# A multivariable multiobjective predictive controller

Faten Ben Aicha; Faouzi Bouani; Mekki Ksouri

International Journal of Applied Mathematics and Computer Science (2013)

- Volume: 23, Issue: 1, page 35-45
- ISSN: 1641-876X

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topFaten Ben Aicha, Faouzi Bouani, and Mekki Ksouri. "A multivariable multiobjective predictive controller." International Journal of Applied Mathematics and Computer Science 23.1 (2013): 35-45. <http://eudml.org/doc/251312>.

@article{FatenBenAicha2013,

abstract = {Predictive control of MIMO processes is a challenging problem which requires the specification of a large number of tuning parameters (the prediction horizon, the control horizon and the cost weighting factor). In this context, the present paper compares two strategies to design a supervisor of the Multivariable Generalized Predictive Controller (MGPC), based on multiobjective optimization. Thus, the purpose of this work is the automatic adjustment of the MGPC synthesis by simultaneously minimizing a set of closed loop performances (the overshoot and the settling time for each output of the MIMO system). First, we adopt the Weighted Sum Method (WSM), which is an aggregative method combined with a Genetic Algorithm (GA) used to minimize a single criterion generated by the WSM. Second, we use the NonDominated Sorting Genetic Algorithm II (NSGA-II) as a Pareto method and we compare the results of both the methods. The performance of the two strategies in the adjustment of multivariable predictive control is illustrated by a simulation example. The simulation results confirm that a multiobjective, Pareto-based GA search yields a better performance than a single objective GA.},

author = {Faten Ben Aicha, Faouzi Bouani, Mekki Ksouri},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {closed loop performance; coupled multivariable system; generalized predictive control; multiobjective optimization; weighted sum method; NSGA-II; non-dominated sorting genetic algorithm II (NSGA-II)},

language = {eng},

number = {1},

pages = {35-45},

title = {A multivariable multiobjective predictive controller},

url = {http://eudml.org/doc/251312},

volume = {23},

year = {2013},

}

TY - JOUR

AU - Faten Ben Aicha

AU - Faouzi Bouani

AU - Mekki Ksouri

TI - A multivariable multiobjective predictive controller

JO - International Journal of Applied Mathematics and Computer Science

PY - 2013

VL - 23

IS - 1

SP - 35

EP - 45

AB - Predictive control of MIMO processes is a challenging problem which requires the specification of a large number of tuning parameters (the prediction horizon, the control horizon and the cost weighting factor). In this context, the present paper compares two strategies to design a supervisor of the Multivariable Generalized Predictive Controller (MGPC), based on multiobjective optimization. Thus, the purpose of this work is the automatic adjustment of the MGPC synthesis by simultaneously minimizing a set of closed loop performances (the overshoot and the settling time for each output of the MIMO system). First, we adopt the Weighted Sum Method (WSM), which is an aggregative method combined with a Genetic Algorithm (GA) used to minimize a single criterion generated by the WSM. Second, we use the NonDominated Sorting Genetic Algorithm II (NSGA-II) as a Pareto method and we compare the results of both the methods. The performance of the two strategies in the adjustment of multivariable predictive control is illustrated by a simulation example. The simulation results confirm that a multiobjective, Pareto-based GA search yields a better performance than a single objective GA.

LA - eng

KW - closed loop performance; coupled multivariable system; generalized predictive control; multiobjective optimization; weighted sum method; NSGA-II; non-dominated sorting genetic algorithm II (NSGA-II)

