Оглавление
Liuping Wang. PID Control System Design and Automatic Tuning using MATLAB/Simulink
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
PID Control SystemDesign and Automatic Tuning using MATLAB/Simulink
Preface
Acknowledgment
List of Symbols and Acronyms
About the Companion Website
1 Basics of PID Control. 1.1 Introduction
1.2 PID Controller Structure
1.2.1 Proportional Controller
Example 1.1
1.2.2 Proportional Plus Derivative Controller
1.2.3 Proportional Plus Integral Controller
Example 1.2
Example 1.3
1.2.4 PID Controllers
Example 1.4
1.2.5 The Commercial PID Controller Structure
1.2.6 Food for Thought
1.3 Classical Tuning Rules for PID Controllers
1.3.1 Ziegler–Nichols Oscillation Based Tuning Rules
Example 1.5
1.3.2 Tuning Rules based on the First Order Plus Delay Model
1.3.3 Food for Thought
1.4 Model Based PID Controller Tuning Rules
1.4.1 IMC-PID Controller Tuning Rules
1.4.2 Padula and Visioli Tuning Rules
1.4.3 Wang and Cluett Tuning Rules
1.4.4 Food for Thought
1.5 Examples for Evaluations of the Tuning Rules
1.5.1 Examples for Evaluating the Tuning Rules
Example 1.6
Example 1.7
Example 1.8
1.5.2 Fired Heater Control Example
Example 1.9
1.6 Summary
1.7 Further Reading
Problems
Notes
2 Closed-loop Performance and Stability. 2.1 Introduction
2.2 Routh–Hurwitz Stability Criterion
2.2.1 Determining Closed-loop Poles
Example 2.1
2.2.2 Routh–Hurwitz Stability Criterion
Example 2.2
2.2.3 Food for Thought
2.3 Nyquist Stability Criterion
2.3.1 Nyquist Diagram
2.3.1.1 Gain Margin
2.3.1.2 Phase Margin
2.3.1.3 Delay Margin
Tutorial 2.1
Step by Step
2.3.2 Rework of Tuning Rules based PID Controllers. Example 2.3
2.3.3 Food for Thought
2.4 Control System Structures and Sensitivity Functions
2.4.1 One Degree of Freedom Control System Structure
2.4.2 Two Degrees of Freedom Design
2.4.2.1 Two degrees of freedom implementation of PI controllers
2.4.3 Sensitivity Functions in Feedback Control
2.4.4 Food for Thought
2.5 Reference Following and Disturbance Rejection
2.5.1 Closed-loop Bandwidth
2.5.2 Reference Following and Disturbance Rejection with PID Controllers
Example 2.4
2.5.3 Reference Following and Disturbance Rejection with Resonant Controllers
2.5.4 Food for Thought
2.6 Disturbance Rejection and Noise Attenuation
2.6.1 Conflict between Disturbance Rejection and Noise Attenuation
2.6.2 PID Controller for Disturbance Rejection and Noise Attenuation
Example 2.5
Example 2.6
2.6.3 Food for Thought
2.7 Robust Stability and Robust Performance
2.7.1 Modeling Errors
2.7.2 Robust Stability
2.7.3 Case Study: Robust Control of Polymer Reactor. Example 2.7
2.7.4 Food for Thought
2.8 Summary
2.9 Further Reading
Problems
3 Model-Based PID and Resonant Controller Design. 3.1 Introduction
3.2 PI Controller Design
3.2.1 Desired Closed-loop Performance Specification
3.2.2 Model and Controller Structures
Example 3.1
3.2.3 Closed-loop Transfer Functions for Different Configurations
Example 3.2
3.2.4 Food for Thought
3.3 Model Based Design for PID Controllers
3.3.1 PD Controller Design
Tutorial 3.1
Step by Step
Example 3.3
3.3.2 Analytical Examples for Ideal PID with Pole-zero Cancellation
Example 3.4
3.3.3 Analytical Examples for PID Controllers with Filters
Example 3.5
Example 3.6
Example 3.7
3.3.4 PID Controller Design without Pole–Zero Cancellation
Example 3.8
3.3.5 MATLAB Tutorial on Solution of a PID Controller with Filter. Tutorial 3.2
Step by Step
3.3.6 Food for Thought
3.4 Resonant Controller Design
3.4.1 Resonant Controller Design
3.4.2 Steady-state Error Analysis
Example 3.9
3.4.3 Pole–Zero Cancellation in the Design of a Resonant Controller. Example 3.10
3.4.4 Food for Thought
3.5 Feedforward Control
3.5.1 Basic Ideas about Feedforward Control
3.5.2 Three Springs and Double Mass System
Example 3.11
3.6.2.1 PID Controller with Filter
Closed-loop Simulation Studies
Example 3.12
3.5.3 Food for Thought
3.6 Summary
3.7 Further Reading
Problems
Notes
4 Implementation of PID Controllers. 4.1 Introduction
