Evaluation of controllers and fractional filters in reducing the cross-coupling interaction in the nonlinear model of a hydroelectric station
PDF (Español (España))
XML (Español (España))


potencia hidroeléctrica
control de estaciones de poder
control de orden fraccional
filtros de orden fraccional
interacción del acoplamiento cruzado
aplicaciones del control
modelo matemático
controlador Proporcional
error cuadrático hydroelectric power
power station control
fractional order control
fractional order filters
cross-coupling interaction
control applications
mathematical model
proportional integral derivative
squared error

How to Cite

Muñoz-Hernández, G. A., Díaz-Sánchez, A., Gracios-Marín, C. A., & Castañeda-Camacho, J. (2021). Evaluation of controllers and fractional filters in reducing the cross-coupling interaction in the nonlinear model of a hydroelectric station. Nova Scientia, 13(26). https://doi.org/10.21640/ns.v13i26.2681


In this paper, a non-linear multivariable mathematical model of a pump storage hydroelectric power plant, developed in Matlab-Simulink, is used to evaluate the performance of a Proportional Integral Derivative (pseudo derivative) controller with anti-windup, where the integral and derivative actions are of fractional order. This control is robust, maintaining its performance in the case of direct response and in the case of cross coupling response. Similarly, the advantage of using a filter to reduce the cross-coupling interaction of this system is shown. The effect of this filter, of fractional order, on the performance of the system, is shown by reducing the integral of the squared error.

PDF (Español (España))
XML (Español (España))


S P Mansoor, "PhD. Thesis. Behaviour and Operation of Pumped Storage Hydro Plants," Bangor University, Dean Street, Bangor, Gwynedd, UK, LL57 1UT, 2000.

G. A. Munoz-Hernandez, "PhD Thesis. Application of Model Based Predictive Control to a Pumped Storage Hydroelectric Plant," Bangor University, Dean Street, Bangor, Gwynedd, UK, LL57 1UT, 2005.

G. A. Munoz-Hernandez, S. P. Mansoor, and D. I. Jones, Modelling and Controlling Hydropower Plants, M. J. Grimble and M. A. Johnson, Eds. London, U.K.: Springer, 2013. DOI 10.1007/978-1-4471-2291-3.

G Prasad, G W Irwin, E Swidenbank, and B W Hogg, "G. Prasad, G. W. Irwin, E. Swidenbank and B. W. Hogg, "A hierarchical physical model-based approach to predictive control of a thermal power plant for efficient plant-wide disturbance rejection," Transactions of the Institute of Measurement and Control, vol. 24, no. 2, pp. 107-128, 2002. DOI: https://doi.org/10.1191/0142331202tm053oa

J A Rossiter, P W Neal, and L Yao, "Applying predictive control to a fossil-fired power station," Transactions of the Institute of Measurement and Control, vol. 3, pp. 177-194, 2002. DOI: https://doi.org/10.1191/0142331202tm055oa

G Ramond, D Dumur, A Libaux, and P Boucher, "Direct Adaptive Predictive Control of an hydro-electric plant," in IEEE Int. Conf. on Control Applications, Mexico D.F., 2001, pp. 606-611. DOI: 10.1109/CCA.2001.973934.

G Sansevero and C Pascoli Botura, "Model Predictive Control Algorithm for Francis Hydro Turbo-Generators," in Waterpower XIII, 2003.

L. Meng and D. Xue, "Fractional order QFT controller for non-minimum phase hydro power plant," in 24th Chinese Control and Decision Conference (CCDC), Taiyuan, China, 2012, pp. 2796-2801, doi: 10.1109/CCDC.2012.6244446.

R. Lamba, S. K. Singla, and S. Sondh, "Design of Fractional Order PID Controller for Load Frequency Control in Perturbed Two Area Interconnected System," Electric Power Components and Systems, vol. 47, no. 11-12, pp. 998-1011, 2019, DOI: 10.1080/15325008.2019.1660736.

O. A. Rosas-Jaimes, G. A. Munoz-Hernandez, G. Mino, J. Castaneda-Camacho, and C. A. Gracios-Marin, "Evaluating Fractional PID Control in a Nonlinear MIMO Model of a Hydroelectric Power Station," Complexity, vol. 2019, p. 9367291, 2019, doi: 10.1155/2019/9367291.

Y. Yang, B. Wang, Y. Tian, and P. Chen, "Fractional-Order Finite-Time, Fault-Tolerant Control of Nonlinear Hydraulic-Turbine-Governing Systems with an Actuator Fault," Energies, vol. 13, p. 3812, 2020, doi: 10.3390/en13153812.

IEEE Working group on prime mover energy supply, "Hydraulic turbine and turbine control model for system dynamic studies," IEEE Transactions on Power Systems, vol. 7, pp. 167-179, 1992. DOI: 10.1109/59.141700.

P Kundur, Power System Stability and Control New York. New York, USA: Mc Graw Hill, 1994.

B. Griffin and C. J. Downing, "Servo response specification using setpoint prefiltering in GPC," in Irish signals and systems conference, Cork, Ireland, 2002, pp. 409-414.

I. Podlubny, "Fractional-Order Systems and PILDu-Controllers," IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 208-214, January 1999. DOI: 10.1109/9.739144

G. C. Goodwin, S. F. Graebe, and M. E. Salgado, Control system design. USA: Prentice Hall, 2001.

R. Sharma, P. Gaur, and A. P. Mittal, "Optimum Design of Fractional-Order Hybrid Fuzzy Logic Controller for a Robotic Manipulator," Arabian Journal for Science and Engineering, vol. 42, pp. 739–750, 2017. DOI: https://doi.org/10.1007/s13369-016-2306-0

C. Muniz-Montero, L. A. Sanchez-Gaspariano, C. Sanchez-Lopez, V. R. Gonzalez-Diaz, and E. Tlelo-Cuautle, "On the Electronic Realizations of Fractional-Order Phase-Lead-Lag Compensators with OpAmps and FPAAs," in Fractional Order Control and Synchronization of Chaotic Systems, J. Kacprzyk, Ed. Cham, Switzerland: Springer, 2017, pp. 131-164, DOI 10.1007/978-3-319-50249-6_5.

C. A. Monje, Y. Chen, B. M. Vinagre, D. Xue, and V. Feliu, Fractional Order Systems and Controls: Fundamentals and Applications, Michael J. Grimble and Michael A. Johnson, Ed. London, U.K.: Springer-Verlag, 2010.

I. Petras, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, 1st ed., A. C. J. Luo and N. H. Ibragimov, Ed. Beijing, China: Springer, 2011.

O. D. I. Nwokah, "Pseudo-Derivative Feedback Control," in American Control Conference, Minneapolis, USA, 1987, pp. 1811-1814, doi: 10.23919/ACC.1987.4789606.

L. R. da Silva, R. C. C. Flesch, and J. E. Normey-Rico , "Analysis of Anti-windup Techniques in PID Control of Processes with Measurement ," in 3rd IFAC Conference on Advances in Proportional-Integral-Derivative Control PID, vol. 51, Ghent, Belgium, 2018, pp. 948-953, https://doi.org/10.1016/j.ifacol.2018.06.100.

A. E. A. Awouda and R. B. Mamat, "Refine PID tuning rule using ITAE criteria," in 2010 The 2nd International Conference on Computer and Automation Engineering (ICCAE), Singapure, 2010, pp. 171-176. DOI: 10.1109/ICCAE.2010.5451484

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2021 Nova Scientia