Stability and Control Performance Analysis of Double EWMA Controller With Metrology Delay

This paper mainly focuses on establishing the stability conditions of the double exponentially weighted moving average (d-EWMA) controller with metrology delay when the process experiences a general disturbance and analyzing its control performance under some typical types of process disturbance. The necessary and sufficient conditions for stability are established by Routh-Hurwitz criteria. It has been shown that if the process gain mismatch is greater than 4/3, metrology delay will make the feasible region of two weighting factors in the d-EWMA controller decrease, and the larger metrology delay is, the smaller the feasible region is. Moreover, given two weighting factors, it is found that metrology delay will weaken the robustness of the d-EWMA controller. The influence of metrology delay on the asymptotical control performance is evaluated based on asymptotical mean square error (AMSE). Optimal weighting factors and AMSE can be solved based on analytical expression of the AMSE, which is derived by using the Yule-Walker equations to avoid function summing limit operation. Through numerical simulations, it demonstrates that metrology delay may increase the variability of the process output under certain conditions. Finally, the chemical mechanical polishing process in semiconductor manufacturing is used to illustrate the validity of theoretical results.