Geometric tuning of controllers from a data-driven approach
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boost power converter, data-driven control, Experimental bode, stabilizing set
Background: Tuning PI controllers by conventional methods involves knowing the plant model and applying trial and error techniques. Objective: To adjust the parameters of a PI compensator using a control methodology based on frequency response data. Method: The basis of the presented calculation is the geometrical interpretation for the stability margins of the system, constituting a feasible dynamic specification space. Simulation analysis and laboratory experimental validation are presented for electrical systems involving step-up type DC-DC power electronic converters. Results: The construction of an experimental Bode diagram allowed to eliminate the dependence of the controller parameter calculation on the explicit knowledge of an analytical model of the system. Conclusion: Through numerical simulations and laboratory measurements it was possible to verify the dynamic regulation of the power converter, including saturation restrictions for the establishment of stabilising sets.
A. J. den Hamer, S. Weiland y M. Steinbuch, “Model-free norm-based fixed structure controller synthesis”, in Proc. 48th IEEE Conference on Decision and Control, (Shanghai), pp. 4030-4035, IEEE, 2009. Doi: 10.1109/CDC.2009.5400924
G. Battistelli, D. Mari, D. Selvi y P. Tesi, “Unfalsified approach to data-driven control design”, in Proc. 53rd IEEE Conference on Decision and Control, (Los Angeles), pp. 6003-6008, IEEE, 2014. Doi: 10.1109/CDC.2014.7040329
A. Corleta, C. Lorenzini, J. V. Flores y L. Campestrini, “Data-driven control design applied to uninterruptible power supplies”, in Proc. IEEE Conference on Control Applications (CCA), (Buenos Aires), pp. 1312-1317, IEEE, 2016. Doi: 10.1109/CCA.2016.7587988
C. De Persis y P. Tesi, “Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness,” in IEEE Transactions on Automatic Control, vol. 65, no. 3, pp. 909-924, March 2020. Doi: 10.1109/TAC.2019.2959924
G. R. Gonçalves da Silva, A. S. Bazanella, C. Lorenzini y L. Campestrini, “Data-Driven LQR Control Design,” in IEEE Control Systems Letters, vol. 3, no. 1, pp. 180-185, January. 2019. Doi: 10.1109/LCSYS.2018.2868183
I. Markovsky y F. Dorfler, “Behavioral systems theory in data-driven analysis, signal processing, and control”, Annual Reviews in Control, vol. 52, no. 1, pp. 42-64, June 2021. Doi: 10.1016/j.arcontrol.2021.09.005
M. P. Ho, A. Datta y S. P. Bhattacharyya, “Robust and non-fragile PID controller design”, International Journal of Robust and Nonlinear Control, vol. 11, no. 7, pp. 681-708, June 2001.Doi: 10.1002/rnc.618
L. H. Keel y S. P. Bhattacharyya, “Controller Synthesis Free of Analytical Models: Three Term Controllers”, IEEE Transactions on Automatic Control, vol. 53, no. 6, pp. 1353-1369, August 2008. Doi: 10.1109/TAC.2008.925810
R. Kumar, S. K. Singla y V. Chopra, “Comparison among some well-known control schemes with different tuning methods”, Journal of Applied Research and Technology, vol. 13, Issue 3, pp. 409-415, June 2015. Doi: 10.1016/j.jart.2015.07.007
S. V. K. Arun, U. Subramaniam, S. Padmanaban, M. S. Bhaskar y D. Almakhles, “Investigation for Performances Comparison PI, Adaptive PI, Fuzzy Speed Control Induction Motor for Centrifugal Pumping Application,” in Proc. 13th International Conference on Compatibility, Power Electronics and Power Engineering, (Sonderborg), pp. 1-6, IEEE, 2019. Doi: 10.1109/CPE.2019.8862351
D. F. Torres-Garzón, , P. A. Fonseca-Flórez y B. A. Sánchez-Duque, ‘Control para drone como periférico de entrada en sistema de medición de humedad y temperatura’, Mundo FESC, vol. 7, no. 13, pp. 73-85, Enero 2017
K. J. Astrom y T. Hagglund, “The Future of PID Control”, IFAC Proceedings Volumes, Vol. 33, Issue 4, pp. 19-30, April 2000. Doi: 10.1016/S1474-6670(17)38216-2
S. Khadraoui, H. Nounou, M. Nounou, A. Datta y S. P. Bhattacharyya, “A model-free design of reducedorder controllers and application to a DC servomotor”, Automatica, vol. 50, no. 8, pp. 2142-2149, August 2014.Doi: 10.1016/j.automatica.2014.06.001
