Identification Of Fractional-order System Based On Operational Matrix And Tuning Of Fractional-order Controller

Fractional order system is the generalization of integer order system. Compared with the integer order system, the fractional order system has greater flexibility in describing dynamic systems, due to the order of the fractional order system can be arbitrary real number. In addition, the fractional-order controller has a new advantage over the integer-order controller, in which the order is adjustable. Therefore,fractional system analysis and fractional control methods have become a hotspot.However, fractional differentiation is a nonlocal operator, which is much more complex than the integer order differentiation. So, fractional integration operational matrix was used to carry out the research of fractional order system analysis,fractional order system identification and other related issues. The main works are concluded:Considering the nonlocal features of fractional differentiation, we take Haar wavelet to approximate the input and output signals of the system, a fractional system analysis method based on Haar wavelet integral operation matrix is given.The correctness of the proposed method was verified by comparing the exact solution of the system and the results of other algorithms. The reason for the fractional order system identification is more complicated than the integer order system identification, lies in the order identification of the system. If the fractional order is directly identified as a parameter, it will lead to a nonlinear optimization problem. For this reason, we transformed the problem into the least squares optimization problem by given orders of the system, and then the optimal order is found in a certain range by the errors between the identified system and the real one.Besides, inspired by the wavelet multi-resolution analysis, we developed a method to speed up the fractional system identification by abandoning the input and output high frequency coefficients to reduce the dimension of operational matrix. The feasibility and correctness of the method are verified by the identification of the known system.As application, the proposed method is applied to the identification of multi-mass elastic torsion system. The mean square error of the identified integer order model and fractional order model show that the fractional order model is more advantage than the integer order model. In the end, according to the identified model of multi-mass elastic torsion system, the PI?D? controller is designed to control the system. The simulation results show that the fractional order PI?D? controller has better control effect than the integer order PID controller, and the control effect of fractional order PI?D? is verified on the real platform.