# Introduction to Discrete Linear Controls

## 1st Edition

### Theory and Application

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eBook ISBN: 9781483277905
Published Date: 28th January 1975
Page Count: 394
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## Description

Introduction to Discrete Linear Controls: Theory and Applications focuses on the design, analysis, and operation of discrete-time decision processes.

The publication first offers information on systems theory and discrete linear control systems, discrete control-system models, and the calculus of finite differences. Discussions focus on the calculus of finite differences and linear difference equations, summations, control of cylinder diameter, generalized discrete process controller with sampling, difference equations, control theory, and system models. The text then examines classical solution of linear difference equations with constant, inverse transformation, and measures and environmental effects of system performance.

The manuscript takes a look at parameter selection in first-order systems considering sampling and instrumentation errors, second-order systems, and system instability, including responses of the generalized second-order process controller; criterion for stability of discrete linear systems; and proportional-plus-difference control.

The publication is a valuable source of information for engineers, operations researchers, and systems analysts.

﻿Preface

Acknowledgments

Chapter I Systems Theory and Discrete Linear Control Systems

1.1 Systems Theory

1.2 Discrete Systems

1.3 Control Theory

1.4 Control Systems

1.5 System Models

Exercises

Chapter II Discrete Control-System Models

2.1 Difference Equations

2.2 Control of Cylinder Diameter

2.3 Generalized Discrete Process Controller with Sampling

2.4 Production-Inventory Control System

2.5 Criminal Justice System Feedback Model

2.6 Conclusion

Exercises

Chapter III The Calculus of Finite Differences

3.1 Differences

3.2 Factorial Polynomials

3.3 Summations

3.4 The Calculus of Finite Differences and Linear Difference Equations

Exercises

Chapter IV Classical Solution of Linear Difference Equations with Constant Coefficients

4.1 The Nature of Solutions

4.2 The Homogeneous Solution

4.3 The Particular Solution

4.4 Boundary Conditions

4.5 Finding the Roots of the Characteristic Equation

Exercises

Chapter V The z Transform

5.1 The Basic Transform

5.2 Properties of the z Transform

5.3 Tables

5.4 Transformation of Linear Difference Equations

5.5 The z Transform as a Probability Generating Function

Exercises

Chapter VI Inverse Transformation

6.1 Contour Integration

6.2 Table of Transform Pairs

6.3 Power Series Expansion

6.4 Maclaurin Series Expansion

6.5 Partial Fraction Expansion

6.6 The Special Case of zn = 0

6.7 Transfer Functions

6.8 Solution of Difference Equations with Generalized Forcing Functions

6.9 Conclusion

Exercises

Chapter VII System Performance: Measures and Environmental Effects

7.1 Control-System Performance Criteria

7.2 The Cylinder-Diameter Controller

7.3 Impulse Perturbation

7.4 Step Perturbation

7.5 Sinusoidal Perturbation

7.6 Random Perturbations

7.7 Selection of K

Exercises

Chapter VIII Parameter Selection in First-Order Systems Considering Sampling and Instrumentation Errors

8.1 The Simple Proportional Process Controller with Measurement Error

8.2 Properties of Measurement Error ɛ(i)

8.3 Sampling

8.4 Instrumentation

8.5 Distribution of Individual Product Units

8.6 Maximum Speed of Response with Bounded Steady-State Process-Output Variance

8.7 Maximum Speed of Response with Bounded Steady-State Variance of Individual Product Units

8.8 Maximum Speed of Response with Random Perturbation and Bounded Steady-State Process-Output Variance

8.9 Maximum Speed of Response with Random Perturbation and Bounded Steady-State Variance of Individual Product Units

8.10 Minimum Steady-State Mean-Square Deviation of Process Output

8.11 Minimum Steady-State Mean-Square Deviation of Individual Product Units

8.12 Maximum Steady-State Probability of Acceptable Process Output

8.13 Maximum Steady-State Probability of Acceptable Individual Product Units

8.14 Other Possibilities

Exercises

Chapter IX System Stability

9.1 General Definitions

9.2 Criterion for Stability of Discrete Linear Systems

9.3 Tests for Stability

Exercises

Chapter X Second-Order Systems

10.1 The Second-Order System

10.2 The Generalized Second-Order, Rapid-Response Process Controller

10.3 Responses of Generalized Second-Order Process Controller

10.4 Proportional-Plus-Difference Control

10.5 Proportional-Plus-Summation Control

10.6 Proportional Control with One-Period Delay

Exercises

Chapter XI nth-Order and Complex Systems

11.1 Signal Flow Graphs

11.2 Step-Function Response of nth-Order Generalized Process Controller

11.3 Effects of Delay on Process Controller Stability

11.4 Determination of Frequency Response from the System Transfer Function

Exercises

References

Index

## Details

No. of pages:
394
Language:
English
Published:
28th January 1975
Imprint: