Nonlinear Model Predictive Control based on Hammerstein and Wiener Models

• Nonlinear Model Predictive Control based on Hammerstein and Wiener Models
  • Researchers
  • Abstract
  • Objectives
  • References

• Nonlinear Model Predictive Control based on Hammerstein and Wiener Models
  • Researchers: J.C. Gómez (UNR); and E. Baeyens (University of Valladolid, Spain)
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  • Abstract
    Model Predictive Control (MPC) is a methodology that refers to a class of control algorithms in which a dynamic model of the plant is used to predict and optimize the future behaviour of the process. At each control interval, the MPC algorithm computes an open-loop sequence of the manipulated variables in such a way to optimize the future behaviour of the plant. The first value in this optimal sequence is injected into the plant, and the optimization process is repeated at the subsequent control intervals (see for instance, the recent book by Maciejowski [1]).
    MPC has been used in industry for more than 30 years, and has become an industry standard (mainly in the petrochemical industry) due to its intrinsic capability for dealing with constraints and with multivariable systems. Most commercially available MPC technologies are based on a linear model of the process. For processes that are highly nonlinear, the performance of an MPC based on a linear model can be poor. This has motivated the development of Nonlinear Model Predictive Control (NMPC), where a more accurate (nonlinear) model of the plant is used for prediction and optimization (see for instance [2],[3] for the state of the art and future directions on NMPC).
    Many of the current NMPC schemes are based on physical models of the process. However, in many cases such models are difficult to obtain, and often not available at all. In this cases it makes sense to use a nonlinear empirical model, identified from input-output measurements [5]. Some works where this approach has been followed are for instance: [6] where a nonlinear predictive control scheme based on radial basis functions models is proposed, and [7] where the NMPC is based on a Hammerstein model.
    While NMPC offers potential for improved process operation, it also offers theoretical and practical problems which are considerably more challenging than those associated with linear MPC. In particular, the problems associated with the nonlinear optimization program which must be solved on-line at each sample period to generated the optimal control sequence. This is in contrast to linear MPC in which the optimization take the form of a highly structured convex Quadratic Program (QP), for which reliable solution algorithms and software can easily be found. This is important because the solution algorithm must converge reliably to the optimum in no more than a few miliseconds to be useful in practical applications. The question then arise if within the wide class of nonlinear models there exist a particular family of models for which the optimization problem associated with a NMPC scheme can still be put in the form of a QP, for which efficient solution algorithms are available. Some preliminary results in this direction show that this is possible for the so called block-oriented nonlinear models (consisting of interconnections of linear time invariant systems and static nonlinearities), and particularly for Hammerstein and Wiener models within this class [8]. These results are promising since they would allow to extend results of linear MPC to NMPC based on a wide class of nonlinear models which has been successfully used to represent nonlinear systems in many practical applications [9],[10].
    Key on the derivation of the results in [8] has been the particular parametrization of the nonlinear model and the nonlinear identification method employed to estimate the model parameters. Specifically, the subspace identification method proposed in [11] has been used to estimate a model in a format which can be used in a standard (linear) MPC scheme.
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  • Objectives
    Among the objectives of this research project, the following can be mentioned:
    • The development of nonlinear identification algorithms which deliver a model in a format suitable for their use in NMPC schemes.
    • The stability analysis of the proposed NMPC algorithms.
    • The development of recursive nonlinear identification algorithms which would allow the on-line updating of the models in NMPC (adaptive) schemes.
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  • References
    
    • [1] Maciejowski, J.M..Predictive Control with Constraints, Prentice Hall, N.J., 2002.
    • [2] Henson, M. "Nonlinear Model Predictive Control: current status and future directions", Computers and Chemical Engineering, Vol. 23, pp:187-202, 1998.
    • [3] Qin, S.J. and T.A Badgwell. "An overview of nonlinear model predictive control applications". In [4], pp:369-392, 2000.
    • [4] Allgöwer, F. and A. Zheng, editors. Nonlinear Model Predictive Control, Birkhäuser, 2000.
    • [5] Ljung, L.. System Identification. Theory for the user, 2nd edition, Prentice Hall, 1999.
    • [6] Pottmann, M. and D. Seborg. "A nonlinear predictive control strategy based on radial basis functions models", Computers and Chemical Engineering, Vol. 21, No. 9, pp:965-980, 1997.
    • [7] Fruzzetti, K., A. Palazoglu and K.A. McDonald. "Nonlinear Model Predictive Control using Hammerstein models", Journal of Process Control, 7(1):31-41, 1997.
    • [8] Gómez, J.C. and A. Jutan. "Identification and Model Predictive Control of a pH Neutralization Process based on Linear and Wiener models". Accepted for presentation at the 13th IFAC Symposium on System Identification SYSID2003, Rotterdam, August 2003.
    • [9] Henson, M. and D. Seborg. " Adaptive Nonlinear Control of a pH Neutralization Process", IEEE Transactions on Control Systems Technology, Vol. 2, No. 3, pp:169-182, 1994.
    • [10] Kalafatis, A; N. Arifin; L. Wang and W. Cluett. "A new approach to the identification of pH processes based on the Wiener model", Chemical Engineering Science, Vol. 50, No. 23, pp:3693-3701, 1995.
    • [11] Gómez, J.C. and E. Baeyens. "Subspace Identification of multivariable Hammerstein and Wiener models". In Proceedings of the 15th IFAC World Congress, Barcelona, Spain, pp:2849-2854, July 2002.
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