International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Nonlinear Optimal Control of an Input-Constrained and Enclosed Thermal Processing System

  • Gwak, Kwan-Woong (School of Mechanical and Aerospace Engineering, Sejong University) ;
  • Masada, Glenn Y. (Department of Mechanical Engineering, The University of Texas at Austin)
  • Published : 2008.04.30
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Abstract

Temperature control of an enclosed thermal system which has many applications including Rapid Thermal Processing (RTP) of semiconductor wafers showed an input-constraint violation for nonlinear controllers due to inherent strong coupling between the elements [1]. In this paper, a constrained nonlinear optimal control design is developed, which accommodates input constraints using the linear algebraic equivalence of the nonlinear controllers, for the temperature control of an enclosed thermal process. First, it will be shown that design of nonlinear controllers is equivalent to solving a set of linear algebraic equations-the linear algebraic equivalence of nonlinear controllers (LAENC). Then an input-constrained nonlinear optimal controller is designed based on that LAENC using the constrained linear least squares method. Through numerical simulations, it is demonstrated that the proposed controller achieves the equivalent performances to the classical nonlinear controllers with less total energy consumption. Moreover, it generates the practical control solution, in other words, control solutions do not violate the input-constraints.

Keywords

References

  1. K. W. Gwak and G. Y. Masada, "Regularization embedded nonlinear control designs for illconditioned thermal processes," ASME Journal of Dynamics Systems, Measurements and Control, vol. 126, no. 3, pp. 574-582, 2004 https://doi.org/10.1115/1.1789973
  2. T. Breedijk, T. F. Edgar, and I. Trachtenberg, "Model-Based Control of Rapid Thermal Processes," Proc. of American Control Conference, pp. 887-891, 1994
  3. S. A. Norman and S. P. Boyd, "Multivariable feedback control of semiconductor wafer temperature," Proc. of American Control Conference, pp. 811-816, 1992
  4. C. J. Huang, C. C. Yu, and S. H. Shen, "Selection of measurement locations for the control of rapid thermal processor," Automatica, vol. 36, pp. 705-715, 2000 https://doi.org/10.1016/S0005-1098(99)00197-1
  5. Y. M. Cho and P. Gyugyi, "Control of rapid thermal processing: A system theoretic approach," IEEE Trans. on Control Systems Technology, vol. 5, no. 6, pp. 644-653, 1997 https://doi.org/10.1109/87.641407
  6. K. S. Balakrishinan and T. F. Edgar "Modelbased control in rapid thermal processing," Thin Solid Films, vol. 365, no. 2, pp. 322-333, 2000 https://doi.org/10.1016/S0040-6090(99)01049-4
  7. K. S. Balakrishinan and T. F. Edgar "Modelbased control in rapid thermal processing," Thin Solid Films, vol. 365, no. 2, pp. 322-333, 2000 https://doi.org/10.1016/S0040-6090(99)01049-4
  8. J. Y. Choi and H. Y. Do, "A learning approach of wafer temperature control in a rapid thermal processing system," IEEE Trans. on Semiconductor Manufacturing, vol. 14, no. 1, pp. 1-10, 2001 https://doi.org/10.1109/66.909649
  9. J. Baker and P. D. Christofides, "Output feedback control of parabolic PDE system with nonlinear spatial differential operators," Ind. Eng. Chem. Res. vol. 38, pp. 4372-4380, 1999 https://doi.org/10.1021/ie990131c
  10. H. M. Park, T. Y. Yoon, and O. Y. Kim, "Optimal control of rapid thermal processing systems by empirical reduction of modes," Ind. Eng. Chem. Res., vol. 38, pp. 3964-3975, 1999 https://doi.org/10.1021/ie990017u
  11. C. D. Schaper, T. Kailath, and Y. J. Lee, "Decentralized control of wafer temperature for multizone rapid thermal processing systems," IEEE Trans. on Semiconductor Manufacturing, vol. 12, no. 2, pp. 193-199, 1999 https://doi.org/10.1109/66.762877
