An Optimal Model-Following Problem for Linear Systems with Variable Disturbances

A model following problem referring to a linear time invariant system with time variant disturbances is studied. An adequate behaviour of the system is achieved by imposing its dynamics to be near to a chosen model. The proposed algorithm uses results from linear quadratic optimal control theory. Simulation tests referring to the discussed problem are presented.

I. Introduction

Starting from the imposed performances and from the mathematical model of the plant, the design of an adequate controller can be performed using different procedures. One of them is to impose a convenient behaviour of the controlled system. For instance, a way is to control the system in a manner which ensures a similar behaviour with a chosen physical model, or with an implicit one. In the latter case, the approach is named the model following. The nearness between the system and the model is appreciated based on an adequate criterion, most frequently being used a quadratic one. For linear systems, this approach leads to a linear quadratic (LQ) optimal problem [1], [2].