R. Alzate, V. A. Oliveira, R. Magossi y S. P. Bhattacharyya, “Double loop control design for boost converters based on frequency response data”, in Proc. 20th IFAC World Congress, (Toulouse), pp. 10413-10418, IFAC, 2017. Doi: 10.1016/j.ifacol.2017.08.1968
Muhammad H. Rashid and others, Power Electronics Handbook: Devices, Circuits and Applications. 3rd ed. Butterworth-Heinemann, 2011
S. Mariethoz, S. Almer, M. Baja, A. G. Beccuti, D. Patino, A. Wernrud, J. Buisson, H. Cormerais, T. Geyer, H. Fujioka, U. T. Jonsson, C. Y. Kao, M. Morari, G. Papafotiou, A. Rantzer y P. Riedinger, “Comparison of Hybrid Control Techniques for Buck and Boost DC-DC Converters”, IEEE Transactions on Control Systems Technology, vol. 18, no. 5, pp. 1126-1145, September 2010. Doi: 10.1109/TCST.2009.2035306
Z. Chen, W. Gao, J. Hu y X. Ye, “Closed-Loop Analysis and Cascade Control of a Nonminimum Phase Boost Converter”, IEEE Transactions on Power Electronics, vol. 26, no. 4, pp. 1237-1252, April 2011. Doi: 10.1109/TPEL.2010.2070808
O. Lopez-Santos, L. Martinez-Salamero, G. Garcia, H. Valderrama-Blavi y T. Sierra-Polanco, “Robust Sliding-Mode Control Design for a Voltage Regulated Quadratic Boost Converter”, IEEE Transactions on Power Electronics, vol. 30, no. 4, pp. 2313-2327, April 2015. Doi: 10.1109/TPEL.2014.2325066
R. Saadi, O. Kraa, M. Y. Ayad, M. Becherif, H. Ghodbane, M. Bahri y A. Aboubou, “Dual loop controllers using PI, sliding mode and flatness controls applied to low voltage converters for fuel cell applications (Periodical style)”, International Journal of Hydrogen Energy, vol. 41, no. 42, pp. 19154-19163, September 2016. Doi: 10.1016/j.ijhydene.2016.08.171
X. Zhu, “Practical PID Controller Implementation and the Theory Behind,” Second International Conference on Intelligent Networks and Intelligent Systems, (Tianjian), pp. 58-61, IEEE, 2009. Doi: 10.1109/ICINIS.2009.24
H. Quiroga, “Prototipo para generación de energía basado en una máquina de inducción”, Trabajo de grado (Ingeniero Electrónico). Universidad Industrial de Santander, Bucaramanga, 2020
Background: Tuning PI controllers by conventional methods involves knowing the plant model and applying trial and error techniques. Objective: To adjust the parameters of a PI compensator using a control methodology based on frequency response data. Method: The basis of the presented calculation is the geometrical interpretation for the stability margins of the system, constituting a feasible dynamic specification space. Simulation analysis and laboratory experimental validation are presented for electrical systems involving step-up type DC-DC power electronic converters. Results: The construction of an experimental Bode diagram allowed to eliminate the dependence of the controller parameter calculation on the explicit knowledge of an analytical model of the system. Conclusion: Through numerical simulations and laboratory measurements it was possible to verify the dynamic regulation of the power converter, including saturation restrictions for the establishment of stabilising sets.
A. J. den Hamer, S. Weiland y M. Steinbuch, “Model-free norm-based fixed structure controller synthesis”, in Proc. 48th IEEE Conference on Decision and Control, (Shanghai), pp. 4030-4035, IEEE, 2009. Doi: 10.1109/CDC.2009.5400924
G. Battistelli, D. Mari, D. Selvi y P. Tesi, “Unfalsified approach to data-driven control design”, in Proc. 53rd IEEE Conference on Decision and Control, (Los Angeles), pp. 6003-6008, IEEE, 2014. Doi: 10.1109/CDC.2014.7040329
A. Corleta, C. Lorenzini, J. V. Flores y L. Campestrini, “Data-driven control design applied to uninterruptible power supplies”, in Proc. IEEE Conference on Control Applications (CCA), (Buenos Aires), pp. 1312-1317, IEEE, 2016. Doi: 10.1109/CCA.2016.7587988
C. De Persis y P. Tesi, “Formulas for Data-Driven Control: Stabilization, Optimality, and Robustness,” in IEEE Transactions on Automatic Control, vol. 65, no. 3, pp. 909-924, March 2020. Doi: 10.1109/TAC.2019.2959924
