Research On Iterative Learning Control Algorithms For Singular Systems

Iterative Learning Control(ILC) is suitable for a controlled system with repetitive motion, particularly when the system is strongly nonlinear and difficult to build a mathematical model, iterative learning control has certain advantages. the ILC has achieved fruitful results in both theory and application with the development of more than thirty years.Singular system has a wide application background, such as power systems, economic systems, etc. Compared to the normal system, the form of singular system is more general and the essence of system structure is also different. While, existing researches of ILC are most aimed at normal system, there are very limited studies on ILC for singular system. Therefore,the study of ILC for singular system in this paper is significant, and the main works are shown as follows.(1) The output convergence of ILC for a class of linear time-invariant singular system with fixed initial value(not the desired value) is studied in this paper. A kind of closed-loop D-type ILC algorithm is proposed and it's proved theoretically that the output of the system is uniformly convergent to a neighborhood of the desired trajectory under the given convergence condition.(2) The initial value problem of ILC for a class of linear time-invariant singular system is studied, the strategy that let initial value and control input both to “learn” at same time is adopted, it is proved theoretically that the output of the system can track the desired trajectory completely under the given learning law. The numerical simulation results show the validity of the learning strategy and the correctness of the conclusion.(3) Based on a kind of restricted equivalent form of singular system, the state track problem of ILC for a class of discrete-time singular system is studied. A kind of closed-loop leading-type ILC algorithm is proposed, the convergence of the algorithm is proved in theory and the state of the system can track the desired trajectory, the numerical simulation verify the effectiveness of the algorithm.(4) For a class of linear singular system with multiple state time-delays, a kind ofclosed-loop PD-type ILC algorithm is proposed, convergence conditions of the algorithm is given, and it's proved in theory that the state and output of the system can both track the desired trajectory.(5) For a class of nonlinear singular system with state disturbance, the robustness problem of ILC is studied. It is proved that the tracking error of the system is uniformly bounded, and the output of the system can track the desired trajectory if the disturbance is gradually disappeared.