TAILIEUCHUNG - Iterative learning control - what is it all about?
The main objective of this paper is to show how one can benefit from using Iterative Learning Control instead of conventional feedback control. As a main result it is shown that even if the nominal plant satisfies a given uncertainty condition, there always exists ILC algorithms that can drive the tracking error monotonically to zero. This same result cannot be achieved with conventional feedback control, or by inverting a nominal model of the plant. Hence ILC offers an unique tool to invert dynamical systems with uncertainty. | IFAC Workshop on Adaptation and Learning in Control and Signal Processing, and IFAC Workshop on Periodic Control Systems, Yokohama, Japan, August 30 – September 1, 2004 ITERATIVE LEARNING CONTROL - WHAT IS IT ALL ABOUT? J Hätönen ∗,1 , T J Harte ∗,1 , D H Owens ∗ , J Ratcliffe ∗∗,1 , P Lewin ∗∗ and E Rogers ∗∗ ∗ Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD,United Kingdom Email: ∗∗ Department of Electronics and Computer Science University of Southampton Southampton SO17 1BJ United Kingdom Abstract: The main objective of this paper is to show how one can benefit from using Iterative Learning Control instead of conventional feedback control. As a main result it is shown that even if the nominal plant satisfies a given uncertainty condition, there always exists ILC algorithms that can drive the tracking error monotonically to zero. This same result cannot be achieved with conventional feedback control, or by inverting a nominal model of the plant. Hence ILC offers an unique tool to invert dynamical systems with uncertainty. Keywords: Iterative learning control, robust control, positive-real systems Even if some of these results on causal ILC could be viewed to be of minor theoretical interest, in reality, the focus of Iterative Learning Control research has for a long time been concentrated on ‘non-causal’ algorithms. Already the publication (Furuta and Yamakita, 1987) uses non-causal ILC to achieve monotonic convergence for a large class of continuous-time LTI systems. In other words, the idea of using noncausal ILC is at least 17 years old. Also (Amann et al., 1996) proposes an inherently non-causal algorithm, termed Norm-Optimal Iterative Learning Control algorithm, which results in geometric convergence for an arbitrary discrete-time LTI plant. Furthermore, these non-causal algorithms have been implemented with good results on real systems, see (Al-Towaim et al., .
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