PID Control System Design and Automatic Tuning using MATLAB/Simulink

LIUPING WANG, PHD, is a Professor at RMIT University in Australia. An electrical engineer by training, 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 four books in the areas of model predictive control, control systems for electric drives and power converters, system identification, and PID control.

• Preface xvAcknowledgment xviiList of Symbols and Acronyms xixAbout the Companion Website xxi1 Basics of PID Control 11.1 Introduction 11.2 PID Controller Structure 11.2.1 Proportional Controller 11.2.2 Proportional Plus Derivative Controller 31.2.3 Proportional Plus Integral Controller 51.2.4 PID Controllers 91.2.5 The Commercial PID Controller Structure 121.2.6 Food for Thought 131.3 Classical Tuning Rules for PID Controllers 131.3.1 Ziegler–Nichols Oscillation Based Tuning Rules 131.3.2 Tuning Rules based on the First Order Plus Delay Model 151.3.3 Food for Thought 171.4 Model Based PID Controller Tuning Rules 181.4.1 IMC-PID Controller Tuning Rules 181.4.2 Padula and Visioli Tuning Rules 191.4.3 Wang and Cluett Tuning Rules 201.4.4 Food for Thought 211.5 Examples for Evaluations of the Tuning Rules 211.5.1 Examples for Evaluating the Tuning Rules 211.5.2 Fired Heater Control Example 251.6 Summary 271.7 Further Reading 28Problems 282 Closed-loop Performance and Stability 312.1 Introduction 312.2 Routh–Hurwitz Stability Criterion 312.2.1 Determining Closed-loop Poles 322.2.2 Routh–Hurwitz Stability Criterion 332.2.3 Food for Thought 362.3 Nyquist Stability Criterion 362.3.1 Nyquist Diagram 362.3.1.1 Gain Margin 382.3.1.2 Phase Margin 382.3.1.3 Delay Margin 382.3.2 Rework of Tuning Rules based PID Controllers 402.3.3 Food for Thought 422.4 Control System Structures and Sensitivity Functions 422.4.1 One Degree of Freedom Control System Structure 432.4.2 Two Degrees of Freedom Design 442.4.2.1 Two degrees of freedom implementation of PI controllers 452.4.3 Sensitivity Functions in Feedback Control 452.4.4 Food for Thought 472.5 Reference Following and Disturbance Rejection 472.5.1 Closed-loop Bandwidth 472.5.2 Reference Following and Disturbance Rejection with PID Controllers 502.5.3 Reference Following and Disturbance Rejection with Resonant Controllers 532.5.4 Food for Thought 542.6 Disturbance Rejection and Noise Attenuation 542.6.1 Conflict between Disturbance Rejection and Noise Attenuation 542.6.2 PID Controller for Disturbance Rejection and Noise Attenuation 552.6.3 Food for Thought 582.7 Robust Stability and Robust Performance 592.7.1 Modeling Errors 592.7.2 Robust Stability 602.7.3 Case Study: Robust Control of Polymer Reactor 622.7.4 Food for Thought 652.8 Summary 652.9 Further Reading 67Problems 673 Model-Based PID and Resonant Controller Design 713.1 Introduction 713.2 PI Controller Design 713.2.1 Desired Closed-loop Performance Specification 713.2.2 Model and Controller Structures 723.2.3 Closed-loop Transfer Functions for Different Configurations 753.2.4 Food for Thought 773.3 Model Based Design for PID Controllers 783.3.1 PD Controller Design 783.3.2 Analytical Examples for Ideal PID with Pole-zero Cancellation 813.3.3 Analytical Examples for PID Controllers with Filters 843.3.4 PID Controller Design without Pole–Zero Cancellation 923.3.5 MATLAB Tutorial on Solution of a PID Controller with Filter 943.3.6 Food for Thought 953.4 Resonant Controller Design 963.4.1 Resonant Controller Design 963.4.2 Steady-state Error Analysis 973.4.3 Pole–Zero Cancellation in the Design of a Resonant Controller 993.4.4 Food for Thought 1013.5 Feedforward Control 1023.5.1 Basic Ideas about Feedforward Control 1023.5.2 Three Springs and Double Mass System 1033.5.3 Food for Thought 1083.6 Summary 1083.7 Further Reading 108Problems 1094 Implementation of PID Controllers 1134.1 Introduction 1134.2 Scenario of a PID