Variable Gain Feedback $PD^{\alpha}$ -Type Iterative Learning Control for Fractional Nonlinear Systems With Time-Delay

A variable gain feedback PD
^α
-type iterative learning control (ILC) update rate is proposed for the fractional-order nonlinear systems with time delay. The learning update rate combines the open-loop and closed-loop strategy, in which the system's current tracking error and the previous iterative control of the tracking error are simultaneously used to correct the control effect. So, the proposed method could both speed up the convergence rate along the iteration direction and reduce the tracking error along the time direction. Furthermore, the algorithm ensures that the system has good learning efficiency and control performance at the different running time and iterative batches due to the time-iteration-variable learning gain. The sufficient condition for the convergence of the proposed algorithm is analyzed. Finally, the validity of the proposed method is verified on a numerical example and a wind power generation system.