A model-free technique for designing fixed-order controllers

This paper suggests a model-free control design technique for unknown stable single-input-single-output (SISO) systems. In traditional control design approaches, a mathematical model of the plant is first identified using a set of measurements, then a controller is designed on the basis of this model. However, the use of such identified models, which are often subject to several uncertainties due to the complexity involved in many practical applications, usually results in degradation of the controller performance. Unlike model-based control approaches, we propose here to directly utilize the measured data in the controller design without going through a model identification. Our proposed control method consists in finding a suitable fixed-order controller for which the closed-loop frequency response is very close to a desired frequency response that describes some desired closed-loop performance indices. This problem is formulated as a minimization problem, where the objective function is defined by the integral of the squared relative error between the closed-loop frequency response and the desired frequency response. The main feature of our proposed method is that the design process does not depend on the increasing order and complexity of the system. Moreover, it enables to design loworder controllers. For simulation purposes, a PID controller is designed to illustrate the feasibility and demonstrate the efficacy of the proposed technique. Index Terms-Model-free control; Unknown systems; Reduced-order controller; Frequency response; Relative error minimization.