Controller at work 1134.3 PID Controller Implementation using the Position Form 1144.3.1 The Steady-state Information Needed 1144.3.2 Discretization of a PID Controller 1154.3.3 Food for Thought 1164.4 PID Controller Implementation using the Velocity Form 1174.4.1 Discretization of a PI Controller 1174.4.2 Discretization of a PID Controller using the Velocity Form 1194.4.3 Improving Accuracy in a Slower Sampling Environment 1204.4.4 Food for Thought 1224.5 Anti-windup Implementation using the Position Form 1224.5.1 Integrator Windup Scenario 1224.5.2 Anti-windup Mechanisms in the Position Form of PI Controllers 1244.5.3 Food for Thought 1254.6 Anti-windup Mechanisms in the Velocity Form 1264.6.1 Anti-windup Mechanism on the Amplitude of the Control Signal 1264.6.2 Limits on the Rate of Change of the Control Signal 1294.6.3 Food for Thought 1294.7 Tutorial on PID Anti-windup Implementation 1304.8 Dealing with Other Implementation Issues 1334.8.1 Plant Start-up 1344.8.2 Dealing with Quantization Errors in PID Controller Implementation 1354.9 Summary 1364.10 Further Reading 137Problems 1375 Disturbance Observer- Based PID and Resonant Controller 1395.1 Introduction 1395.2 Disturbance observer-Based PI Controller 1395.2.1 Estimation of Disturbance with Control 1395.2.1.1 Choice of Proportional Controller K1 1405.2.1.2 Compensation of Steady-state Error 1405.2.1.3 The closed-loop poles 1415.2.1.4 Implementation procedure 1425.2.2 Equivalence to PI controller 1435.2.3 MATLAB Tutorial for Implementation of a PI Controller via Estimation 1445.2.4 Examples for Estimator based PI Controllers 1455.2.5 Food for Thought 1485.3 Disturbance observer-Based PID Controller 1495.3.1 Proportional Plus Derivative Control 1495.3.2 Adding Integral Action 1505.3.3 Equivalence to a PID Controller 1515.3.4 MATLAB Tutorial on the Implementation of a disturbance observer-based PID Controller 1535.3.5 Examples for Disturbance observer-based PID Controller 1555.3.6 Food for Thought 1565.4 Disturbance observer-Based Resonant Controller 1565.4.1 Resonant Controller Design 1565.4.2 Resonant Controller Implementation 1585.4.3 Equivalence to a Resonant Controller 1595.4.4 MATLAB Tutorial on Disturbance observer-Based Resonant Controller Implementation 1605.4.5 Examples for Disturbance observer-Based Resonant Controllers 1625.4.6 Food for Thought 1675.5 Multi-frequency Resonant Controller 1675.5.1 Adding Integral Action to the Resonant Controller 1685.5.2 Adding More Periodic Components 1705.5.3 Food for Thought 1715.6 Summary 1725.7 Further Reading 172Problems 1736 PID Control of Nonlinear Systems 1796.1 Introduction 1796.2 Linearization of the Nonlinear Model 1796.2.1 Approximation of a Nonlinear Function 1796.2.2 Linearization of nonlinear differential equations 1816.2.3 Case Study: Linearization of the Coupled Tank Model 1816.2.4 Case Study: Linearization of the Induction Motor Model 1846.2.5 Food for Thought 1866.3 Case Study: Ball and Plate Balancing System 1876.3.1 Dynamics of the Ball and Plate Balancing System 1876.3.2 Linearization of the Nonlinear Model 1886.3.3 PID Controller Design 1896.3.4 Implementation and Experimental Results 1906.3.4.1 Disturbance Rejection 1916.3.4.2 Making a Square Movement 1926.3.4.3 Making a Circle Movement 1926.3.4.4 Making more Complicated Movements 1946.3.5 Food for Thought 1946.4 Gain Scheduled PID Control Systems 1946.4.1 TheWeighting Parameters 1946.4.2 Gain Scheduled Implementation using PID Velocity Form 1966.4.3 Gain Scheduled Implementation using an Estimator Based PID Controller 1976.4.4 Food for Thought 1996.5 Summary 1996.6 Further Reading 199Problems 2007 Cascade PID Control Systems 2037.1 Introduction 2037.2 Design of a Cascade PID Control System 2037.2.1 Design Steps for a Cascade Control System 2037.2.2 Simple Design Examples 2047.2.3 Achieving Closed-loop Performance