  12. H. Aling, J. Abedor, J. L. Ebert, A. Emami- Naeini, and R. L. Kosut, "Application of feedback linearization to models of rapid thermal processing (RTP) reactors," Proc. of the 3rd Int'l Rapid Thermal Processing Conference, pp. 356-366, 1995
  13. K. S. Balakrishnan, W. Cho, and T. F. Edgar, "Comparison of controller tuning methods for temperature uniformity control in a rapid thermal processor," SPIE, vol. 2336, pp. 70-80, 1994
  14. G. Pappas, J. Lygeros, and D. Godbole, "Stabilization and tracking of feedback linearizable systems under input constraints," Proc. of the 34th IEEE Conf. on Decision and Control, pp. 596-601, 1995
  15. J. L. Aguilar, R. A. Garcia, and C. E. D'attellis, "Exact linearization of nonlinear systems: trajectory tracking with bounded controls and state constraints," International Journal of Control, vol. 65, no. 3, pp. 455-467, 1996 https://doi.org/10.1080/00207179608921706
  16. P. Yip and J. Hedrick, "Controller design for nonlinear systems under input constraints," Proc. of ASME Dynamic Systems and Control Division, pp. 359-363, 1995
  17. M. Soroush and S. Valluri, "Calculation of optimal feasible controller output in multivariable processes with input constraints," Proc. of American Control Conf., vol. 5, pp. 3475-3479, 1997
  18. T. Kendi and F. Doyle III, "Nonlinear internal model control for systems with measured disturbances and input constraints," Industrial and Engineering Chemistry Research, vol. 37, pp. 489-505, 1998 https://doi.org/10.1021/ie970357k
  19. N. Kapoor and P. Daoutidis, "An observer-based anti-windup scheme for non-linear systems with input constraints," International Journal of Control, vol. 72, no. 1, pp. 18-29, 1999 https://doi.org/10.1080/002071799221361
  20. K.-K. Shyu and H.-Y. Lin, "Adaptive sliding mode control for variable structure systems with constraint control input," Dynamics and Control, vol. 6, pp. 49-61, 1996 https://doi.org/10.1007/BF02169461
  21. Y.-S. Lu and J.-S. Chen, "Design of a global sliding-mode controller for a motor drive with bounded control," International Journal of Control, vol. 62, no. 5, pp. 1001-1019, 1995 https://doi.org/10.1080/00207179508921579
  22. R. Okabayashi and K. Furuta, "Design of sliding mode control systems with constrained inputs," Proc. the 35th IEEE Conf. on Decision and Control, pp. 3492-3497, 1996
  23. S. Qin and T. Badgwell, "A survey of industrial model predictive control technology," Control Engineering Practice, vol. 11, no. 7, pp. 733-764, 2003 https://doi.org/10.1016/S0967-0661(02)00186-7
  24. M. Kurtz, G.-Y. Zhu, and M. Henson, "Constrained output feedback control of a multivariable polymerization reactor," IEEE Trans. on Control Systems Technology, vol. 8, no. 1, pp. 87-97, 2000. https://doi.org/10.1109/87.817694
  25. M. Botto, T. V. D. Boom, A. Krijgsman, and J. S. D. Costa, "Predictive control based on neural network models with I/O feedback linearization," International Journal of Control, vol. 72, no. 17, pp. 1538-1554, 1999 https://doi.org/10.1080/002071799220038
  26. M. Kurtz, and M. Henson, "Input-output linearizing control of constrained nonlinear processes," Journal of Process Control, vol. 7, no. 1, pp. 3-17, 1997 https://doi.org/10.1016/S0959-1524(96)00006-6
  27. H. A. B. te Braake, M. Ayala Botto, H. J. L. van Can, J. Sa da Costa, H. B. Verbruggen, "Linear predictive control based on approximate inputoutput feedback linearization," IEE Proc. Control Theory and Applications, vol. 146, no. 4, pp. 295-300, 1999
  28. M. Kurtz and M. Henson, "Feedback linearzing control of discrete-time nonlinear systems with input constraints," International Journal of Control, vol. 70, no. 4, pp. 603-616, 1998 https://doi.org/10.1080/002071798222226
  29. M. Henson and M. Kurtz, "Input-output linearization of constrained nonlinear processes," Proc. of AIChE Annual Meeting, San Francisco, pp. 1-20, 1994
  30. H. Erturk, O. A. Ezekoye, and J. R. Howell, "Inverse transient boundary condition estimation problem in a radiating enclosure," Proc. of ASME National Heat Transfer Congress, 2001