Digital Control Applications Illustrated with MATLAB®
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Digital Control Applications Illustrated with MATLAB®
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Book Description
Digital Control Applications Illustrated with MATLAB® covers the modeling, analysis, and design of linear discrete control systems. Illustrating all topics using the micro-computer implementation of digital controllers aided by MATLAB®, Simulink®, and FEEDBACK<<®, this practical text:
- Describes the process of digital control, followed by a review of Z-transforms, feedback control concepts, and s-to-z plane conversions, mappings, signal sampling, and data reconstruction
- Presents mathematical representations of discrete systems affected by the use of advances in computing methodologies and the advent of computers
- Demonstrates state-space representations and the construction of transfer functions and their corresponding discrete equivalents
- Explores steady-state and transient response analysis using Root-Locus, as well as frequency response plots and digital controller design using Bode Plots
- Explains the design approach, related design processes, and how to evaluate performance criteria through simulations and the review of classical designs
- Studies advances in the design of compensators using the discrete equivalent and elucidates stability tests using transformations
- Employs test cases, real-life examples, and drill problems to provide students with hands-on experience suitable for entry-level jobs in the industry
Digital Control Applications Illustrated with MATLAB® is an ideal textbook for digital control courses at the advanced undergraduate and graduate level.
Table of Contents
Preface
Author
Digital Control Introduction and Overview
Overview of Process Control: Historical Perspective
Feedback Control Structures for Continuous Systems: Mathematical Representation of (Sub) System Dynamics
Basic Feedback Control Loop: Single Input Single Output (SISO) System
Goal
Continuous Control Structures: Output Feedback
Continuous Control Structures: State Variable Feedback
Digital Control Basic Structure
Relationship of Time Signals and Samples
A Typical Algorithm for H
Differences in Digital versus Analog Control Methods
Computing the Time Response of a Linear, Time Invariant, Discrete Model to an Arbitrary Input
Review of z-Transforms for Discrete Systems
Some Useful Results for One-Sided z-Transforms
How to Find y(k) Using z-Transforms
Use of z-Transforms to Solve nth Order Difference Equations
Stability of the Time Response
Continuous versus Discrete Relationships
s-to-z Plane Mappings
LOCI of Constant Damping Ratio (ζ) and Natural Frequency (ωn) in s-Plane to z-Plane Mapping
Signal Sampling and Data Reconstruction
Impulse Sampling
Laplace Transform of a Sampled Signal
Nyquist Theorem
Nyquist Result
Recovering f(t) from f*(t)
Aliasing
How to Avoid Aliasing
Interpretation of Aliasing in s-Plane
Example of Aliasing in a Control Setting
Problems
Mathematical Models of Discrete Systems
Discrete Time System Representations
Difference Equation Form
Signal Flow Diagram and Analysis
State Equations from Node Equations
State Variable Forms: I
State Variable Forms
Transfer Function of a State-Space Model
State Variable Transformation
Example
Obtaining the Time Response X(k)
Computing G(z) from A, B, C, d
Leverier Algorithm Implementation
Analysis of the Basic Digital Control Loop
Discrete System Time Signals
Models for Equivalent Discrete System, GÞ(Z)
Computing Φ and Γ (or Ψ)
Algorithm for Obtaining Ψ(h) and Φ, Γ
Some Discussion on the Selection of h
Examples
Discrete System Equivalents: Transfer Function Approach
Relationship between G(s) and GÞ□(z)
Comparison of a Continuous and Discrete Equivalent Bode Plot
Effects of Time Step h on GÞ (z = e jωh)
Anatomy of a Discrete Transfer Function
Modeling a Process with Delay in Control, τ = Mh + ϵ
State Model for a Process with Fractional Delay ϵ < h
State Model for a Process with Large Delay
Transfer Function Approach to Modeling a Process with Delay
Problems
Performance Criteria and the Design Process
Design Approaches and the Design Process
Elements of Feedback System Design
Elements of FB System Design II
Closed-Loop System Zeros
Design Approaches to be Considered
Performance Measure for a Design Process
Stability of the Closed-Loop System
Speed of Transient Response
Sensitivity and Return Difference
Example: Evaluation and Simulation
Simulation of Closed-Loop Time Response
Simulation Structure
Flow Diagram for Simulation Program for a Control Algorithm
