Identification of linear fractional order systems using the relay feedback approach

Abstract

The relay feedback approach has been used to identify integer order models. Fractional order systems are usually identified by many other approaches. Yet, using the relay feedback to identify a fractional order system has not been reported. This paper investigates this interesting and useful topic by means of extending the relay feedback identification method from integer order systems to a class of linear fractional order systems. Equations are derived for model parameter calculation. Simulation and experiments are presented to verify the feasibility and effectiveness of the proposed approach. I. INTRODUCTION data or need much knowledge of the system to be identified; hence, they lack the vitality in industry. In this paper, the identification of a fractional order plus dead time (FOPDT) model in frequency domain using the relay feedback approach is proposed. The describing function method is utilized as a tool to obtain the system information at the self-sustained oscillation point. Compared with the integer order systems, the difference lies in the equations for computing the model parameters, especially the fractional order, α. Thus, the major contribution of this paper is to generalize the equations for integer order models to fractional order models, which further reveals that the equations for IO systems are particular cases of those for FO systems. Simulation and experiments based on relay feedback tests at multiple frequency points are presented to demonstrate the proposed method. The benefits and limitations of this method are commented and the identification error is briefly discussed. The rest of the paper is organized as follows. First, the proposed method is elaborated through math derivations; then the implementation procedure of the method is demon- strated in simulation and an experiment, respectively; finally, the advantages, limitation and potential improvement are commented.