State Space Model Predictive Control of an Aerothermic Process with Actuators Constraints

Affiliation(s)

ASTIMI Laboratory, High School of Technology, Université Mohammed V Agdal, Rabat, Morocco.

UFR Automatic and Information Technologies, Faculty of Science, Rabat, Morocco.

Automatic Laboratory, Mohammadia School of Engineering, Rabat, Morocco.

ASTIMI Laboratory, High School of Technology, Université Mohammed V Agdal, Rabat, Morocco.

UFR Automatic and Information Technologies, Faculty of Science, Rabat, Morocco.

Automatic Laboratory, Mohammadia School of Engineering, Rabat, Morocco.

ABSTRACT

This paper investigates State Space Model Predictive Control (SSMPC) of an aerothermic process. It is a pilot scale heating and ventilation system equipped with a heater grid and a centrifugal blower, fully connected through a data acquisition system for real time control. The interaction between the process variables is shown to be challenging for single variable controllers, therefore multi-variable control is worth considering. A multi-variable state space model is obtained from on-line experimental data. The controller design is translated into a Quadratic Programming (QP) problem, in which a cost function subject to actuators linear inequality constraints is minimized. The outcome of the experimental results is that the main control objectives, such as set-point tracking and perturbations rejection under actuators constraints, are well achieved for both controlled variables simultaneously.

This paper investigates State Space Model Predictive Control (SSMPC) of an aerothermic process. It is a pilot scale heating and ventilation system equipped with a heater grid and a centrifugal blower, fully connected through a data acquisition system for real time control. The interaction between the process variables is shown to be challenging for single variable controllers, therefore multi-variable control is worth considering. A multi-variable state space model is obtained from on-line experimental data. The controller design is translated into a Quadratic Programming (QP) problem, in which a cost function subject to actuators linear inequality constraints is minimized. The outcome of the experimental results is that the main control objectives, such as set-point tracking and perturbations rejection under actuators constraints, are well achieved for both controlled variables simultaneously.

Cite this paper

M. Ramzi, H. Youlal and M. Haloua, "State Space Model Predictive Control of an Aerothermic Process with Actuators Constraints,"*Intelligent Control and Automation*, Vol. 3 No. 1, 2012, pp. 50-58. doi: 10.4236/ica.2012.31007.

M. Ramzi, H. Youlal and M. Haloua, "State Space Model Predictive Control of an Aerothermic Process with Actuators Constraints,"

References

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[2] M. Nachidi, F. Rodriguez, F. Tadeo and J. L. Guzmanb, “Takagi-Sugeno Control of Nocturnal Temperature in Greenhouses Using Air Heating,” ISA Transactions, Vol. 50, No. 2, 2011, pp. 315-320. doi:10.1016/j.isatra.2010.11.007

[3] R. F. Escobar, et al., “Sensor Fault Detection and Isolation via High-Gain Observers: Application to a DoublePipe Heat Exchanger,” ISA Transactions, Vol. 50, No. 3, 2011; pp. 480-486. doi:10.1016/j.isatra.2011.03.002

[4] M. F. Rahmat, N. A. Mohd Subha, K. M. Ishaq and N. Abdul Wahab, “Modeling and Controller Design for the VVS-400 Pilot Scale Heating and Ventillation System,” International Journal on Smart Sensing and Intelligent Systems, Vol. 2, No. 4, 2009, pp. 579-601.

[5] H. L. Ho, A. B. Rad, C. C. Chan and Y. K. Wong, “Comparative Studies of Three Adaptive Controllers,” ISA Transactions, Vol. 38, No. 1, 1999, pp. 43-53. doi:10.1016/S0019-0578(99)00004-X

[6] T. Kealy and A. O’Dwyer, “Closed Loop Identification of a First Order plus Dead Time Process Model under PI Control,” Proceedings of the Irish Signals and Systems Conference, University College, Cork, 25-26 June 2002, pp. 9-14.

[7] D. M. de la Pena, D. R. Ramirez, E. F. Camacho and T. Alamo, “Application of an Explicit Min-Max MPC to a Scaled Laboratory Process,” Control Engineering Practice, Vol. 13, No. 12, 2005, pp. 1463-1471. doi:10.1016/j.conengprac.2004.12.008

[8] R. Mooney and A. O’Dwyer, “A Case Study in Modeling and Process Control: The Control of a Pilot Scale Heating and Ventilation System,” Proceedings of the 23rd International Manufacturing Conference, University of Ulster, Jordanstown, August 2006, pp. 123-130.

[9] N. A. M. Subha, M. F. Rahmat and K. M. Ishaq, “Controller Design for a Pilot-Scale Heating and Ventilation System Using Fuzzy Logic Approach,” Jurnal Teknologi Keluaran Khas, Vol. 54, 2011, pp. 123-139.

[10] L. P. Wang, “Model Predictive Control System Design and Implementation Using MATLAB,” Springer, Berlin, 2009.