Modifications to Time Delay
Control (Cntrl) Algorithm Simulation
Simulation of Time Delay, τ
Required Modifications to Simulation Flow Diagram
Tools for Control Design and Analysis
Overview of Classical Design Techniques (Continuous Time)
Lag Compensator Design, H(s)
Lead Compensator Design
Example of Lag Compensator Design
Lag Compensation Design
Example of Lead Compensator Design
Lead Compensation Design
Critique of Continuous Time H(s) Design
Problems
Compensator Design via Discrete Equivalent
Stability of Discrete Systems
Jury Test
Stability with Respect to a Parameter β
Stability with Respect to Multiple Parameters: α, β
A More Complicated, State-Space Example
Example State-Space Example Plots
Fundamentals of Digital Compensator Design
H(z) Design via Discrete Equivalent: H(s) − HÞ(z)
Forms of Discrete Integration
General Algorithm for Tustin Transformation
Tustin Equivalence with Frequency Prewarping
Discrete Equivalent Designs
Summary of Discrete Equivalence Methods
Example of a Discrete Equivalent Design
Discrete Equivalent Computations
Evaluation of Digital Control Performance
Continuous versus Discrete System Loop Gain
Methods to Improve Discrete CL Performance
Problems
Compensator Design via Direct Methods
Direct Design Compensation Methods
RL Design of H(z)
Example of Design Approach: Antenna Positioning Control
RL Redesign (After Much Trial and Error)
An Example of a Poor Design Choice
w-Plane Design of H(z)
Design Approach
General z → w Plane Mapping
Example of Design Approach
Frequency Domain Evaluation
PID Design
Digital PID Controller
Integral Windup Modifications
Example
Other PID Considerations
PID Initial Tuning Rules
Real-Time PID Control of an Inverted Pendulum Using FEEDBACK≪®: Page 26 of 33–936 S of FEEDBACK≪® Document
A Technique for System Control with Time Delay
Smith Predictor/Compensator
Example of Smith Predictor Motor-Positioning Example with τ 1 S, h = 1 S (i.e., M = 1)
Implementation of High-Order Digital Compensators
Summary of Compensator Design Methods
Problems
State-Variable Feedback Design Methods
Linear State-Variable Feedback
Control in State-Space
Controllability
Open-Loop versus CL Control
Discrete SVFB Design Methods
Continuous → Discrete Gain Transformation Methods
Average Gain Method
Example: Satellite Motor Control
State Variable Feedback Control: Direct Pole Placement
Discrete System Design
Pole Placement Methods
Transformation Approach for Pole Placement
Ackermann Formula
Algorithm to Obtain pd(Φ)
CL System Zeros
Inverted Pendulum on a Cart
Equivalent Discrete Design u(k) = −KÞX(k)
Direct Digital Design: Inverted Pendulum
CL Simulation Inverted Pendulum X(0) = [0.2, 0, 1, 0]′
Deadbeat Controller Inverted Pendulum X(0) = [0.2, 0, 1, 0]″
Summary of Pole Placement Design by SVFB
SVFB with Time Delay in Control: τ = Mh + ε
State Prediction
Implementation of the Delay Compensator: General Case
Example—Inverted Pendulum
Comparison with Smith Predictor Structure (ε = 0)
Command Inputs to SVFB Systems
Integral Control in SVFB
Problems
Advanced Design Methods
Lyapunov Stability Theory Preliminaries
Application to Stability Analysis
Main Theorem for Linear Systems
Practical Use of Lyapunov Theorem
Numerical Solution of the Lyapunov Equation
Algorithm to Solve Lyapunov Equation (DLINEQ)
Constructive Application of Lyapunov Theorem to SVFB
Discussion of Stabilization Result
Lyapunov ("Bang-Bang") Controllers
Introduction to Least-Squares Optimization
Problem Definition General Comments
Optimization Approach and Algorithm
Continued Method for Obtaining K1 from P0
The Discrete Riccati Equation
Comments and Extensions
Application of the Optimal Control
Properties of the Optimal CL System-1
Properties of the Optimal CL System-2
Examples and Applications
Examples with FEEDBACK≪® Hardware and Software Package
Summary of Optimal Control Design Method
Rate Weighting
Weighting of Control Rate
Properties of a Rate-Weighted Controller
Compensation for Fractional Time Delay
Problems
Estimation of System State
State Estimation
"Observation" of System State
System Observability Requirement
Observer Pole Placement Problem
Selection of Observer CL Poles
Example of State Estimation
Mechanics of Observer Dynamics
Implementation of the Observer-Controller Pair
Implementation: Some Practical Considerations
Composite CL Observer and Controller
Example Satellite Control with Command Input
Transfer Function of Composite CL Observer and Controller
Poles and Zeros of Composite T(z)
Reduced-Order Observers
Reduced-Order Observer Design for Xb
Implementation of Reduced-Order Observer/Controller
Loop Gain Analysis of RO Observer/Controller
