Robustness diagrams based optimal design of run-to-run control subject to deterministic and stochastic disturbances. (March 2018) - Hwang, Shyh-Hong; Lin, Jui-Chi; Wang, Hsin-Chun
Graphical abstract: Highlights: A design methodology is presented for run-to-run control under ARMA disturbances. A closed-form tradeoff index well assesses the real performance with random nature. A better controller is proposed to replace the conventional EWMA controller. Robustness diagrams can enclose optimal designs with desired stability margins. A diagram-based procedure is provided to find rapidly the globally optimal design. Abstract: 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.