Iterative Learning Control by Two-Dimensional System Theory applied to a Motion System

For systems that repeatedly perform a given task, iterative learning control (ILC) makes it possible to update the control signal to the system during successive trials in order to improve the tracking performance. Iterative learning control has an inherent 2-D system structure since there are two independent variables, i.e. time and trials. In this paper, the 2-D structure is exploited in a method that yields in a one step synthesis both a stabilizing feedback controller in the time domain and an ILC controller, which guarantees convergence in the trial domain. A norm-bounded uncertainty model is added to guarantee a robust controller performance. The controller synthesis can be performed by means of linear matrix inequalities. The effectiveness of the theoretical results will be illustrated using a motion system.