Alternative Generalized Predictive Control for Output Disturbed Multi-Input Multi-Output Discrete-Time Systems
Main Article Content
Abstract
This article proposes an option to execute conveniently the traditional Model Predictive Control (GPC), called the Alternative Generalized Predictive Control (AGPC). In this AGPC the disturbed discrete-time input-output mapping of controlled plant is utilized directly for the prediction of plant outputs, instead of its transfer function as being done in conventional approach. Hence, the solving Diophantine equations will be avoided. Within this AGPC all recorded values of plant inputs/outputs in the last time-horizon are matched into separate vectors for computing predictive control signals at the next control step, which helps therefore that its implementation becomes more manageable. To verify via virtually real simulation the control performance of this proposed AGPC a Simscape water tank model, which is chosen as the controlled plant, had been created among Thermal Fluids Toolbox. The simulation is carried out for two different circumstances, one by using AGPC and the other by applying conventional PID, for comparison purpose. The simulation demonstrates also how to realize this AGPC in practise.
Keywords
MPC, alternative GPC, PID, optimization, virtually real tank model
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
[1] J. M. Maciejowski, Predictive Control: With Constraints. Hoboken, NJ, USA: Prentice Hall, 2002, pp.108-144.
[2] J. Richalet, A. Rault, J. L. Testud and J. Papon, Model predictive heuristic control: Applications to industrial processes, Automatica, vol. 14, no 5, pp. 413-428, Sept.1978, https://doi.org/10.1016/0005-098(78)90001-8.
[3] A. Ramdani and S. Grouni, Dynamic matrix control and generalized predictive control, comparison study with IMC-PID, International Journal of Hydrogen Energy, vol. 42, no. 28, p. 17561-17570, July 2017, https://doi.org/10.1016/j.ijhydene.2017.04.015.
[4] J-P.Corriou, Generalized Predictive Control. In Process Control: Theory and Applications, 2nd ed., Gewerbestrasse, Cham, Switzerland: Springer International Publishing AG, 2018, pp. 611-630.
[5] C. K. Chui, G. Chen, Linear Systems and Optimal Control, Berlin, Heidelberg, Germany: Springer-Verlag Berlin Heidelberg, 1989.
[6] A. J. Krener, Adaptive horizon model predictive control, IFAC-PapersOnLine, vol. 51, no.13, pp. 31-36, Aug. 2018 https://doi.org/10.1016/j.ifacol.2018.07.250.
[7] J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell and T.F. Edgar, Nonlinear modeling, estimation and predictive control in APMonitor, Computers & Chemical Engineering, vol. 70, no.5, pp.133-148, Nov. 2014, https://doi.org/10.1016/j.compchemeng.2014.04.013.
[8] S. Subramanian, Y. Abdelsalam, S. Lucia and S. Engell, Robust tube-enhanced multi-stage nmpc with stability guarantees, IEEE Control Systems Letters, vol. 6, pp.1112–1117, June 2021 https://doi.org/10.1109/LCSYS.2021.3089502.
[9] S. Subramanian, S. Lucia, R. Paulen and S. Engell, Tube-enhanced multi-stage model predictive control for flexible robust control of constrained linear systems, International Journal of Robust and Nonlinear Control, vol. 31, no 9, pp. 4458–4487, Mar. 2021, https://doi.org/10.1002/rnc.5486.
[10] R. Kamyar and E. Taheri, Aircraft optimal terrain/threat-based trajectory planning and control, Journal of Guidance, Control, and Dynamics, vol. 37, no 2, pp. 466–483, Feb. 2014 https://doi.org/10.2514/1.61339.
[11] J. G. Balchen, D. Ljungquist and S. Strand, State-space predictive control, Chemical Engineering Science, vol. 47, no. 4, pp.787-807, 1992 https://doi.org/10.1016/0009-2509(92)80268-H.
[12] Q-L. Su, M. W. Hermanto, R. D. Braatz and M-S. Chiu, Just-in-time-learning based extended prediction selfadaptive control for batch processes, Journal of Process Control, vol. 43, pp. 1-9, July 2016, https://doi.org/10.1016/j.jprocont.2016.04.009.
[2] J. Richalet, A. Rault, J. L. Testud and J. Papon, Model predictive heuristic control: Applications to industrial processes, Automatica, vol. 14, no 5, pp. 413-428, Sept.1978, https://doi.org/10.1016/0005-098(78)90001-8.
[3] A. Ramdani and S. Grouni, Dynamic matrix control and generalized predictive control, comparison study with IMC-PID, International Journal of Hydrogen Energy, vol. 42, no. 28, p. 17561-17570, July 2017, https://doi.org/10.1016/j.ijhydene.2017.04.015.
[4] J-P.Corriou, Generalized Predictive Control. In Process Control: Theory and Applications, 2nd ed., Gewerbestrasse, Cham, Switzerland: Springer International Publishing AG, 2018, pp. 611-630.
[5] C. K. Chui, G. Chen, Linear Systems and Optimal Control, Berlin, Heidelberg, Germany: Springer-Verlag Berlin Heidelberg, 1989.
[6] A. J. Krener, Adaptive horizon model predictive control, IFAC-PapersOnLine, vol. 51, no.13, pp. 31-36, Aug. 2018 https://doi.org/10.1016/j.ifacol.2018.07.250.
[7] J.D. Hedengren, R. Asgharzadeh Shishavan, K.M. Powell and T.F. Edgar, Nonlinear modeling, estimation and predictive control in APMonitor, Computers & Chemical Engineering, vol. 70, no.5, pp.133-148, Nov. 2014, https://doi.org/10.1016/j.compchemeng.2014.04.013.
[8] S. Subramanian, Y. Abdelsalam, S. Lucia and S. Engell, Robust tube-enhanced multi-stage nmpc with stability guarantees, IEEE Control Systems Letters, vol. 6, pp.1112–1117, June 2021 https://doi.org/10.1109/LCSYS.2021.3089502.
[9] S. Subramanian, S. Lucia, R. Paulen and S. Engell, Tube-enhanced multi-stage model predictive control for flexible robust control of constrained linear systems, International Journal of Robust and Nonlinear Control, vol. 31, no 9, pp. 4458–4487, Mar. 2021, https://doi.org/10.1002/rnc.5486.
[10] R. Kamyar and E. Taheri, Aircraft optimal terrain/threat-based trajectory planning and control, Journal of Guidance, Control, and Dynamics, vol. 37, no 2, pp. 466–483, Feb. 2014 https://doi.org/10.2514/1.61339.
[11] J. G. Balchen, D. Ljungquist and S. Strand, State-space predictive control, Chemical Engineering Science, vol. 47, no. 4, pp.787-807, 1992 https://doi.org/10.1016/0009-2509(92)80268-H.
[12] Q-L. Su, M. W. Hermanto, R. D. Braatz and M-S. Chiu, Just-in-time-learning based extended prediction selfadaptive control for batch processes, Journal of Process Control, vol. 43, pp. 1-9, July 2016, https://doi.org/10.1016/j.jprocont.2016.04.009.