Analysis Of Convergence Rate Of Iterative Learning Control Algorithm

For the control systems to perform the same task repetitively, ILC (Iterative Learning Control) strategy is very simple and effective, and needs the less prior knowledge. It can improve the tracking performance in the finite time interval.The main contents and results studied in this thesis are as follow:(1) The first order open-closed-loop P-Type ILC algorithm is proposed. By means of the Contraction Mapping Principle, its convergence is proven. And its convergent rate is discussed with the robust optimal design. So it is arrived that the proposed algorithm converges faster than the only open-loop P-Type ILC algorithm.(2) The second order open-closed-loop P-Type ILC algorithm is given. By means of the same method as first order algorithm, the convergence rate of second order law is analyzed. It is found that the proposed law converges faster than second order open-loop law but lower than the proposed first order law.(3) The M-order open-closed-loop P-Type ILC algorithm is proposed. By means of the similar way as the first order law, its convergence rate is faster than the same order open-loop law. And it is proven that the M-order ILC law converges faster than the (M+1)-order law. So convergent speed of the first order ILC law is the fastest, whose main reason is that the simply linear combination of the previous errors can not provide the control systems with the new information. And it is possible to degrade the performance of the control systems.(4) The nonlinear ILC algorithms, Newton-Type and Secant-Type, are studied. The former converges faster than the latter. Although their convergence speed is faster than the linear ILC law, their convergent conditions are restrictive, that is, the Newton-Type and Secant-Type ILC algorithms are locally convergent. On the other hand, the faster their convergence speeds are, the more restrictive the convergent conditions are. In order to accelerate the convergence rate,the new scheme associating the nonlinear ILC law with the proposed first order ILC algorithms is proposed.