Iterative Learning Control Design for Discrete-time Systems Using 2-D System Theory

A two-dimensional (2-D) system theory based iterative learning control (ILC) method for a class of linear discrete-time uncertain systems is presented in this paper. We consider a general ILC scheme comprises a learning controller for betterment along iteration axis and two feedback controllers, a state feedback controller and a dynamic error compensator for robustness and convergence along time axis. A 2-D Roesser’s model for a class of learning controllers is established, which reveals the connections between ILC systems and 2-D system theory. By representing the ILC system into a 2-D system model, certain fundamental results from stabilization of 2-D systems can be utilized for the ILC design. In this paper we adopt simple methods for the calculation of controller gain matrices, by solving two decoupled lower dimensional Riccati equations. The proposed methodology reduces the complexity in learning controller design and robust with respect to small perturbations of the system parameters and with variable initial conditions. The proposed learning algorithm is applied to injection molding process control problem. Simulation results verify the feasibility of the proposed design procedure.