Research On Iterative Learning Control Algorithms

Iterative learning control (ILC for short) is a new addition to the control techniques. With a great foreground in the control for the industry robot, numerical machine and other plants with repetition property, it is feasible in dealing with the nonlinear systems and un-modeling systems and so on. Many researchers have paid their attention to iterative learning control because of its simplicity and effectiveness in recent years. The content of research included learning algorithm, convergence, robustness, initial state and learning rate etc...This paper's main work includes the following aspects: Firstly, the paper introduced a PID-type closed loop ILC algorithm in the linear and nonlinear system and discussed the convergence of the algorithm and the robustness against those disturbances such as initial state error. This algorithm has advantages in excellent robustness and rapid learning rate. Also, the simulation examples were provided in the paper. Then, aimed at the problem of iterative learning control for nonlinear discrete time-variant system, the improved iterative learning control algorithm was given in the paper. The new learning control rule not only incorporated a state compensation in the conventional ILC formula but also adopted the wavelet transform to filter learnable tracking errors without phase shift. The actual output trajectory of the system achieved better convergence to the desired trajectory by using the iterative learning control algorithm. Then, the convergence of the new algorithm was proved in the theory and the simulation examples were also provided. Finally, an iterative learning algorithm was presented for a MIMO linear time-varying system in the paper and a necessary and sufficient condition for the existence of convergent algorithm was proved. Then, we proved that the same condition is sufficient for the robustness of the proposed learning algorithm against state disturbance, output measurement noise, and initialization error. Lastly, a simulation example was given to illustrate the results.