System identification for generic model control

Abstract

System identification methods build mathematical models of dynamical systems based on observed data. The intended use of the model should always be reflected in the methods and techniques used for identification. In this paper an identification scheme is derived for the case where the model is going to be used for GMC controller design. The aim of GMC control is to make the output approach a setpoint along a given desired trajectory. This is reflected in the identification scheme which is non-standard in two ways. Firstly, the emphasis is on the output trajectories of the models, and secondly we try to make the prediction errors follow an error trajectory determined by the controller parameters. Simulation studies are included which show that the derived identification scheme performs well.

Introduction

System identification deals with the problem of building mathematical models of dynamical systems based on observed data. System identification is always done with a purpose, and the intended use of the obtained model should be reflected in the methods and criteria used.

Recently system identification for control has attracted much attention, see e.g. the surveys by Gevers[1] and Van den Hof and Schrama[2]. In this paper identification for Generic Model Control (GMC) is considered. GMC3, 4, is a control strategy for nonlinear systems which is popular in the process industry. It is closely related to feedback linearisation (see e.g. Isidori[5]). The aim of GMC is to make the output approach a given setpoint along a prespecified desired trajectory. This aim is reflected in the derived identification method. The predictors employed put emphasis on the output trajectories of the models and not on the individual equation errors. Hence the identification method has common features with methods inspired by the behavioural framework6, 7, 8.

The paper is organised as follows. In Section 2we give a brief introduction to GMC control before we derive the identification method in Section 3. Section 4is devoted to a simulation study where we compare the derived method to other system identification methods. We end with some concluding remarks in Section 5.

In the paper the identification approach is illustrated on a linear system. This may seem a bit strange since GMC is a control strategy for nonlinear systems. However, the principles and techniques remain the same for a nonlinear model structure.