Run-to-Run Control Methods Based on the DHOBE Algorithm
Since process models are typically not known exactly in real problems, it is important to estimate the process parameters before one applies the optimal control to a process. In this paper, the Dasgupta–Huang optimal bounding ellipsoid (DHOBE) algorithm is employed to estimate process parameters in semiconductor process run-to-run (RtR) control. At each iteration, the DHOBE algorithm returns an outer bounding ellipsoid of the likely process parameter set. If the vector center of the ellipsoid is taken as the estimate of the process parameter vector, then a model-reference controller results; if the vector within the ellipsoid that produces the worst expected cost is taken as the process parameter estimate, then a worst-case controller results. These two methods are compared with other RtR control schemes: the exponentially weighted moving average (EWMA) method and the optimizing adaptive quality controller (OAQC). Simulation results show that the performance of the model-reference RtR controller based on the DHOBE algorithm is comparable to or better than that of the other two RtR controllers in some specific examples of semiconductor processes.