Robust Iterative Learning Control For Uncertain Nonlinear Systems

There are various kinds of uncertainties existing in actual systems, and it is usually difficult to obtain accurate mathematical model of the nonlinear system. Iterative learning control techniques are applicable to the controlled objects operating repeatedly in a fix interval. It aims to achieve complete tracking of system output to a desired trajectory over a pre-specified interval through updating the controller input by taking advantages of the previous control experience. Repeated uncertainties and periodic perturbations can be compensated completely by ILC. But there existed many kinds of non-repetitive uncertainties in real application, which can not be compensated completely only by iterative learning control. Robust control technology offers an approach to address the problems caused by various kinds of uncertainties involving non-repetitive and non-periodic ones. In this paper, robust iterative learning control algorithms are proposed for a class of nonlinear systems with uncertainties. Detailed theoretical analysis, numerical simulations and applicable researches are given and the major work covers the following aspects:(1) An iterative learning control algorithm is proposed for a class of nonlinear systems with uncertainties operating repeatedly over a finite time interval. The controller makes the system output converge to a given trajectory and the boundedness of all the signals in the closed-loop is guaranteed.(2) Combined with nonlinear robust control techniques, two kinds of robust iterative learning control algorithms are proposed for nonlinear systems with non-repetitive uncertainties. In order to eliminate the chattering phenomenon, unit vector continuous function and saturation function are used in nonlinear robust control respectively in stead of sign functions. Due to the learning ability of the iterative learning control, the tracking errorover finite interval is completely eliminated, and the boundedness of all the signals in the closed loop system are guaranteed. Numerical simulations are given to verify the effectiveness of the two algorithms.(3) Due to the limitation of the mechanical properties of the system itself, the pehenomenon of input saturation existed in the actual systems. A robust iterative learning controller with input saturation is given to ensure the control input be limited in a given range. The effectiveness of the algorithm is verified by numerical simulations.(4) The above controller design methods are extended to the n degree of freedom robot systems. Theoretical analysis shows that all signals in the closed loop systems are bounded, and the convergence of the tracking error is established. The feasibility and effectiveness of the algorithms are verified through the simulations of the 2 degree of freedom robot systems by using Matlab tools.