Iterative learning control for processes with uncertain time delay using minimum entropy

In most batch processes, quality control measurements cannot be completed before the next batch operation. Thus, the corrective step is often delayed by one batch or more. The uncertain duration of delay with stochastic characteristics can be treated as a random variable of unknown distribution. Coupled with inaccurate process models, the delay may lead to significant process output variations even with EWMA controllers. This paper proposes a new method of handling the uncertain metrology delay and its ensuing complications. The run-to-run controller is designed based on minimization of error entropy, and the probability density function of the tracking error can be estimated by the historical operation data. The simulation example demonstrates the effectiveness of the proposed method.