A control design method for unknown systems using frequency domain data

Abstract

This paper deals with fixed-structure controller design for stable linear systems by using measurements. Most control design approaches developed in the literature are generally based on a mathematical model which can be obtained via identification system by using a set of measured data. However, an identified model, which is often built on the basis of some assumptions, cannot perfectly describe complex behaviors characterizing physical systems. Thus, the performance expected for the closed-loop system will be limited by the quality of such models used in the control design process. Hence, data-based controller design methods can be viewed as a possible alternative to model-based methods. In this paper, we propose to directly utilize frequency response data in the controller design. The principle is to design fixed-structure controllers for which the closed-loop frequency response fits a desired frequency response. This problem is formulated as an error minimization problem. The main feature of our proposed approach is that controller can be designed free of any mathematical model, which allows to avoid errors associated with identification process. Moreover, it enables to select low-order controllers, which are suitable for embedded systems. A simulation example is given to illustrate and validate the efficacy the proposed approach.