Modifications for Time Delay τ = Mh + ϵ
Further/Advanced Topics in State Estimation
Case Study: State Estimation in Passive Target Tracking
Problems
Implementation Issues in Digital Control
Mechanization of the Control Algorithm on Microcontrollers Motivation
Microprocessor Implementation Structure
Binary Representation of Quantized Numbers
Digital Quantization of a Continuous Value
Sources of Numerical Errors in Digital Control
Algorithm Realization Structures
Analysis of Control Algorithm Implementation
Response of Discrete Systems to White Noise
Propagation of Multiplication Errors through the Controller
Parameter Errors and Sensitivity Analysis
Nonlinear Effects
Case Study
Concluding remarks
Problems
Bibliography
Appendix I: MATLAB® Primer
Appendix II: FEEDBACK≪® Guide for Applications in the Text
Appendix III: Suggested MATLAB® Code for Algorithms and Additional
Examples from FEEDBACK≪®
Index
Author(s)
Biography
Hemchandra Madhusudan Shertukde, SM’92, IEEE, holds a B.Tech from the Indian Institute of Technology Kharagpur, as well as an MS and Ph.D in electrical engineering with a specialty in controls and systems engineering from the University of Connecticut, Storrs, USA. Currently, he is professor of electrical and computer engineering for the College of Engineering, Technology, and Architecture (CETA) at University of Hartford, Connecticut, USA. He is also senior lecturer at the Yale School of Engineering and Applied Sciences (SEAS), New Haven, Connecticut, USA. The principal inventor of two commercialized patents, he has published several journal articles and written three solo books.
Dr. Shertukde is the recipient of the 2017 IEEE EAB/SA Standards Education Award, 2017 IEEE-PES CT Chapter Outstanding Engineer Award, and the 2016 IEEE Award as the Chair of the Working Group C.5.159. He continues to be in leadership positions for several other Working Groups enabling IEEE-TC to publish different standards and User's Guides for Electrical Power Transformers.
Featured Author Profiles
Hemchandra Madhusudan Shertukde
Professor, CETA/University of Hartford
West Hartford, CT, USA
Reviews
"This book is an asset for practicing controls engineers as well as students of advanced control systems courses. Books on this topic have been usually quite theoretically oriented, and a common complaint of the students is that they do not get a practical flavor after going through a course, or even multiple courses. The author brings a fresh approach, backed up by decades of teaching and professional experience, which is oriented toward practical application. I look forward to having this book on my shelf."
—Amit Patra, Indian Institute of Technology Kharagpur"The author provides a mathematically detailed yet accessible presentation of topics in digital control theory. After introducing digital control systems and reviewing the modeling and performance of discrete systems, several chapters are dedicated to different design methods. These methods include discrete equivalent, direct, state-variable feedback, Lyapunov, and optimal. Throughout the book, the emphasis is on application of the theory rather than on theorems and abstract mathematics."
—Patricia Mellodge, University of Hartford, Connecticut, USA"This book has an excellent flow of material for teaching design of digital control or computer control of dynamic systems. In particular, and following the well-organized design chapters, the microprocessor/computer implementation hardware and software aspects in chapter 9 are very valuable, well presented, and certainly well appreciated in this book. Chapters 1 through 4 provide clear and concise presentation of prerequisite material/knowledge for a digital control system design course, and could be very well appreciated in a previous senior-level control design course. The design chapters 5 through 8 progress effectively with the right sequence of techniques, starting with design by digital equivalents, followed by transformed domain techniques, and then moving into the time domain state space design including state estimators both full order and reduced order. Using MATLAB® software and simulations for examples and case studies provides students with valuable practice opportunities for the material presented throughout the book. This fits exactly in how I teach my first in a two-graduate-course sequence 'Computer Control of Dynamic Systems' here at California State University, Chico (the second is 'Adaptive Control Systems')."
—Dr. Adel A Ghandakly, California State University, Chico, USA
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