Dual-rate adaptive control

An operator, called the dual-rate transfer function, describing a dual-rate discretized continuous-time system is presented. It can be easily related to single-rate transfer functions of the same system, and its parameters can be experimentally estimated. Based on these models, two adaptive control strategies are outlined, and some results are illustrated by a simple example. Copyright 0 1996 Elsevier Science Ltd. 1. Introduction Digital control techniques offer many possibilities that are unavailable with linear continuous-time invariant controllers. Finite-time control is one of these, (Isermann, 1981). On the other hand, sampling of continuous-time signals implies loss of some information, and some unexpected problems can appear in the intersampling period. These two features are reinforced if extra control actions are taken in that period. It is a classical result (see e.g. Astrom and Wittenmark, 1984), that the closed-loop discrete-time transfer function zeros may be arbitrarily placed with either a periodic feedback gain or a generalized type of hold circuit. Stronger discrete-time results are obtained if generalized sample-data hold functions or periodic controls are implemented, as explained in Chen and Francis (1991), and Kabamba (1987) respectively. Recent work of Goodwin and Feuer (1992) points out that the intersampling behaviour of the actual process output is sometimes unacceptable. In some industrial applications, and mainly if the controlled output is measured by means of an analyzer-like device, samples of the output are obtained at a rate that is slower than the possible updating control rate. Thus, under these circumstances, dual-rate control is suitable. Lu and Fisher (1992) and Guillandoust et al. (1987), for example, have proposed models for this kind of processes. In the contributions of Salt et al. (1993,1994), a new approach to deal with this problem has been presented. The purpose of this paper is to analyse the features of this new model and to show its suitability to implement an adaptive control scheme, where the output is available at a rate lower than that of the control updating. Obviously, the above-mentioned intersampling-period problems also could appear. Although the available sequences of input and output data are not equally spaced, they have the maximum information about the process behaviour. The proposed approach tries to model the process using this information. In a second stage, a single-rate model is derived, allowing the use of any standard controller design technique. If the designed controller is a slow-rate one, a periodic structure will allow the achievement of …