Issue
Korean Journal of Chemical Engineering,
Vol.27, No.5, 1366-1371, 2010
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.
[References]
  1. Qin SJ, Cherry G, Good R, Wang J, Harrison CA, J. Process Control, 16(3), 179, 2006
  2. Castillo ED. Hurwitz AM, J. Quality Technol., 29, 184, 1997
  3. Pasadyn AJ, Edgar TF, IEEE Transactions on Semiconductor Manufacturing., 18, 592, 2005
  4. Vapnik V, Estimation of Dependences Based on Empirical Data [in Russian] 1979. Nauka, Moscow (English translation: Springer-Verlag, New York, 1982).
  5. Vapnik V, The Nature of Statistical Learning Theory., Springer-Verlag, New York, 1995
  6. Suykens JAK, Van Gestel T, De Brabanter J, De Moor B, Vandewalle J, Least Squares Support Vector Machines., Singapore, World Scientific, 2002
  7. Bode CA, Wang J, He QP, Edgar TF, Annual Reviews in Control., 31, 241, 2007
  8. Wang J, He QP, Edgar TF, American Control Conference., 3636, 2007
  9. Wang J, He QP, Edgar TF, J. Process Control, 19(3), 443, 2009
  10. Suykens K, Brabanter JD, Lukas L, Vandewalle J, Neurocomputing., 48, 85, 2002
  11. Gaddam S, Braun MW, Advanced Semiconductor Manufacturing Conference and Workshop., 17, 2005
  12. Miwa K, Inokuchi T, Takahashi T, Oikawa A, Imaoka K, IEEE Transactions on Semiconductor Manufacturing., 18, 517, 2005