Discrete Fourier Transform based Iterative Learning Control Design for Linear Plants with Experimental Verification

Abstract

A general class of iterative learning control law is examined using the Discrete Fourier Transform and it is shown that if the nominal plant satisfies a given uncertainty condition, there exist algorithms that are capable of driving the tracking error monotonically to zero. The effect of the filters appearing in the algorithm on the convergence rate is then examined using a bi-linear mapping into the space of plant uncertainty. A weighting function for the convergence rate is subsequently specified as a design parameter, and it is shown that the filters can be chosen to maximise the weighted convergence rate over a given region of uncertainty space. This permits the designer to manipulate the convergence and robustness properties of the algorithm in a straightforward manner. It is then demonstrated how the change of input over successive trials and the residual error may also be incorporated into the cost function. Experimental results are presented using a non-minimum phase test facility to show the effectiveness of the design method.

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Identifiers

ORCID for Christopher Freeman: orcid.org/0000-0003-0305-9246

ORCID for Paul Lewin: orcid.org/0000-0002-3299-2556

ORCID for Eric Rogers: orcid.org/0000-0003-0179-9398

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