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