Invariance (Approximate) in a Cascade Structure 2087.2.4 Food for Thought 2097.3 Cascade Control System for Input Disturbance Rejection 2097.3.1 Frequency Characteristics for Disturbance Rejection 2107.3.2 Simulation Studies 2117.3.3 Food for Thought 2137.4 Cascade Control System for Actuator Nonlinearities 2147.4.1 Cascade Control for Actuator with a Deadzone 2147.4.2 Cascade Control for Actuators with Quantization Errors 2187.4.3 Cascade Control for Actuators with Backlash Nonlinearity 2217.4.4 Food for Thought 2277.5 Summary 2307.6 Further Reading 230Problems 2318 PID Controller Design for Complex Systems 2338.1 Introduction 2338.2 PI Controller Design via Gain and Phase Margins 2338.2.1 PI Controller Design Using Gain Margin and Phase Margin Specifications 2338.2.2 Design Examples 2348.2.3 Food for Thought 2388.3 PID Controller Design using Two Frequency Points 2388.3.1 Finding the PID Controller Parameters 2388.3.2 Desired Closed-loop Performance Specification using Two Frequency Points 2408.3.3 Design Examples 2428.3.4 MATLAB Tutorial on PID Controller Design Using two Frequency Points 2438.3.5 PID Controller Design for Beer Filtration Process 2458.3.6 Food for Thought 2488.4 PID Controller Design for Integrating Systems 2498.4.1 The Approximate Model 2498.4.2 Selection of Desired Closed-loop Performance 2508.4.3 Normalization of the Parameters and Empirical Rules 2518.4.4 Gain and Phase Margins 2538.4.5 Simulation Examples 2538.4.6 Food for Thought 2568.5 Summary 2568.6 Further Reading 257Problems 2579 Automatic Tuning of PID Controllers 2599.1 Introduction 2599.2 Relay Feedback Control 2599.2.1 Relay Control with Hysteresis 2599.2.2 Relay Control with Integrator 2639.2.3 Food for Thought 2679.3 Estimation of Frequency Response using the Fast Fourier Transform (FFT) 2679.3.1 FFT Estimation 2689.3.2 MATLAB Tutorial using the FFT for Estimation 2699.3.3 Monte-Carlo Simulation Studies 2709.3.4 Food for Thought 2729.4 Estimation of Frequency Response Using the frequency sampling filter (FSF) 2739.4.1 Frequency Sampling FilterModel 2739.4.2 MATLAB Tutorial on Estimation Using the FSF Model 2769.4.3 Monte-Carlo Simulation using the FSF Estimation 2789.4.4 Food for Thought 2799.5 Monte-Carlo Simulation Studies 2799.5.1 Effect of Unknown Constant Disturbance 2799.5.2 Effect of Unknown Low Frequency Disturbance 2809.5.3 Estimation of the Steady-state Value 2829.5.4 Food for Thought 2839.6 Auto-tuner Design for Stable Plant 2839.6.1 MATLAB Tutorial on Auto-tuner for Stable Plant 2849.6.2 Evaluation of the Auto-tuner for a Stable Plant 2869.6.2.1 PID Controller Parameters 2879.6.2.2 Nyquist Plots 2879.6.2.3 Closed-loop Simulation Results 2889.6.3 Comparative Studies 2899.6.4 Food for Thought 2909.7 Auto-tuner Design for a Plant with an Integrator 2919.7.1 Estimation of an Integrating Plus Delay Model 2919.7.2 Auto-tuner for Integrating Systems 2929.7.3 Auto-tuning of Cascade Control Systems 2979.7.4 Food for Thought 3009.8 Summary 3009.9 Further Reading 301Problems 30210 PID Control of Multi-rotor Unmanned Aerial Vehicles 30510.1 Introduction 30510.2 Multi-rotor Dynamics 30510.2.1 Dynamic Models for Attitude Control 30510.2.2 Actuator Dynamics for Quadrotor UAVs 30710.2.3 Actuator Dynamics of Hexacopters 30910.2.4 Food for Thought 31110.3 Cascade Attitude Control of Multi-rotor UAVs 31110.3.1 Linearized Model for the Secondary Plant 31210.3.2 Linearized Model for the Primary Plant 31310.3.3 Food for Thought 31310.4 Automatic Tuning of Attitude Control Systems 31310.4.1 Test Rigs for Auto-tuning Cascade PI Controllers of Multi-rotor UAVs 31410.4.2 Experimental Results for Quadrotor UAV 31410.4.3 Experimental Results for Hexacopter 32010.4.4 Food for Thought 32410.5 Summary 32410.6 Further Reading 325Problems 325Suggestions to Food for Thought Questions 327Bibliography 331Index 341