Robustness diagrams based optimal design of run-to-run control subject to deterministic and stochastic disturbances

In this article, we present a robust optimal design methodology for run-to-run control to cope with batch processes subject to deterministic shifts of various magnitudes and stochastic disturbances with first-order autoregressive moving average dynamics. A tradeoff performance index is developed in closed form to assess both transient and asymptotic properties of output quality in the presence of fixed metrology delays. The performance index can be easily minimized to find the unconstrained optimal design of a run-to-run controller implemented by a second-order filter in the internal model control framework. Not only do such design results clearly reveal when and why the conventional exponentially weighted moving average controller is not the best choice, but they also indicate that the second-order filter would constitute the best controller structure and achieve superior performance. If the unconstrained design does not satisfy the inequality constraints on robust stability, a constrained optimal design is sought and several robustness diagrams are established to enclose optimal solutions of filter parameters subject to specified gain margins. With the aid of these diagrams, a convenient design procedure for metrology delays of zero and one is furnished to resolve difficulties in constrained optimization and identify rapidly the globally optimal design of the second-order filter. The design methodology is justified by simulated examples faced with a wide variety of deterministic and stochastic disturbances, assigned model mismatch, and different metrology delays.