4.2 Scenario of a PID Controller at work
4.3 PID Controller Implementation using the Position Form
4.3.1 The Steady-state Information Needed
4.3.2 Discretization of a PID Controller
4.3.3 Food for Thought
4.4 PID Controller Implementation using the Velocity Form
4.4.1 Discretization of a PI Controller
4.4.2 Discretization of a PID Controller using the Velocity Form
Example 4.1
4.4.3 Improving Accuracy in a Slower Sampling Environment
4.4.4 Food for Thought
4.5 Anti-windup Implementation using the Position Form
4.5.1 Integrator Windup Scenario
Example 4.2
4.5.2 Anti-windup Mechanisms in the Position Form of PI Controllers
Example 4.3
4.5.3 Food for Thought
4.6 Anti-windup Mechanisms in the Velocity Form
4.6.1 Anti-windup Mechanism on the Amplitude of the Control Signal
Example 4.4
4.6.2 Limits on the Rate of Change of the Control Signal
4.6.3 Food for Thought
4.7 Tutorial on PID Anti-windup Implementation. Tutorial 4.1
Step by Step
Example 4.5
4.8 Dealing with Other Implementation Issues
4.8.1 Plant Start-up
4.8.2 Dealing with Quantization Errors in PID Controller Implementation
4.9 Summary
4.10 Further Reading
Problems
5 Disturbance Observer- Based PID and Resonant Controller. 5.1 Introduction
5.2 Disturbance observer-Based PI Controller
5.2.1 Estimation of Disturbance with Control
5.2.1.1 Choice of Proportional Controller
5.2.1.2 Compensation of Steady-state Error
5.2.1.3 The closed-loop poles
5.2.1.4 Implementation procedure
5.2.2 Equivalence to PI controller
5.2.3 MATLAB Tutorial for Implementation of a PI Controller via Estimation
Tutorial 5.1
Step by Step
5.2.4 Examples for Estimator based PI Controllers. Example 5.1
Example 5.2
Example 5.3
5.2.5 Food for Thought
5.3 Disturbance observer-Based PID Controller
5.3.1 Proportional Plus Derivative Control
5.3.2 Adding Integral Action
5.3.3 Equivalence to a PID Controller
5.3.4 MATLAB Tutorial on the Implementation of a disturbance observer-based PID Controller
Tutorial 5.2
Step by Step
5.3.5 Examples for Disturbance observer-based PID Controller. Example 5.4
5.3.6 Food for Thought
5.4 Disturbance observer-Based Resonant Controller
5.4.1 Resonant Controller Design
5.4.2 Resonant Controller Implementation
5.4.3 Equivalence to a Resonant Controller
5.4.4 MATLAB Tutorial on Disturbance observer-Based Resonant Controller Implementation
Tutorial 5.3
Step by Step
5.4.5 Examples for Disturbance observer-Based Resonant Controllers
Example 5.5
Example 5.6
Example 5.7
5.4.6 Food for Thought
5.5 Multi-frequency Resonant Controller
5.5.1 Adding Integral Action to the Resonant Controller
5.5.2 Adding More Periodic Components
5.5.3 Food for Thought
5.6 Summary
5.7 Further Reading
Problems
6 PID Control of Nonlinear Systems. 6.1 Introduction
6.2 Linearization of the Nonlinear Model
6.2.1 Approximation of a Nonlinear Function
6.2.2 Linearization of nonlinear differential equations
6.2.3 Case Study: Linearization of the Coupled Tank Model
Example 6.1
6.2.4 Case Study: Linearization of the Induction Motor Model
6.2.5 Food for Thought
6.3 Case Study: Ball and Plate Balancing System
6.3.1 Dynamics of the Ball and Plate Balancing System
6.3.2 Linearization of the Nonlinear Model
6.3.3 PID Controller Design
6.3.4 Implementation and Experimental Results
6.3.4.1 Disturbance Rejection
6.3.4.2 Making a Square Movement
6.3.4.3 Making a Circle Movement
6.3.4.4 Making more Complicated Movements
6.3.5 Food for Thought
6.4 Gain Scheduled PID Control Systems
6.4.1 The Weighting Parameters
6.4.2 Gain Scheduled Implementation using PID Velocity Form
6.4.3 Gain Scheduled Implementation using an Estimator Based PID Controller
6.4.4 Food for Thought
6.5 Summary
6.6 Further Reading
Problems
7 Cascade PID Control Systems. 7.1 Introduction
7.2 Design of a Cascade PID Control System
7.2.1 Design Steps for a Cascade Control System
7.2.2 Simple Design Examples. Example 7.1
Example 7.2
7.2.3 Achieving Closed-loop Performance Invariance (Approximate) in a Cascade Structure
7.2.4 Food for Thought
