TABLE OF CONTENTS This chapter discusses a number of issues related to the problem of modelling and identification for control design. The goal is to provide insights and partial answers to the following central question:
How should we identify a model ( ?, ?) in such a way that it is good for control design?
These insights will constitute the thread of this book and each of the following chapters will investigate more deeply some of the questions raised here.
Obviously, a reasonable qualification of a good model ( ?, ?) for control design would be
simultaneous stabilisation: the controller K( ?, ?) designed from this model stabilises both the model ? and the plant G 0, and
similar performance: The performance achieved by the controller K( ?, ?) when it is applied to the real system ( G 0, H 0) is close to the designed performance, i.e., to the performance it achieves with the nominal model ( ?, ?).
The characterisation of all models that satisfy (1), for a model reference control design criterion, was studied in (Blondel et al., 1997) and (Gevers et al., 1997).
Observe that the problem of modelling for control involves three players: the plant ( G 0, H 0), the model ( ?, ?) and the to-be-designed controller K( ?, ?).
(For the sake of simplicity, the latter will simply be denoted...
