Modeling and Compensation of Nonlinear Systems Using Sensitivity Analysis

Abstract

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.