Nonlinear Model Predictive Control
- Nonlinear Model Predictive Control
- Nonlinear Model Predictive Control
- 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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