2nd Edition

Modern Digital Control Systems

By Jacquot Copyright 1995

    This work presents traditional methods and current techniques of incorporating the computer into closed-loop dynamic systems control, combining conventional transfer function design and state variable concepts. Digital Control Designer - an award-winning software program which permits the solution of highly complex problems - is available on the CRC Press Website at http://www.crcpress.com/product/isbn/9780824789145. This edition: supplies new coverage of the Ragazzini technique; describes digital filtering, including Butterworth prototype filters; and more.

    Preface to the Second Edition

    Preface to the First Edition

    Introduction to Digital Control

    The Basic Idea of System Control

    The Computer as a Control Element

    Single-Loop Digital Control System

    Why Digital Control Instead of Analog?

    Data Converters

    The State of Microprocessor Technology

    Example of a Microprocessor-Based Thermal Controller

    Summary

    References

    Linear Difference Equations and the z-Transform

    Introduction

    Scalar Differences Equations

    z-Transform of Simple Sequences

    Useful Theorems Associated with the z-Transform

    Inversion of the z-Transform

    Method of Partial Fraction Expansion

    Solving Linear Difference Equations with the z-Transform

    z-Domain Transfer Function and Impulse Response Sequence

    Relation Between z-Plane Pole Locations and the Nature of Temporal Sequences

    Frequency Response of Discrete-Data Systems

    Relationship Between s- and z-Domain Poles of Sampled Functions

    Discrete-Time Convolution Theorem (Theorem 2.4)

    Final Value Theorem (Theorem 2.5)

    Backdoor Approach to the Sampling Theorem

    Summary

    Problems

    References

    Elementary Digital Control System Design Using Transform Techniques

    Introduction

    Analog-to-Digital and Digital-to-Analog Convertors

    Continuous-Time Plant Driven by a Zero-Order Hold with Sampled Output

    Implementation of Digital Control Strategies

    Closed-Loop Characteristic Equation

    Conventional Digital Control Design Techniques

    Conventional Control System Design Specifications

    Elementary z-Domain Design Considerations
    Effect of Disturbances on the Closed-Loop System

    Concept of the Dynamic Controller or Compensator

    Summary

    Problems

    References

    Advanced Digital Control System Design Techniques Employing the z-Transform

    Introduction

    General PID Direct Digital Control Algorithm

    Ziegler-Nichols Tuning Procedure for PID Control

    Direct Design Method of Ragazzini

    Summary

    Problems

    References

    Digital Filtering and Digital Compensator Design

    Introduction

    Conventional Design Techniques for Digital Compensators

    Approximate Numerical Integration Techniques

    Another Look at the Bilinear Transformation

    Bilinear Transformation with Prewraping

    Matched Pole-Zero Technique

    Zero-Order-Hold Approximation

    Impulse Invariant Method

    Using Prototypes to Design Digital Filters

    z-Plane Design of Digital Compensators

    Summary

    Problems

    References

    State-Variable Representation in Digital Control Systems

    Introduction

    Continuous-Time State-Variable Problem

    Solution of the State Equation

    Matrix Exponential Series Approach

    Solution of the Discrete State Equation

    Transfer Functions from State Equation

    Controllability

    Observability

    State-Variable Representation of Discrete Single-Input/Single-Output Systems

    State-Variable Representation of Composite Control Systems

    Summary

    Problems

    References

    Quantization and Error Effects

    Introduction

    Quantization Errors (Type 1 Errors)

    Response of a Discrete Transfer Function to Quantization Errors

    Bound on the Output Magnitude (Bertram’s Bound)

    Multiplication Errors (Type 2 Errors)

    Finite-World-Length Representation of Digital Filter Coefficients (Type 3 Errors)

    Root Sensitivity Analysis

    Summary

    Problems

    References

    State-Space Approach to Control System Design

    Introduction

    State-Variable Feedback and System Design

    Feedback Control with Incomplete State Information

    Open-Loop Estimator or Observer

    Asymptotic Prediction Estimator or Observer

    Current Estimator or Observer

    Reduced-Order Estimator or Observer

    Algorithm for Gain Calculations for Single-Input Systems

    Regulation with Nonzero Reference Inputs

    Reference Inputs for Systems with Prediction Observers

    Summary

    Problems

    References

    Linear Discrete-Time Optimal Control

    Introduction

    Discrete Linear Regulator Problem

    Cost of Control

    Reciprocal Eigenvalues and Reciprocal Root Locus

    Steady-State Regulator Problem by Eigenvector Decomposition

    Optimal control About Nonzero Set Points

    Suboptimal Control Employing Estimated State Feedback

    Summary

    Problems

    References

    Discrete-Time Stochastic Systems

    Introduction

    Probability and Random Variables

    Expectation Operator and Statistical Moments

    Dependence, Independence, and Conditional Probabilities

    Joint Gaussian Random Variables

    Linear Combinations and Linear Transformations of Gaussian Random Variables

    Scalar Discrete Random Sequences

    Markov and Purely Random Sequences

    Vector Random Sequence

    Random Sequences in Discrete-Time Dynamic Systems

    Stationary Solutions

    Summary

    Problems

    References

    State Estimation in the Presence of Noise

    Introduction

    Derivation of the Discrete-Time Vector Kalman Filter

    Steady-State Kalman Filter Gains by Eigenvector Decomposition

    Summary

    Problems

    References

    Discrete-Time Stochastic Control Systems

    Introduction

    Optimal Control with Random Disturbances and Noiseless Measurements

    Control of Randomly Distributed Systems with Noise-Contaminated Measurements

    Average Behavior of the Controlled System

    Steady-State Control System Dynamics

    Summary

    Problems

    References

    Introduction to System Identification

    Introduction

    Least-Squares Technique

    Transfer Function Estimation Using Least Squares

    Weighted Least Squares

    Recursive Least Squares

    Effects of Noise

    Summary

    Problems

    References

    Appendix A: Tables and Properties of z-Transforms

    A.1 Proof of the Complex Inversion Integral for the z-Transform

    Appendix B: Algebraic Eigenvalue-Eigenvector Problem

    B.1 Introduction

    B.2 Statement of the Problem

    B.3 Application of the Eigenvalue Problem to Discrete-Time Systems

    B.4 Controllability and Observability

    B.5 Cayley-Hamilton Theorem

    References

    Appendix C: Proof of the Matrix Inversion Lemma

    Appendix D: Digital Control Designer

    Index

    Biography

    Raymond G. Jacquot

    ". . .ideal for any student of classical theory. "
    ---Proceedings of the Institution of Mechanical Engineers Vol 209