7.3 Cascade Control System for Input Disturbance Rejection
7.3.1 Frequency Characteristics for Disturbance Rejection
7.3.2 Simulation Studies
Example 7.3
7.3.3 Food for Thought
7.4 Cascade Control System for Actuator Nonlinearities
7.4.1 Cascade Control for Actuator with a Deadzone
Example 7.4
Example 7.5
7.4.2 Cascade Control for Actuators with Quantization Errors
Example 7.6
Example 7.7
7.4.3 Cascade Control for Actuators with Backlash Nonlinearity
Example 7.8
Example 7.9
7.4.4 Food for Thought
7.5 Summary
7.6 Further Reading
Problems
8 PID Controller Design for Complex Systems. 8.1 Introduction
8.2 PI Controller Design via Gain and Phase Margins
8.2.1 PI Controller Design Using Gain Margin and Phase Margin Specifications
8.2.2 Design Examples
Example 8.1
Example 8.2
8.2.3 Food for Thought
8.3 PID Controller Design using Two Frequency Points
8.3.1 Finding the PID Controller Parameters
Example 8.3
8.3.2 Desired Closed-loop Performance Specification using Two Frequency Points
8.3.3 Design Examples. Example 8.4
8.3.4 MATLAB Tutorial on PID Controller Design Using two Frequency Points
Tutorial 8.1
Step by Step
Tutorial 8.2
Step by Step
8.3.5 PID Controller Design for Beer Filtration Process
8.3.6 Food for Thought
8.4 PID Controller Design for Integrating Systems
8.4.1 The Approximate Model
8.4.2 Selection of Desired Closed-loop Performance
8.4.3 Normalization of the Parameters and Empirical Rules
8.4.4 Gain and Phase Margins
8.4.5 Simulation Examples. Example 8.5
8.4.6 Food for Thought
8.5 Summary
8.6 Further Reading
Problems
9 Automatic Tuning of PID Controllers. 9.1 Introduction
9.2 Relay Feedback Control
9.2.1 Relay Control with Hysteresis
Tutorial 9.1
Step by Step
Example 9.1
9.2.2 Relay Control with Integrator
Tutorial 9.2
Step by Step
Example 9.2
9.2.3 Food for Thought
9.3 Estimation of Frequency Response using the Fast Fourier Transform (FFT)
9.3.1 FFT Estimation
9.3.2 MATLAB Tutorial using the FFT for Estimation
Tutorial 9.3
Step by Step
9.3.3 Monte-Carlo Simulation Studies
Example 9.3
Example 9.4
9.3.4 Food for Thought
9.4 Estimation of Frequency Response Using the frequency sampling filter (FSF)
9.4.1 Frequency Sampling Filter Model
9.4.2 MATLAB Tutorial on Estimation Using the FSF Model. Tutorial 9.4
Step by Step
9.4.3 Monte-Carlo Simulation using the FSF Estimation
Example 9.5
9.4.4 Food for Thought
9.5 Monte-Carlo Simulation Studies
9.5.1 Effect of Unknown Constant Disturbance
9.5.2 Effect of Unknown Low Frequency Disturbance
9.5.3 Estimation of the Steady-state Value
9.5.4 Food for Thought
9.6 Auto-tuner Design for Stable Plant
9.6.1 MATLAB Tutorial on Auto-tuner for Stable Plant. Tutorial 9.5
Step by Step
9.6.2 Evaluation of the Auto-tuner for a Stable Plant
9.6.2.1 PID Controller Parameters
9.6.2.2 Nyquist Plots
9.6.2.3 Closed-loop Simulation Results
9.6.3 Comparative Studies
9.6.4 Food for Thought
9.7 Auto-tuner Design for a Plant with an Integrator
9.7.1 Estimation of an Integrating Plus Delay Model
9.7.2 Auto-tuner for Integrating Systems
Example 9.6
Example 9.7
9.7.3 Auto-tuning of Cascade Control Systems
Example 9.8
9.7.4 Food for Thought
9.8 Summary
9.9 Further Reading
Problems
Note
10 PID Control of Multi-rotor Unmanned Aerial Vehicles. 10.1 Introduction
10.2 Multi-rotor Dynamics
10.2.1 Dynamic Models for Attitude Control
10.2.2 Actuator Dynamics for Quadrotor UAVs
10.2.3 Actuator Dynamics of Hexacopters
10.2.4 Food for Thought
10.3 Cascade Attitude Control of Multi-rotor UAVs
10.3.1 Linearized Model for the Secondary Plant
10.3.2 Linearized Model for the Primary Plant
10.3.3 Food for Thought
10.4 Automatic Tuning of Attitude Control Systems
10.4.1 Test Rigs for Auto-tuning Cascade PI Controllers of Multi-rotor UAVs
10.4.2 Experimental Results for Quadrotor UAV
10.4.3 Experimental Results for Hexacopter
10.4.4 Food for Thought
10.5 Summary
10.6 Further Reading
Problems
Suggestions to Food for Thought Questions
Bibliography
Index
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