UR - http://eudml.org/doc/251312

ER -

## References

top- Al-Gherwi, W., Budman, H. and Elkamel, A. (2010). Election of control structure for distributed model predictive control in the presence of model errors, Journal of Process Control 20: 270-284.
- Behroozsarand, A. and Shaffei, S. (2010). Optimal control of distillation column using non-dominated sorting genetic algorithm II, Journal of Loss Prevention in the Process Industries 24(1): 25-33.
- Bemporada, A. and Munoz de la Penab, D. (2009). Multiobjective model predictive control, Automatica 45(12): 2823-2830. Zbl1192.93069
- Ben Abdennour, R., Ksouri, M. and Favier, G. (1998). Application of fuzzy logic to the on-line adjustment of the parameters of a generalized predictive controller, Intelligent Automation and Soft Computing 4(3): 197-214.
- Berro, A. (2001). Optimisation multiobjectif et strat'egies d'evolution en environment dynamique, Ph.D. thesis, Université des Sciences Sociales Toulouse I, Toulouse.
- Boussaid, B., Aubrun, C., Abdelkrim, M.N. and Ben Gayed, M.K. (2011). Performance evaluation based fault tolerant control with actuator saturation avoidance, International Journal of Applied Mathematics and Computer Science 21(3): 457-466, DOI: 10.2478/v10006-011-0034-x. Zbl1235.93090
- Camacho, E.F. and Bordons, C. (1995). Model Predictive Control in the Process Industry, Springer Verlag, London.
- Clarke, W., Mohtadi, C. and Tuffs, P. S. (1987). Generalized predictive control, Parts 1 and 2, Automatica 23(2): 137-160. Zbl0621.93033
- Coello Coello, C.A., Van Veldhuizen, D.A. and Lamont, G.B. (2002). Evolutionary Algorithms for Solving MultiObjective Problems, Kluwer Academic Publishers, New York, NY. Zbl1130.90002
- Colette, Y. and Siarry, P. (2002). Optimisation multiobjectif, Éditions Eyrolles, Paris.
- Deb, K. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation 6(2): 182-197.
- Deb, K. and Agrawal, R.B. (1995). Simulated binary crossover for continuous search space, Complex Systems 9: 115-148. Zbl0843.68023
- Gambier, A. (2007). Multi-objective optimal control: An overview, Proceedings of the 16th IEEE International Conference on Control Applications, Singapore, pp. 170-175.
- Gambier, A. (2008). MPC and PID control based on multi-objective optimization, Proceedings of the American Control Conference, ACC 2008, Seattle, WA, USA, pp. 4727-4732.
- Kinnaert, M. (1989). Adaptive generalized predictive controller for MIMO systems, International Journal of Control 50(1): 161-172. Zbl0683.93050
- Królikowski, A. and Jerzy, D. (2001). Self-tuning generalized predictive control with input constraints, International Journal of Applied Mathematics and Computer Science 11(2): 459-479. Zbl0969.93500
- Mohtadi, H., Shah, S. and Clarke, D. (1987). Generalized predictive control of multivariable systems, Proceedings of the 5th Workshop on Applications of Adaptive Systems Theory, New Haven, CT, USA, pp. 54-59.
- Muldera, E.F., Tiwari, P.Y. and Kothare, M.V. (2009). Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization, Automatica 45(3): 805-811. Zbl1168.93344
- Popov, A., Farag, A. and Werner, H. (2005). Tuning of a PID controller using a multi-objective optimization technique applied to a neutralization plant, IEEE Conference on Decision and Control, Seville, Spain, pp. 7139-7143.
- Qin, S. and Badgwell, T. (2003). A survey of industrial model predictive control technology, Control Engineering Practice 11: 733-764.
- Richalet, J., Lavielle, G. and Mallet, J. (2005). La commande prédictive: Mise en oeuvre et applications industrielles, Éditions Eyrolles, Paris.
- Srinivas, N. and Deb, K. (1995). Multiobjective function optimization using nondominated sorting genetic algorithms, IEEE Transactions on Evolutionary Computation 2(3): 221-248.
- Talbi, E.G. (2001). Learning logic, Technical report, Lille University of Sciences and Technologies, Lille.
- Tatjewski, P. (2010). Supervisory predictive control and on-line set-point optimization, International Journal of Applied Mathematics and Computer Science 20(3): 483-495, DOI: 10.2478/v10006-010-0035-1. Zbl1211.93036
- Veldhuizen, D. and Lamont, G. B. (2000). Multiobjective evolutionary algorithms: Analyzing the state-of-the-art, IEEE Transactions on Evolutionary Computation 18(2): 125-147.
- Yang, Z. and Pedersen, G. (2006). Automatic tuning of PID controller for a 1-D levitation system using a genetic algorithm: A real case study, IEEE International Symposium on Intelligent Control, Munich, Germany, pp. 3098-3103.
- Zenghui, W., Zengqiang, C., Qinglin, S. and Zhuzhi, Y. (2006). Multivariable decoupling predictive control based on QFT theory and application in CSTR chemical process, Chinese Journal of Chemical Engineering 14(6): 765-769.

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