[11] L. Wang and P. C. Young, “An Improved Structure for Model Predictive Control Using Non-Minimal State Space Realisation,” Journal of Process Control, Vol. 16, No. 4, 2006, pp. 355-371. doi:10.1016/j.jprocont.2005.06.016

[12] J. M. Maciejowski, “Predictive Control with Constraints,” Prentice Hall, Upper Saddle River, 2002.

[13] A. Bemporad, F. Borrelli and M. Morari, “Model Predictive Control Based on Linear Programming the Explicit Solution,” IEEE Transactions on Automatic Control, Vol. 47, No. 12, 2002, pp. 1974-1985. doi:10.1109/TAC.2002.805688

[14] J. H. Lee and B. L. Cooley, “Min-Max Predictive Control Techniques for a Linear State-Space System with a Bounded Set of Input Matrices,” Automatica, Vol. 36, No. 3, 2000, pp. 463-473. doi:10.1016/S0005-1098(99)00178-8

[15] S. J. Qin, V. M. Martinez and B. A. Foss, “An Interpolating Model Predictive Control Strategy with Application to a Waste Treatment Plant,” Computers and Chemical Engineering, Vol. 21, No. 1, 1997, pp. S881-S886. doi:10.1016/S0098-1354(97)00160-9

[16] T. Kawabe, “Robust MPC Method for BMI Based Wheelchair,” Intelligent Control and Automation, Vol. 2, No. 2, 2011, pp. 340-350. doi:10.4236/ica.2011.24039

[17] P. V. Overschee and B. D. Moor, “N4sid: Subspace Algorithms for the Identification of Combined Deterministic-Stochastic Systems,” Automatica, Vol. 30, No. 1, 1994, pp. 75-93. doi:10.1016/0005-1098(94)90230-5

[18] M. Verhagen, “Identification of the Deterministic Part of Mimo State Space Models Given in Innovations form from Input-Output Data,” Automatica, Vol. 30, No. 1, 1994, pp. 61-74. doi:10.1016/0005-1098(94)90229-1

[19] S. J. Qina, W. Lina and L. Ljung, “A Novel Subspace Identification Approach with Enforced Causal Models,” Automatica, Vol. 41, No. 12, 2005, pp. 2043-2053. doi:10.1016/j.automatica.2005.06.010

[20] M. Viberg, “Subspace-Based Methods for the Identification of Linear Time-Invariant Systems,” Automatica, Vol. 31, No. 12, 1995, pp. 1835-1852. doi:10.1016/0005-1098(95)00107-5

[21] M. Lovera, T. Gustafsson and M. Verhagen, “Recursive Subspace Identification of Linear and Nonlinear Wiener State Space Models,” Automatica, Vol. 36, No. 11, 2000, pp. 1639-1650. doi:10.1016/S0005-1098(00)00103-5

[22] T. C. S. Wibowo and N. Saad, “MIMO Model of an Interacting Series Process for Robust MPC via System Identification,” ISA Transactions, Vol. 49, No. 3, 2010, pp. 335-347. doi:10.1016/j.isatra.2010.02.005

[23] http://www.didalab-didactique.fr/2008/achat/produit_details.php?id=32&lng=FR

[24] E. Yesil, M. Guzelkaya, I. Eksin and O. A. Tekin, “Online Tuning of Set-Point Regulator with a Blending Mechanism Using PI Controller,” Turkish Journal of Electrical Engineering, Vol. 16, No. 2, 2008.

[25] P. J. Gawthrop and L. Wang, “Intermittent Predictive Control of an Inverted Pendulum,” Control Engineering Practice, Vol. 14, No. 11, 2006, pp. 1347-1356. doi:10.1016/j.conengprac.2005.09.002

[1] N. Bennis, J. Duplaix, G. Enéa, M. Haloua and H. Youlal, “Greenhouse Climate Modelling and Robust Control,” Computers and Electronics in Agriculture, Vol. 61, No. 2, 2008, pp. 96-107. doi:10.1016/j.compag.2007.09.014

[2] M. Nachidi, F. Rodriguez, F. Tadeo and J. L. Guzmanb, “Takagi-Sugeno Control of Nocturnal Temperature in Greenhouses Using Air Heating,” ISA Transactions, Vol. 50, No. 2, 2011, pp. 315-320. doi:10.1016/j.isatra.2010.11.007

[3] R. F. Escobar, et al., “Sensor Fault Detection and Isolation via High-Gain Observers: Application to a DoublePipe Heat Exchanger,” ISA Transactions, Vol. 50, No. 3, 2011; pp. 480-486. doi:10.1016/j.isatra.2011.03.002

[4] M. F. Rahmat, N. A. Mohd Subha, K. M. Ishaq and N. Abdul Wahab, “Modeling and Controller Design for the VVS-400 Pilot Scale Heating and Ventillation System,” International Journal on Smart Sensing and Intelligent Systems, Vol. 2, No. 4, 2009, pp. 579-601.

