Research On The Design And Realization Methods For Fractional Order Control Systems

Integer order systems are finite dimensional, while fractional order systems are infinite dimensional with the fractional order of calculus. while the research of fractional order sys-tems is very important. With the fractional calculus theory penetrating into various research fields, its combination with control theory attracted more and more attention to fractional or-der system. Related studies indicated that, using fractional order controllers may obtain better performances than traditional integer order controllers. Design of fractional order controller has become one of the hot topics of the fractional order system researches.This paper mainly studies the approximations of fractional order systems and the de-signs of the fractional order controllers. In the aspect of fractional order system approxima-tion, based on the improvement of Chareff’s method, a continuous approximation method is proposed, which is based on the optimization process to approximation both amplitude and phase characteristics of the original system. In the aspect of fractional order controller design, ITAE optimization indexes is used to design fractional order PID controllers in time domain. It is analyzed for the control performance of fractional order PID controller to be better than that of the integer order PID controller. For the system with high uncertainty and disturbance, combined with quantitative feedback theory (Quantitative Feedback Theory, QFT) robust design method, a design method of the fractional order QFT controller is proposed.In this paper, the innovative research work and achievements can be summarized as follows:In the third chapter, for fractional order system with various structures, a continuous approximation method is proposed, which is based on the PSO optimization process and perform well both in amplitude approximation and phase approximation. Firstly, Based on the study of Chareff continuous approximation method, for single pole fractional order sys-tem, an optimal approximation method, with amplitude and phase as the optimized target, is proposed. Secondly, the approximate method is extended to multiple fractional poles sys-tem, FO[FO] transfer function and the fractional order oscillating system. Finally the real non-integer order is extended to complex non-integer order. In the fourth chapter, based on the ITAE optimization index, fractional order PID con-troller is designed for the integer and fractional system, and it is demonstrated for fractional order PID controller is better than the best integer order PID controller in the closed-loop performance. Whether in the ITAE index of the output response or in the robustness with the system parameter changes, the control effect of the fractional order PID controller is better than that of the integer order PID controller.In the fifth chapter, the design method of fractional order PID controller is proposed based on the multi-objective optimization. Fractional order PID controller, due to the two extra variable orders, is able to meet more system performance indexes. These indexes may restrict each other and even be contradictory, so the best controller, meeting all the indexes, can not be found. While using the multi-objective optimization, Pareto preference solution set of fractional order PID controller method can be obtained. Then policymakers can choose the right the controller parameters depending on their requirements.In the sixth chapter, firstly for high uncertainty and disturbance of the system, based on quantitative feedback theory (QFT), the design of the fractional order QFT controller is studied. It includes the designs of fractional feedback controller and fractional prefilter. Secondly, the design of the fractional order QFT controller is extended to non-minimum phase system and unstable system with one unstable pole. The main idea is that the phase shift will transform the design of fractional order QFT controller for non-minimum phase systems and unstable systems into that for stable minimum phase systems. Finally, the design of fractional order QFT controllers is extended to some nonlinear systems. The main idea is that the original nonlinear systems are replaced by the equivalent linear system set, and then the method above is used to design of fractional order QFT controller.