ITERATIVE LEARNING CONTROLLER DESIGN FOR MULTIVARIABLE SYSTEMS Manuel Olivares 1 Pedro Albertos Antonio Sala Dept. of Electronics, Univ. Técnica F. Santa María P.O. Box 110-V, Valparaíso, Chile mos@elo.utfsm.cl Dept. of Syst. Eng. and Control, Univ. Politécnica de Valencia P.O. Box 22012, E-46071 Valencia, Spain pedro@aii.upv.es asala@isa.upv.es Abstract: In this paper, a novel expression for the convergence of an iterative learning control algorithm for sampled linear multivariable systems is stated. The convergence analysis shows that, applying this algorithm, the input sequence converges to the system output inverse sequence, specified as a finite-time output trajectory, with zero tracking error on all the sampled points. Also, it gives insight on the learning gain matrix selection to act on the convergence speed or the decoupling of inputs, allowing for an easy tuning using methods from modern control theory. The results are illustrated by some examples, showing a number of options to be investigated. Copyright ©2002 IFAC Keywords: Iterative learning control, multivariable systems, feedforward control, decoupling. 1. INTRODUCTION Iterative learning is a well known methodology allow- ing to incorporate the acquainted experience in the use of preliminary designs to get the final one. Since the seminal work of Arimoto, (Arimoto et al., 1984), this has been successfully applied in the field of control, mainly for repetitive working conditions, like it is the case in many manufacturing applications, with a finite time control horizon. The iterative feature is very attractive from the user viewpoint but a number of formal problems arise, the main one being the existence of a final design, in some sense defined as optimal, to which the iterative solution converges. Some sufficient conditions have been proved, (Moore, 1993; Chen and Wen, 1999), for special cases. Another important problem, if this approach is intended to be applied in a more general range of working conditions, is the need of general- 1 Partially supported by projects USM 23.01.11 and GV00-100-14 ization, that is, to get a final design able to control the plant under operating conditions differing to those in which the learning process was carried out. This can be partially solved in the case of affine in control systems, where some sort of scaling can be applied. One of the drawbacks of the approach is that the controller tends to implement the inverse model of the plant, restricting its application to stable and inverse stable open loop plants. Again, the a priori knowledge of the plant model is a usual requirement that also limits the range of applications. The way the iterative learning approach is imple- mented, usually leads to a feedforward controller. In any control application, an additional control loop would be required to guarantee some kind of distur- bance rejection (Amann et al., 1996b), bounded steady state error and stability margin, as basic controlled system features. In the literature, like in (Shoureshi, 1991; Amann et al., 1996a), there are many proposed algorithms Copyright © 2002 IFAC 15th Triennial World Congress, Barcelona, Spain