State Feedback Control and Kalman Filtering with MATLAB/Simulink Tutorials

Liuping Wang, PhD, is a Professor of Control Engineering at RMIT University, Australia. She obtained her PhD from the Department of Control Engineering at the University of Sheffield, UK. Professor Wang gained substantial process control experience by working in the Chemical Engineering Department at the University of Toronto, Canada, and the Center for Integrated Dynamics at the University of Newcastle, Australia. She is the author of five books in systems and control. Robin Ping Guan, PhD, obtained his Masters in Electrical Engineering from the University of Melbourne, Australia, in 2014 and his PhD from RMIT University, Australia in 2019. He is currently a research fellow in RMIT University.

• Author Biography xiiiPreface xvAcknowledgments xxiList of Symbols and Acronyms xxiiiAbout the Companion Website xxvPart I Continuous-time State Feedback Control 11 State Feedback Controller and Observer Design 31.1 Introduction 31.2 Motivation for Going Beyond PID Control 41.3 Basics in State Feedback Control 121.3.1 State Feedback Control 121.3.2 Controllability 181.3.3 Food for Thought 211.4 Pole-assignment Controller 211.4.1 The Design Method 211.4.2 Similarity Transformation for Controller Design 241.4.3 MATLAB Tutorial on Pole-assignment Controller 271.4.4 Food for Thought 291.5 Linear Quadratic Regulator (LQR) Design 291.5.1 Motivational Example 291.5.2 Linear Quadratic Regulator Design 321.5.3 Selection of Q and R Matrices 341.5.4 LQR with Prescribed Degree of Stability 391.5.5 Food for Thought 461.6 Observer Design 471.6.1 Motivational Example for Observer 471.6.2 Observer Design 501.6.3 Observability 531.6.4 Duality between Controller and Observer 551.6.5 Observer Implementation 561.6.6 Food for Thought 571.7 State Estimate Feedback Control System 581.7.1 State Estimate Feedback Control 581.7.2 Separation Principle 591.7.3 Food for Thought 601.8 Summary 611.9 Further Reading 62Problems 632 Practical Multivariable Controllers in Continuous-time 672.1 Introduction 672.2 Practical Controller I: Integral Action via Controller Design 682.2.1 The Original Control Law 682.2.2 Integrator Windup Scenarios 692.2.3 Proposed Practical Multivariable Controller 712.2.4 Anti-windup Implementation 742.2.5 MATLAB Tutorial on Design and Implementation 772.2.6 Application to Drum Boiler Control 852.2.7 Food for Thought 912.3 Practical Controller II: Integral Action via Observer Design 922.3.1 Integral Control via Disturbance Estimation 922.3.2 Anti-windup Mechanism 952.3.3 MATLAB Tutorial on Design and Implementation 962.3.4 Application to Sugar Mill Control 1022.3.5 Design for Systems with Known States 1032.3.6 Food for Thought 1062.4 Drive Train Control of aWind Turbine 1072.4.1 Modelling of Wind Turbine’s Drive Train 1072.4.2 Configuration of The Control System 1102.4.3 Design Method I 1112.4.4 Design Method II 1152.4.5 MATLAB Tutorial on Design Method II 1162.4.6 Food for Thought 1212.5 Summary 1212.6 Further Reading 122Problems 122Part II Discrete-time State Feedback Control 1273 Introduction to Discrete-time Systems 1293.1 Introduction 1293.2 Discretization of Continuous-time Models 1303.2.1 Sampling of a Continuous-time Model 1303.2.2 Stability of Discrete-time System 1333.2.3 Examples of Discrete-time Models from Sampling 1343.2.4 Food for Thoughts 1413.3 Input and Output Discrete-time Models 1423.3.1 Input and Output Models 1423.3.2 Finite Impulse Response and Step Response Models 1443.3.3 Non-minimal State Space Realization 1483.3.4 Food for Thought 1483.4 z-Transforms 1493.4.1 z-Transforms for Commonly Used Signals 1493.4.2 z-Transfer Functions 1523.4.3 Food for Thought 1543.5 Summary 1553.6 Further Reading 156Problems 1564 Discrete-time State Feedback Control 1614.1 Introduction 1614.2 Discrete-time State Feedback Control 1614.2.1 Basic Ideas 1614.2.2 Controllability in Discrete-time 1654.2.3 Food for Thought 1674.3 Discrete-time Observer Design 1674.3.1 Basic Ideas about Discrete-time Observer 1674.3.2 Observability in Discrete-time 1714.3.3 Food for Thought 1734.4 Discrete-time Linear Quadratic