1st Edition

Digital Control Applications Illustrated with MATLAB®

ISBN 9781482236699
Published February 13, 2015 by CRC Press
384 Pages 287 B/W Illustrations

USD $140.00

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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



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


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)


How to Avoid Aliasing

Interpretation of Aliasing in s-Plane

Example of Aliasing in a Control Setting


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


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


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


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


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


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


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


State-Variable Feedback Design Methods

Linear State-Variable Feedback

Control in State-Space


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


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


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


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



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≪®


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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.

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"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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