Robust Optimal Design of Run-to-Run Controllers Based on Stability Diagrams

Abstract

In semiconductor batch processes run-to-run control is commonly utilized to adjust the input recipe of each run so as to reduce the variability in the product quality caused by disturbances However because of inaccurate controller structures inappropriate performance criteria and poor robustness many run-to-run controllers cannot operate optimally In this thesis a suitable tradeoff performance index and an efficient analysis method for robust stability are developed to establish a robust optimal design procedure for run-to-run controllers subject to various disturbances and different fixed metrology delays This thesis investigates deterministic disturbances of shift and drift types and describes stochastic disturbances by auto-regressive and moving average models The design of a run-to-run controller is based on the internal model control framework which involves second-order and third-order filters to cope with shift and drift disturbances respectively Subsequently transient performance indices are developed to assess the effects of deterministic disturbances and asymptotic performance indices are provided to assess the long-term effects of stochastic disturbances Finally a tradeoff performance index is formed by combining a transient and an asymptotic performance index which can serve as a criterion to assess the overall performance of the controller When two controller designs possess the same gain margins their Nyquist plots may still differ in shape thus making a difference in control performance In general under the robust optimal design the run-to-run controller with robustness constraints should have a Nyquist plot that is similar to that given by the unconstrained optimal control Therefore a robustness analysis method based on the classification of Nyquist plots is furnished by establishing the projected diagrams for robust stability As a result a complete design procedure for the robust optimal run-to-run controller is developed utilizing the tradeoff performance index and robust stability diagrams Simulation studies manifest that the derived second-order and third-order filters are superior to the conventional EWMA and double EWMA filters respectively

Date of Award	2019
Original language	English
Supervisor	Shyh-Hong Hwang (Supervisor)