A Discrete-Time Approach for system Analysis
Published on 1. January 1969
236 pages
978-0-323-16229-6 (ISBN)
Description
A Discrete-Time Approach for System Analysis is a five-chapter text that considers the underlying principles and application of a discrete-time approach to system analysis. Chapter 1 presents several different unit functions that are used in practice and describes how to obtain a closed form for the sequence of unit functions by using the E- and the z-transforms. This chapter also compares some aspects of spectral analysis and impulse analysis, and finally, discusses some aspects of interpolation between sampled data of the functions by impulse analysis techniques. Chapter 2 provides the functional operations using the sequences of unit functions, namely, addition, subtraction, multiplication, convolution, deconvolution, integration, and differentiation. Chapter 3 examines linear, time-varying, nonlinear and partial differential equations, and the use of the discrete time approach to solve these equations. Chapters 4 and 5 discuss several applications of impulse analysis to control problems, basically, system analysis and identification. This book is particularly useful to engineers with an introduction to some techniques for finding solutions of certain time-invariant, time-varying, and nonlinear differential equations arising in physical systems.
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Content
Preface 1. Basic Concepts of Impulse Analysis Introduction 1.1 Unit Functions 1.2 Functional Approximation and Sequences 1.3 The E- and z-Transforms 1.4 Impulse Analysis and Frequency Analysis 1.5 Interpolation 2. Operations with Impulse Analysis Introduction 2.1 Addition, Subtraction, Multiplication 2.2 Convolution 2.3 Deconvolution 2.4 Integration 2.5 Differentiation 3. Approximate Solution of Differential Equations Introduction 3.1 Linear Differential Equations 3.2 Time-Varying Differential Equations 3.3 Nonlinear Differential Equations 3.4 Partial Differential Equations 4. Accuracy Considerations Introduction 4.1 Errors and Accuracy Considerations 4.2 Spectral Errors of Integrating Operators 4.3 Error Buildup 4.4 Selecting the Independent Variable Increment 5. Applications of Impulse Analysis to Control Problems Introduction 5.1 System Response to Deterministic Inputs 5.2 System Response to Stochastic Inputs 5.3 Multivariable Systems 5.4 System Identification 5.5 Nonlinear Control Systems 5.6 Conclusions References Table of Main Formulas Appendix: Problems Index
