Fractional System Identification And Tuning Of Fractional Controller Based On Frequency Property

In recent years, with the development and progress of science and new technology, requirements for control systems are becoming increasingly high, especially in some special fields, such as:viscoelastic material, electrolysis chemistry and so on. The common integer order calculus control theory cannot meet the requirements very well. The fractional calculus theory, especially the fractional calculus control theory has attracted more and more attention from researches, and has been developed rapidly. However, its application research in the control area has just started, so there are many aspects needed to be studied.In this paper, a further study has been made about the following aspects of fractional order calculus control theory on the basis of previous studies:The general fractional SISO system (the order is an arbitrary positive number) transfer function model parameter identification problem is proposed according to the frequency characteristics of fractional differential operator. According to the characteristics of identification problem the variable damping least square method (Levenberg-Marquardt Method) is applied to solve this nonlinear identification question. The feasibility and effectiveness of this approach is proved by the simulation results.As the characteristics of commensurate fractional order system, this paper presented an iterative least square identification algorithm for this kind of fractional order systems in frequency-domain. In order to predigest the calculation, a method of separated the real part and the imaginary part of the frequency data to calculation process is introduced. Simulation results show that even with the noise interference the method also has the significantly affect of improving the identification accuracy.According to the frequency characteristics of a fractional order controller PDμ, tuning method for the fractional order controller is deduced to make it satisfy the phase margin and gain robust for the plant which contains the pure integrator segment. Simulation results show the effectiveness of this tuning method.