Context-kernel support vector machines (KSVM) based run-to-run control for nonlinear processes
Past studies on multi-tool and multi-product (MTMP) processes have focused on linear systems. In this paper, a novel run-to-run control (RtR) methodology designed for nonlinear semiconductor processes is presented. The proposed methodology utilizes kernel support vector machines (KSVM) to perform nonlinear modeling. In this method, the original variables are mapped using a kernel function into a feature space where linear regression is done. To eliminate the effects of unknown disturbances and drifts, the KSVM expression for the KSVM controller is modified to include constants that are updated in a manner similar to the weights used in double exponential weighting moving average method and the control law for KSVM controllers is derived. Illustrative examples are presented to demonstrate the effectiveness of KSVM and its method in process modeling and control of processes. Even if there is limited data in process modeling, KSVM still has the good capability of characterizing the nonlinear behavior. The performance of the proposed KSVM control algorithm is highly satisfactory and is superior to the other MTMP control algorithms in controlling MTMP processes.
Key wordsBatch Process Kernel Support Vector Machines Nonlinear Processes Run-to-run Control
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- 2.E. D. Castillo and A. M. Hurwitz, J. Quality Technol., 29, 184 (1997).Google Scholar
- 4.V. Vapnik, Estimation of Dependences Based on Empirical Data [in Russian] 1979. Nauka, Moscow (English translation: Springer-Verlag, New York, 1982).Google Scholar
- 5.V. Vapnik, The Nature of Statistical Learning Theory, Springer-Verlag, New York (1995).Google Scholar
- 7.C.A. Bode, J. Wang, Q. P. He and T. F. Edgar, Annual Reviews in Control, 31, 241 (2007).Google Scholar
- 8.J. Wang, Q. P. He and T. F. Edgar, American Control Conference, 3636 (2007).Google Scholar
- 11.S. Gaddam and M.W. Braun, Advanced Semiconductor Manufacturing Conference and Workshop, 17 (2005).Google Scholar