFOB 202.5 Internal Model and Two-degrees-of-freedom Control 242.5.1 Internal Model Principle 242.5.2 Feedforward Control 282.5.3 Control System with Disturbance Observer and Feedforward 292.6 Effect of Observation Noise and Modeling Error 312.6.1 Effect of Observation Noise 312.6.2 Effect of Modeling Error 312.6.3 Effect of Viscous Friction 322.6.4 Effect of Varying Mass 332.7 Real System Modeling 372.7.1 DC Motor Torque Control Model 372.7.2 Without Current Feedback 382.7.3 Relationship Between the Cart Model and Rotary-type Motor 382.8 Idea of Robust Control 39References 413 Stabilized Control and Coprime Factorization 453.1 Coprime Factorization and Derivation of Stabilizing Controller 453.1.1 Derivation of Parameters for Coprime Factorization 463.1.2 Stabilizing Controller and Free Parameters 503.1.3 Double Coprime Factorization Involving Q(s) 523.2 Relationship with Disturbance Observer 523.3 Coprime Factorization and Structure of Two-degrees-of-freedom Control System 53References 564 Disturbance Observer in State Space 594.1 Identity Input Disturbance Observer 594.1.1 How to Design the Identity Input Disturbance Observer in Continuous System 594.1.2 Controllability and State Feedback 684.1.3 Continuous-time Servo System with Identity Disturbance Observer 694.2 Identity Reaction Force Observer 724.3 Identity Output Disturbance Observer 754.4 Identity Higher Order Disturbance Observer Design 794.5 Minimal Order Disturbance Observer 824.6 Design of Periodic Disturbance Observer 894.7 Observability and Noninput/Output Disturbances 944.7.1 Mathematical Model of a DC Motor 944.7.2 DC Motor Observable Matrix and Rank 954.7.3 Observability of Disturbance Estimation 974.7.4 Noninput/Output Disturbance Observer and Control 97References 1005 Digital Disturbance Observer Design 1015.1 Identity Digital Disturbance Observer Design 1015.2 Confirmation of Separation Theorem 1085.3 Minimal Order Digital Disturbance Observer 1095.4 Identity High-order Digital Disturbance Observer 119References 1226 Disturbance Observer of Vibrating Systems 1236.1 Modeling of the Two-inertia System 1236.2 Vibration Suppression Control in Transfer Function Representation 1266.3 Disturbance Observer and Stabilization for Two-inertia Systems 1296.3.1 Observer to Estimate Input Shaft Disturbance τd1 1296.3.2 Observer to Estimate Output Shaft Disturbance τd2 1326.4 Servo System with DOB for Two-inertia Systems 1356.4.1 Input Shaft Servo System Considering Input Shaft Disturbance τd1 1366.4.2 Output Shaft Servo System Considering Output Shaft Disturbance τd2 138References 1407 Communication Disturbance Observer 1417.1 Smith Method Overview 1417.2 Communication Disturbance Observer 1427.3 Control with Communication DOB Under Disturbance 146References 1498 Multirate Disturbance Observer 1518.1 Multirate System Modeling 1518.2 Multirate Disturbance Observer (Method 1) 1538.2.1 Disturbance Observer Design (Method 1) 1538.2.2 Controller Design Using Multirate Observer (Method 1) 1548.3 Multirate Disturbance Observer (Method 2) 158References 1619 Model Predictive Control with DOB 1639.1 Model Predictive Control (MPC) 1639.1.1 Overview of MPC 1639.1.2 Formulation and Objective Function for the MPC Design 1659.2 Constraint Descriptions 1679.2.1 Treatment of Constraints on the Control Input û(k) 1689.2.2 Constraints on the Control Variable ẑ(k) 1699.2.3 Constraints on Δû(k) Change in the Control Input 1699.2.4 Constraints on the Control Inputs and Quantities 1709.3 MPC System Design 1709.4 Design of Disturbance Observer-Merged MPC System 174References 17810 Kalman Filter with Disturbance Estimation (KFD) 17910.1 Design of Kalman Filter with Disturbance Estimation 17910.2 Design of Stationary Kalman Filter with Disturbance Estimation (skfd) 19010.3 Design of Extended Kalman Filter with Disturbance Estimation (ekfd) 193References 20011 Adaptive Disturbance Observer 20111.1 Structure of an Adaptive Observer 20111.2 Derivation of Observable Canonical System for Adaptive DOB 20211.3 Creating State Variable Filter 20311.4 Design of Kreisselmeier-Type Adaptive Disturbance Observer 208References 21412 Methods for Measuring and Estimating Velocities 21712.1 Importance of Velocity Measurement 21712.2 Velocity Measurement and Estimation Methods 21912.2.1 Pseudo-derivative 21912.2.2 Counting and Timekeeping Methods 22012.2.3 M∕T Method 22212.2.4 Synchronous Counting Method 22312.2.5 Instantaneous Velocity Observer 225References 227Appendix A Mathematical Foundations and Control Theory 229A.1 Mathematics 229A.1.1 Definition and Calculus of Matrix Exponential Functions 229A.1.2 Positive Definite Matrix 229A.1.3 Matrix Rank 230A.2 Basic Classical Control Theory 230A.2.1 Poles and Zeros 230A.2.2 PI Velocity Control 231A.2.3 PID Position Control System 232A.2.4 Final Value and Initial Value Theorems 232A.3 Basic Modern Control Theory 233A.3.1 State and Output Equations 233A.3.2 Solution of the State Equation for the Continuous System 234A.3.3 Equation of State to Transfer Function 234A.3.4 Poles and Zeros of Continuous Systems 234A.3.5 Controllability and Observability of Continuous Systems 235A.3.6 Duality Theorem 236A.3.7 State Feedback Control of Continuous Systems 236A.3.8 Servo System Design 243A.4 Doyle’s Notation and Double Coprime Factorization 244A.4.1 Doyle’s Notation 244A.4.2 Confirmation of Double Coprime Factorization 245A.5 Foundations of Digital Control Theory 245A.5.1 Digital Control and State and Output Equations 245A.5.2 Poles and Zeros of Digital Systems 247A.5.3 Reachability and Observability of Digital Systems 247A.5.4 Digital State Feedback Control System Design 248A.5.5 Digital Servo System Design 248A.6 Representation and Meaning of Optimal Programming 250A.6.1 What Is Optimal Programming? 250A.6.2 fmincon Function 250A.6.3 Example of a Drawing Program 252References 254Index 255