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Nonlinear Model Based Process Control pp 495–511Cite as

A Computationally Efficient Nonlinear Model Predictive Control Algorithm with Guaranteed Stability

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Part of the book series: NATO ASI Series ((NSSE,volume 353))

Abstract

A novel Nonlinear Model Predictive Control algorithm is proposed for control of large nonlinear constrained systems. The basic idea is to calculate exactly the first control move, which is implemented, and approximate all other control moves which are never implemented. Regardless of the control horizon, the number of decision variables for the on-line optimization problem equals the number of manipulated variables, resulting in significant savings in on-line computational time. Asymptotic stability of the closed loop system is guaranteed if and only if the on-line optimization problem is feasible initially, under reasonable assumptions. The feasibility for a practical implementation of the proposed algorithm is demonstrated on two examples including the Tennessee-Eastman Challenge problem involving ten inputs and ten outputs.

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References

  1. L.T. Biegler and J. B. Rawlings. Optimization approaches to nonlinear model predictive control. In Conf. Chemical Process Control (CPC-IV), pages 543–571, South Padre Island, Texas, 1991. CACHE-AIChE.

    Google Scholar 

  2. H. Chen and F. Allgöwer. A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability. Automatica, 1997. in press.

    Google Scholar 

  3. S.L. De Oliveira and M. Morari. Robust model predictive control for nonlinear systems. In Proceedings of the 33rd IEEE Conference on Decision and Control, pages 3561–3567, Orlando, Florida, 1994.

    Google Scholar 

  4. S.L. De Oliveira, V. Nevistic, and M. Morari. Control of nonlinear systems subject to input constraints. In Proceedings of IFAC Symposium on Nonlinear Control Systems Design, pages 15–20, Tahoe City, CA, 1995.

    Google Scholar 

  5. J.J. Downs and E. F. Vogel. A plant-wide industrial-process control problem. Computers and Chemical Engineering, 17(3):245–255, 1993.

    Article  CAS  Google Scholar 

  6. J.W. Eaton and J. B. Rawlings. Feedback control of nonlinear processes using on-line optimization techniques. Comp. and Chem. Eng., 14:469–479, 1990.

    Article  CAS  Google Scholar 

  7. J.W. Eaton and J. B. Rawlings. Model-predictive control of chemical processes. Chem. Eng. Sci., 47:705–720, 1992.

    Article  CAS  Google Scholar 

  8. C. E. García. Quadratic dynamic matrix control of nonlinear processes. An application to a batch reactor process. In AIChE Annual Meeting, San Francisco, CA, 1984.

    Google Scholar 

  9. G. Gattu and E. Zafiriou. Nonlinear quadratic dynamic matrix control with state estimation. Ind. Eng. Chem. Res., 31(4):1096–1104, 1992.

    Article  CAS  Google Scholar 

  10. G. Gattu and E. Zafiriou. Observer based nonlinear quadratic dynamic matrix control for state space and input/output models. Canadian Journal of Chemical Engineering, 73:883–895, Dec. 1995.

    Article  CAS  Google Scholar 

  11. S. Jang, B. Joseph, and H. Mukai. On-line optimization of constrained multivariable chemical processes. AIChE Journal, 33:26–42, 1987.

    Article  CAS  Google Scholar 

  12. M.J. Kurtz and M. A. Henson. Linear model predictive control of input-output linearized processes with constraints. In CPC V, Lake Tahoe, CA, 1996.

    Google Scholar 

  13. J.H. Lee and N. L. Ricker. Extended Kaiman filter based on nonlinear model predictive control. Ind. Eng. Chem. Res., 33:1530–1541, 1994.

    Article  CAS  Google Scholar 

  14. D.Q. Mayne. Nonlinear model predictive control: An assessment. In CPC V, Lake Tahoe, CA, 1996.

    Google Scholar 

  15. H. Michalska and D. Mayne. Robust receding horizon control of constrained nonlinear systems. IEEE Trans. Aut. Control, 38(11):1623–1633, November 1993.

    Article  Google Scholar 

  16. A.M. Morshedi. Universal dynamic matrix control. In Proceedings of CPC III, New York, 1986.

    Google Scholar 

  17. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes—The Art of Scientific Computing. Cambridge University Press, 1986.

    Google Scholar 

  18. J. B. Rawlings and K. R. Muske. The stability of constrained receding horizon control. IEEE Trans. Aut. Control, 38(10):1512–1516, October 1993.

    Article  Google Scholar 

  19. N. L. Ricker. Decentralized control of the tennessee eastman challenge process. Journal of Process Control, 6:205–221, 1996.

    Article  CAS  Google Scholar 

  20. N. L. Ricker, T. Subrahmanian, and T. Sim. Case studies of model-predictive control in pulp and paper production. In Model Based Process Control — Proc. of the 1988 IFAC Workshop. Pergamon Press, Oxford, 1989.

    Google Scholar 

  21. T. H. Yang and E. Polak. Moving horizon control of nonlinear systems with input saturation, disturbances and plant uncertainty. Int. J. Control, 58(4):875–903, September 1993.

    Article  Google Scholar 

  22. A. Zheng. Model predictive control: Is QP necessary? In AIChE Annual Meeting, Chicago, IL, 1996.

    Google Scholar 

  23. A. Zheng. A computationally efficient nonlinear model predictive control algorithm. In Proceedings of American Control Conf., Albuquerque, NM, 1997.

    Google Scholar 

  24. A. Zheng, V. Balakrishnan, and M. Morari. Constrained stabilization of discrete-time systems. International Journal of Robust and Nonlinear Control, 5(5):461–485, Aug. 1995.

    Article  Google Scholar 

  25. A. Zheng and M. Morari. Stability of model predictive control with mixed constraints. IEEE Trans. Aut. Control, 40(10):1818–1823, October 1995.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Chemical Engineering, University of Massachusetts, Amherst, MA, 01003-3110, USA

    Alex Zheng

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  1. Alex Zheng
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Ankara University, Tandoğan, Ankara, Turkey

    Ridvan Berber

  2. Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan, USA

    Costas Kravaris

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© 1998 Springer Science+Business Media Dordrecht

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Zheng, A. (1998). A Computationally Efficient Nonlinear Model Predictive Control Algorithm with Guaranteed Stability. In: Berber, R., Kravaris, C. (eds) Nonlinear Model Based Process Control. NATO ASI Series, vol 353. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5094-1_17

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  • DOI: https://doi.org/10.1007/978-94-011-5094-1_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6140-7

  • Online ISBN: 978-94-011-5094-1

  • eBook Packages: Springer Book Archive

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