Two-dimensional (2-D) system theory based learning controller design

A two-dimensional (2-D) system theory based iterative learning control (ILC) method for a class of linear discrete-time multivariable systems is presented in this paper. Practical ILC schemes comprise of a feed-forward learning controller along with feedback controllers for improved stability and convergence, termed as feedback assisted iterative learning control (FAILC). As a general format we consider that FAILC 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 proper transformation of FAILC system into a 2-D system model, certain fundamental results from the stabilization of 2-D systems can be successfully utilized for the FAILC design. Simple methods are adopted for the learning gain matrix calculation, by solving two decoupled lower dimensional Riccati equations. The proposed method reduces the complexity of the learning controller design, robust with respect to the small perturbations of the system parameters and with variable initial conditions. The proposed learning algorithm is applied to the injection molding velocity control problem and the results show the effectiveness of the design procedure.