An optimal design of PD-type iterative learning control with monotonic convergence

Iterative learning control (ILC) is a technique to make use of the repetitiveness of the tasks a system is commanded to execute in a fixed finite time interval. In this paper, we assume that a measured finite impulse response series of the plant to be controlled is available. We present an optimal design procedure for the commonly used PD-type ILC updating law. The monotonic convergence in a suitable norm topology other than the exponentially weighted sup-norm is emphasized. For practical reasons, an averaged difference formula for a numerical derivative estimate is preferred over the conventional one step backward difference method for smoothing out the high frequency noise. From the analysis, we show a trade-off between noise suppression and the rate of monotonic convergence of the ILC process.