1st Edition

Sensitivity of Automatic Control Systems

ISBN 9780849322938
Published November 23, 1999 by CRC Press
452 Pages

USD $195.00

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Book Description

Although it arose much earlier in a variety of contexts, sensitivity theory became an independent branch of science in the sixties. Since then, researchers from around the world have continued to make great strides in both the theory and its applications. However, much of the work of Russian scientific schools and specialists remain unknown in the West.

Sensitivity of Control Systems summarizes the results of the authors and their disciples in sensitivity theory, addressing the basic notions of the theory and the problem of selecting technical parameters of systems. The authors formulate problems for actual technical systems and their models, and establish relations between sensitivity theory and classical stability problems. They offer a significant, general theory for investigating the sensitivity of boundary problems and use elements of this theory for sensitivity analysis of solutions to nonlinear programming and variational calculus problems, as well as oscillatory processes. The book also presents general investigation methods for discontinuous systems, including those described by operator models.

Full of powerful new methods and results, this book offers a unique opportunity for those in theoretical investigation and in the design, testing, and exploitation of various control systems to explore the work of Russia's leading researchers in sensitivity theory. Furthermore, its techniques for parametric perturbation investigation, Sensitivity of Control Systems will prove useful in fields outside of control theory, including oscillation theory, motion dynamics, and mathematical economy.

Table of Contents

Parametric Models
State Variables and Control System Parameters
Parametric Models of Control Systems
Sensitivity Functions and their Applications
Finite-Dimensional Continuous Systems
Finite-Dimensional Continuous Systems Depending on a Parameter
Second Lyapunov's Method in Sensitivity Theory
Sensitivity on Infinite Time Intervals
Sensitivity Analysis of Self-Oscillating Systems in the Time Domain
Sensitivity of Non-Autonomous Systems
Sensitivity of Solutions of Boundary Value Problems
Finite-Dimensional Discontinuous Systems
Sensitivity Equations for Finite Dimensional Discontinuous Systems
Sensitivity Equations for Relay Systems
Sensitivity Equations for Pulse and Relay-Pulse Systems
Discontinuous Systems Given by Operator Models
Operator Parametric Models of Control Systems
Operator Models of Discontinuous Systems
Sensitivity of Operator Models
Sensitivity Equations of Relay and Pulse Systems
Non-Time Characteristics
Sensitivity of Transfer Function and Frequency Response of Linear Systems
Sensitivity of Zeros and Poles
Sensitivity of Eigenvalues and Eigenvectors of Linear Time Invariant Control Systems
Sensitivity of Integral Quality Indices
Indirect Characteristics of Sensitivity Functions
Sensitivity Invariants
Sensitivity Invariants of Time Characteristics
Root and Transfer Function Sensitivity Invariants
Sensitivity Invariants of Frequency Responses
Sensitivity Invariants of Integral Estimates
Sensitivity Invariants for Gyroscopic Systems
Sensitivity of Mathematical Programming
Sensitivity of Linear Programming Problems
Sensitivity of Optimal Solutions of Non-Linear Programming Problems
Sensitivity of a Simplest Variational Problem
Sensitivity of Variational Problems with Flexible Boundaries and Corner Points
Sensitivity of Variational Problems on Conditional Extremum
Applied Sensitivity Problems
Direct and Inverse Problems of Sensitivity Theory
Identification of Dynamic Systems
Distribution of Parameter Tolerance
Synthesis of Insensitive Systems
Numerical Solution of Sensitivity Equations

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Efim Rozenwass, Rafael Yusupov


"This book covers the sensitivity of both linear and nonlinear discontinuous systems…Rigorously justifies the use of first approximations-which are the basis of most applied problems."
- Mechanical Engineering
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