[5] H. L. Ho, A. B. Rad, C. C. Chan and Y. K. Wong, “Comparative Studies of Three Adaptive Controllers,” ISA Transactions, Vol. 38, No. 1, 1999, pp. 43-53. doi:10.1016/S0019-0578(99)00004-X

[6] T. Kealy and A. O’Dwyer, “Closed Loop Identification of a First Order plus Dead Time Process Model under PI Control,” Proceedings of the Irish Signals and Systems Conference, University College, Cork, 25-26 June 2002, pp. 9-14.

[7] D. M. de la Pena, D. R. Ramirez, E. F. Camacho and T. Alamo, “Application of an Explicit Min-Max MPC to a Scaled Laboratory Process,” Control Engineering Practice, Vol. 13, No. 12, 2005, pp. 1463-1471. doi:10.1016/j.conengprac.2004.12.008

[8] R. Mooney and A. O’Dwyer, “A Case Study in Modeling and Process Control: The Control of a Pilot Scale Heating and Ventilation System,” Proceedings of the 23rd International Manufacturing Conference, University of Ulster, Jordanstown, August 2006, pp. 123-130.

[9] N. A. M. Subha, M. F. Rahmat and K. M. Ishaq, “Controller Design for a Pilot-Scale Heating and Ventilation System Using Fuzzy Logic Approach,” Jurnal Teknologi Keluaran Khas, Vol. 54, 2011, pp. 123-139.

[10] L. P. Wang, “Model Predictive Control System Design and Implementation Using MATLAB,” Springer, Berlin, 2009.

[11] L. Wang and P. C. Young, “An Improved Structure for Model Predictive Control Using Non-Minimal State Space Realisation,” Journal of Process Control, Vol. 16, No. 4, 2006, pp. 355-371. doi:10.1016/j.jprocont.2005.06.016

[12] J. M. Maciejowski, “Predictive Control with Constraints,” Prentice Hall, Upper Saddle River, 2002.

[13] A. Bemporad, F. Borrelli and M. Morari, “Model Predictive Control Based on Linear Programming the Explicit Solution,” IEEE Transactions on Automatic Control, Vol. 47, No. 12, 2002, pp. 1974-1985. doi:10.1109/TAC.2002.805688

[14] J. H. Lee and B. L. Cooley, “Min-Max Predictive Control Techniques for a Linear State-Space System with a Bounded Set of Input Matrices,” Automatica, Vol. 36, No. 3, 2000, pp. 463-473. doi:10.1016/S0005-1098(99)00178-8

[15] S. J. Qin, V. M. Martinez and B. A. Foss, “An Interpolating Model Predictive Control Strategy with Application to a Waste Treatment Plant,” Computers and Chemical Engineering, Vol. 21, No. 1, 1997, pp. S881-S886. doi:10.1016/S0098-1354(97)00160-9

[16] T. Kawabe, “Robust MPC Method for BMI Based Wheelchair,” Intelligent Control and Automation, Vol. 2, No. 2, 2011, pp. 340-350. doi:10.4236/ica.2011.24039

[17] P. V. Overschee and B. D. Moor, “N4sid: Subspace Algorithms for the Identification of Combined Deterministic-Stochastic Systems,” Automatica, Vol. 30, No. 1, 1994, pp. 75-93. doi:10.1016/0005-1098(94)90230-5

[18] M. Verhagen, “Identification of the Deterministic Part of Mimo State Space Models Given in Innovations form from Input-Output Data,” Automatica, Vol. 30, No. 1, 1994, pp. 61-74. doi:10.1016/0005-1098(94)90229-1

[19] S. J. Qina, W. Lina and L. Ljung, “A Novel Subspace Identification Approach with Enforced Causal Models,” Automatica, Vol. 41, No. 12, 2005, pp. 2043-2053. doi:10.1016/j.automatica.2005.06.010

[20] M. Viberg, “Subspace-Based Methods for the Identification of Linear Time-Invariant Systems,” Automatica, Vol. 31, No. 12, 1995, pp. 1835-1852. doi:10.1016/0005-1098(95)00107-5

[21] M. Lovera, T. Gustafsson and M. Verhagen, “Recursive Subspace Identification of Linear and Nonlinear Wiener State Space Models,” Automatica, Vol. 36, No. 11, 2000, pp. 1639-1650. doi:10.1016/S0005-1098(00)00103-5

[22] T. C. S. Wibowo and N. Saad, “MIMO Model of an Interacting Series Process for Robust MPC via System Identification,” ISA Transactions, Vol. 49, No. 3, 2010, pp. 335-347. doi:10.1016/j.isatra.2010.02.005

[23] http://www.didalab-didactique.fr/2008/achat/produit_details.php?id=32&lng=FR

[24] E. Yesil, M. Guzelkaya, I. Eksin and O. A. Tekin, “Online Tuning of Set-Point Regulator with a Blending Mechanism Using PI Controller,” Turkish Journal of Electrical Engineering, Vol. 16, No. 2, 2008.

[25] P. J. Gawthrop and L. Wang, “Intermittent Predictive Control of an Inverted Pendulum,” Control Engineering Practice, Vol. 14, No. 11, 2006, pp. 1347-1356. doi:10.1016/j.conengprac.2005.09.002