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Introduction to Discrete Linear Controls
Theory and Application
- 1st Edition - January 28, 1975
- Author: Albert B. Bishop
- Editor: J. William Schmidt
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 7 9 0 - 5
Introduction to Discrete Linear Controls: Theory and Applications focuses on the design, analysis, and operation of discrete-time decision processes. The publication first offers… Read more
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Request a sales quoteIntroduction 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
- No. of pages: 394
- Language: English
- Edition: 1
- Published: January 28, 1975
- Imprint: Academic Press
- eBook ISBN: 9781483277905
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