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. 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. Via analysis, we show a trade-off between noise suppression and rate of monotonic convergence of the ILC process.