Iterative Learning Control for a Class of Multivariable Distributed Systems With Experimental Validation

This article develops an iterative learning control (ILC) design for a class of multiple-input-multiple-output systems where a distributed heating system is used as a particular example to experimentally validate the design. The class of systems considered is described by a parabolic partial differential equation, which, for control design, is approximated by a finite-dimensional state-space model obtained by applying the method of integro-differential relations combined with a projection approach. In some cases, including the distributed heating system, this approximation may result in a nonminimum phase system and, hence, pose an additional design challenge. In this work, the ILC law is computed in the frequency domain by solving a convex optimization problem, and its performance is evaluated in both simulation and experiment.