Convergence Analysis Of Iterative Learning Control For Several Class Of Fractional Order Systems

Fractional order calculus is an important branch of mathematical analysis, not only expanding the classical integer order system theory, but also can more accurately describing the system dynamic process. With the continuous improvement of the fractional calculus theory, fractional order controllers gradually become a new research hot spot in control field. On the other hand, as a kind of intelligent control algorithm with strict mathematical logic, Iterative learning control is mainly to solve the periodic signal tracking problem which needs a high precision, the algorithms can be accurately implemented with fewer prior knowledge and total calculationamount,and without depending on the mathematical model of dynamic system. Therefore,ILC algorithm has been concerned by many scholars since it was proposed.Considering more adjustable parameters are provided by fractional order controller, so the possibility of controlling precision is further improved by combining the fractional order with ILC control method. And better tracking performance can be achieved by using the fractional order ILC algorithm. In this paper, the convergence conditions of the iterative learning algorithms for several classes of fractional order systems is studied. The main work are as follows:(1) The P type iterative learning control is presented for a class of fractional-order linear system. The integer order system P type open-loop ILC algorithm is applied to the fractional order linear systems, by introducing the ?-norm and using a generalized Gronwall inequality, the sufficient conditions for the convergence of the tracking errors for open-loop first and second-order P-type ILC are obtained respectively. Next, the convergence speed of the two cases is then compared based on the concepts of the Qp factor. Finally, the validity of the methods is verified in the PMSG.(2) The P-type iterative learning control for fractional order nonlinear delay systems is presented. The learning control process is analyzed for a class of fractional order nonlinear delay systems. The design problem of the ILC algorithmtranslates into the stability analysis of sufficient condition for discrete system, by introducing?-norm and Gronwall-Bellman lemma, the sufficient conditions of open-loop P type second order iterative learning control for the convergence of the tracking error and control input are obtained,. The validity of the method is verified by a numericalexample.(3) Iterative Learning Control With Switching Gain PD? Feedback for fractional-order Nonlinear Systems, an iterative learning control algorithm with switching gain PD? feedback of a class of repeated nonlinear time-varying systems containing uncertainties or disturbances is presented, by introducing the ?-norm and using a generalized Gronwall inequality. It is proved that the tracking error of the controlled system is uniformly bounded if the disturbance is bounded.