Regulator (DLQR) 1734.4.1 Objective Function for DLQR 1734.4.2 Optimal Solution 1744.4.3 Observer Design using DLQR 1764.4.4 Food for Thought 1764.5 Discrete-time LQR with Prescribed Degree of Stability 1774.5.1 Basic Ideas about a Prescribed Degree of Stability 1774.5.2 Case Studies 1804.5.3 Food for Thought 1864.6 Summary 1864.7 Further Reading 187Problems 1885 Disturbance Rejection and Reference Tracking via Observer Design 1955.1 Introduction 1955.2 Disturbance Models 1955.2.1 Commonly Encountered Disturbance Signals 1965.2.2 State Space Model with Input Disturbance 1995.2.3 Food for Thought 2005.3 Compensation of Input and Output Disturbances in Estimation 2005.3.1 Motivational Example 2005.3.2 Input Disturbance Observer Design 2025.3.3 MATLAB Tutorial for Augmented State Space Model 2065.3.4 The Observer Error System 2075.3.5 Output Disturbance Observer Design 2095.3.6 Food for Thought 2135.4 Disturbance-Observer-based State Feedback Control 2145.4.1 The Control Law 2145.4.2 MATLAB Tutorial for Control Implementation 2175.4.3 Food for Thought 2225.5 Analysis of Disturbance-Observer-based Control System 2235.5.1 Controller Transfer Function 2235.5.2 Disturbance Rejection 2255.5.3 Reference Tracking 2275.5.4 A Case Study 2285.5.5 Food for Thought 2325.6 Anti-windup Implementation of the Control Law 2335.6.1 Algorithm for Anti-windup Implementation 2335.6.2 Heating Furnace Control 2365.6.3 Example for Bandlimited Disturbance 2395.6.4 Food for Thought 2415.7 Summary 2425.8 Further Reading 243Problems 2436 Disturbance Rejection and Reference Tracking via Control Design 2536.1 Introduction 2536.2 Embedding Disturbance Model into Controller Design 2546.2.1 Formulation of Augmented State Space Model 2546.2.2 MATLAB Tutorial 2566.2.3 Controllability and Observability 2586.2.4 Food for Thought 2596.3 Controller and Observer Design 2606.3.1 Controller Design and Control Signal Calculation 2606.3.2 Adding Reference Signal 2626.3.3 Observer Design and Implementation 2626.3.4 MATLAB Tutorial for Control Implementation 2646.3.5 Food for Thought 2686.4 Practical Issues 2696.4.1 Reducing Overshoot in Reference Tracking 2696.4.2 Anti-windup Implementation 2726.4.3 Control System using NMSS Realization 2766.4.4 Food for Thought 2826.5 Repetitive Control 2836.5.1 Basic Ideas about Repetitive Control 2836.5.2 Determining the Disturbance Model D(z) 2856.5.3 Robotic Arm Control 2906.5.4 Food for Thought 2956.6 Summary 2956.7 Further Reading 296Problems 296Part III Kalman Filtering 3097 The Kalman Filter 3117.1 Introduction 3117.2 The Kalman Filter Algorithm 3127.2.1 State Space Models in the Kalman Filter 3127.2.2 An Intuitive Computational Procedure 3137.2.3 Optimization of Kalman Filter Gain 3157.2.4 Kalman Filter Examples with MATLAB Tutorials 3177.2.5 Compensation of Sensor Bias and Load Disturbance 3257.2.6 Food for Thought 3307.3 The Kalman Filter in Multi-rate Sampling Environment 3317.3.1 KF Algorithm for Missing Data Scenarios 3317.3.2 Case Studies with MATLAB Tutorial 3337.3.3 Food for Thought 3447.4 The Extended Kalman Filter (EKF) 3447.4.1 Linearization in Extended Kalman Filter 3447.4.2 The Extended Kalman Filter Algorithm 3487.4.3 Case Studies with MATLAB Tutorial 3517.4.4 Food for Thought 3597.5 The Kalman Filter with Fading Memory 3597.5.1 The Algorithm for KF with Fading Memory 3607.5.2 Food for Thought 3637.6 Relationship between Kalman Filter and Observer 3647.6.1 One-step Kalman Filter Algorithm 3647.6.2 Kalman Filter and Observer 3657.6.3 Food for Thought 3707.7 Summary 3717.8 Further Reading 372Problems 3728 Addressing Computational Issues in KF 3778.1 Introduction 3778.2 The Sequential Kalman Filter 3778.2.1 Basic Ideas about Sequential Kalman Filter 3778.2.2 Non-diagonal R 3828.2.3 MATLAB Tutorial for Sequential Kalman Filter 3838.2.4 Food for Thought 3878.3 The Kalman Filter using UDUT Factorization 3888.3.1 Gram-Schmidt Orthogonalization Procedure 3888.3.2 Basic Ideas 3908.3.3 Sequential Kalman Filter with UDUT Decomposition 3938.3.4 MATLAB Tutorial 3958.3.5 Food for Thought 3988.4 Summary 3988.5 Further Reading 399Problems 399Bibliography 403Index 413