ABSTRACT
This chapter deals with the problem of determining mathematical models of linear, time-invariant, single-input-single-output discrete-time systems, described by difference equations. In control systems, a mathematical model of a process or system is in most cases necessary for the design of the controller. This becomes apparent if we recall that most of the controller design methods covered in previous chapters are based on the model of the system under control, which was assumed known. A process or a system may be described by several models, ranging from necessarily very detailed and complex microscopic models to simplistic macroscopic models which facilitate the understanding of the gross characteristics of a system’s performance. In many practical cases, it is necessary that parameter estimation takes place concurrently with the system’s operation. This parameter estimation problem is called on-line identification and its methodology usually leads to a recursive procedure for every new measurement.
