The Divide-and-Conquer Method for Modelling and Control of Nonlinear Systems: Some Important Issues Concerning Its Application

Abstract

Divide-and-conquer methods, in the context of nonlinear dynamic systems modelling and control design, break the problem down into a number of simpler, frequently linear modelling and control design problems, each associated with a restricted operating region. The most widespread divide-and-conquer nonlinear control design method is probably gain-scheduling. The gain-scheduling method has been successfully applied in many fields, ranging from process control to aerospace engineering. The basic idea behind the method is to divide the nonlinear system to be controlled into local subsystems described by linear dynamic models. A linear control problem is then solved for each of these subsystems. The global control solution—called gain-scheduling control—is obtained by merging partial local solutions. The idea of divide-and-conquer seems very attractive, but its application is not straightforward. The following issues arising during system modelling and control design are treated in this chapter: the properties of the global nonlinear model vis à vis the properties of the local linear models; controller design from first-principles nonlinear continuous-time models; and control design based on local models identified from measured data. The problems are elaborated on simulated examples that include vehicle dynamics and a continuous stirred tank reactor. How to properly use these methods is illustrated by pressure control design on a semi-industrial gas–liquid separator unit.