The control of nonlinear systems. Part I: Direct search on the performance index

AIChE Journal ◽  
1967 ◽  
Vol 13 (1) ◽  
pp. 101-108 ◽  
Author(s):  
Leon Lapidus ◽  
Rein Luus
Keyword(s):  
Nonlinear Systems ◽  
Performance Index ◽  
Direct Search

Developments in Nonlinear Controller Synthesis: An Overview

1978 ◽  
Vol 100 (1) ◽  
pp. 59-69 ◽  
Author(s):  
Devendra P. Garg
Keyword(s):  
Functional Analysis ◽  
Nonlinear Systems ◽  
Performance Improvement ◽  
Performance Index ◽  
Controller Synthesis ◽  
Analysis Approach ◽  
Nonlinear Controller ◽  
System Synthesis ◽  
Synthesis Techniques ◽  
Nonlinear Controllers

In this paper developments in nonlinear controller synthesis techniques are surveyed. First, the use of functional analysis approach for system synthesis is discussed. Next, the application of intentional nonlinear controllers for performance improvement and optimization via performance index minimization is presented. This is followed by a discussion of signal stabilization using artificial dither. Finally, approaches are given for design of controllers to meet stability requirements for both single and multiple-loop nonlinear systems.

scholarly journals A nonlinear plate control without linearization

2017 ◽  
Vol 15 (1) ◽  
pp. 179-186
Author(s):  
Kenan Yildirim ◽  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Control Problem ◽  
Performance Index ◽  
Control Function ◽  
Initial Boundary ◽  
Quadratic Functional ◽  
Penalty Term ◽  
Nonlinear Plate ◽  
Optimal Control Function

Abstract In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

scholarly journals Performance Index for Optimizing Sensor Fault Detection of a Class of Nonlinear Systems

2018 ◽  
Vol 51 (24) ◽  
pp. 1387-1394 ◽  
Author(s):  
Vasso Reppa ◽  
Stelios Timotheou ◽  
Marios M. Polycarpou ◽  
Christos Panayiotou
Keyword(s):  
Nonlinear Systems ◽  
Fault Detection ◽  
Performance Index ◽  
Sensor Fault ◽  
Sensor Fault Detection

Modeling and Compensation of Nonlinear Systems Using Sensitivity Analysis

1968 ◽  
Vol 90 (2) ◽  
pp. 187-194
Author(s):  
J. G. Thompson ◽  
R. H. Kohr
Keyword(s):  
Sensitivity Analysis ◽  
Nonlinear Systems ◽  
Performance Index ◽  
Characteristic Parameter ◽  
Sensitivity Equation ◽  
System Sensitivity ◽  
System Equation ◽  
Sensitivity Functions ◽  
Minimization Procedure ◽  
Free Parameters

In this paper sensitivity analysis techniques are applied to two aspects of the nonlinear system design problem: The modeling of nonlinear systems and the compensation of nonlinear systems. In the modeling problem the free parameters of the model are selected to minimize an integral performance index where the integrand is a function of the response of the model and the response of the modeled system. Sensitivity functions, which indicate the sensitivity of the response of the model to changes in the free parameters are used in the minimization procedure. Similarly, in the compensation problem, the adjustable parameters of the compensated system are selected to minimize an integral performance index where the integrand is a function of the response of the compensated system and a desired response. Sensitivity functions, which indicate the sensitivity of the response of the compensated system to changes in the adjustable parameters, are again used in the minimization procedure. The sensitivity functions are obtained from multiple solutions of the general sensitivity equation subjected to various forcing functions. The general sensitivity equation is obtained by differentiation of the model equation or of the compensated system equation. The free or the adjustable parameters are determined as functions of some characteristic parameter which represents the magnitude of the input, the degree of the nonlinearity or some other performance characteristic of the system. All the required computations may be performed by a digital computer. Three nonlinear examples are given to illustrate the method.

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