G. R. Gonçalves da Silva, A. S. Bazanella, C. Lorenzini y L. Campestrini, “Data-Driven LQR Control Design,” in IEEE Control Systems Letters, vol. 3, no. 1, pp. 180-185, January. 2019. Doi: 10.1109/LCSYS.2018.2868183
I. Markovsky y F. Dorfler, “Behavioral systems theory in data-driven analysis, signal processing, and control”, Annual Reviews in Control, vol. 52, no. 1, pp. 42-64, June 2021. Doi: 10.1016/j.arcontrol.2021.09.005
M. P. Ho, A. Datta y S. P. Bhattacharyya, “Robust and non-fragile PID controller design”, International Journal of Robust and Nonlinear Control, vol. 11, no. 7, pp. 681-708, June 2001.Doi: 10.1002/rnc.618
L. H. Keel y S. P. Bhattacharyya, “Controller Synthesis Free of Analytical Models: Three Term Controllers”, IEEE Transactions on Automatic Control, vol. 53, no. 6, pp. 1353-1369, August 2008. Doi: 10.1109/TAC.2008.925810
R. Kumar, S. K. Singla y V. Chopra, “Comparison among some well-known control schemes with different tuning methods”, Journal of Applied Research and Technology, vol. 13, Issue 3, pp. 409-415, June 2015. Doi: 10.1016/j.jart.2015.07.007
S. V. K. Arun, U. Subramaniam, S. Padmanaban, M. S. Bhaskar y D. Almakhles, “Investigation for Performances Comparison PI, Adaptive PI, Fuzzy Speed Control Induction Motor for Centrifugal Pumping Application,” in Proc. 13th International Conference on Compatibility, Power Electronics and Power Engineering, (Sonderborg), pp. 1-6, IEEE, 2019. Doi: 10.1109/CPE.2019.8862351
D. F. Torres-Garzón, , P. A. Fonseca-Flórez y B. A. Sánchez-Duque, ‘Control para drone como periférico de entrada en sistema de medición de humedad y temperatura’, Mundo FESC, vol. 7, no. 13, pp. 73-85, Enero 2017
K. J. Astrom y T. Hagglund, “The Future of PID Control”, IFAC Proceedings Volumes, Vol. 33, Issue 4, pp. 19-30, April 2000. Doi: 10.1016/S1474-6670(17)38216-2
S. Khadraoui, H. Nounou, M. Nounou, A. Datta y S. P. Bhattacharyya, “A model-free design of reducedorder controllers and application to a DC servomotor”, Automatica, vol. 50, no. 8, pp. 2142-2149, August 2014.Doi: 10.1016/j.automatica.2014.06.001
R. Alzate, V. A. Oliveira, R. Magossi y S. P. Bhattacharyya, “Double loop control design for boost converters based on frequency response data”, in Proc. 20th IFAC World Congress, (Toulouse), pp. 10413-10418, IFAC, 2017. Doi: 10.1016/j.ifacol.2017.08.1968
Muhammad H. Rashid and others, Power Electronics Handbook: Devices, Circuits and Applications. 3rd ed. Butterworth-Heinemann, 2011
S. Mariethoz, S. Almer, M. Baja, A. G. Beccuti, D. Patino, A. Wernrud, J. Buisson, H. Cormerais, T. Geyer, H. Fujioka, U. T. Jonsson, C. Y. Kao, M. Morari, G. Papafotiou, A. Rantzer y P. Riedinger, “Comparison of Hybrid Control Techniques for Buck and Boost DC-DC Converters”, IEEE Transactions on Control Systems Technology, vol. 18, no. 5, pp. 1126-1145, September 2010. Doi: 10.1109/TCST.2009.2035306
Z. Chen, W. Gao, J. Hu y X. Ye, “Closed-Loop Analysis and Cascade Control of a Nonminimum Phase Boost Converter”, IEEE Transactions on Power Electronics, vol. 26, no. 4, pp. 1237-1252, April 2011. Doi: 10.1109/TPEL.2010.2070808
O. Lopez-Santos, L. Martinez-Salamero, G. Garcia, H. Valderrama-Blavi y T. Sierra-Polanco, “Robust Sliding-Mode Control Design for a Voltage Regulated Quadratic Boost Converter”, IEEE Transactions on Power Electronics, vol. 30, no. 4, pp. 2313-2327, April 2015. Doi: 10.1109/TPEL.2014.2325066
R. Saadi, O. Kraa, M. Y. Ayad, M. Becherif, H. Ghodbane, M. Bahri y A. Aboubou, “Dual loop controllers using PI, sliding mode and flatness controls applied to low voltage converters for fuel cell applications (Periodical style)”, International Journal of Hydrogen Energy, vol. 41, no. 42, pp. 19154-19163, September 2016. Doi: 10.1016/j.ijhydene.2016.08.171
X. Zhu, “Practical PID Controller Implementation and the Theory Behind,” Second International Conference on Intelligent Networks and Intelligent Systems, (Tianjian), pp. 58-61, IEEE, 2009. Doi: 10.1109/ICINIS.2009.24
H. Quiroga, “Prototipo para generación de energía basado en una máquina de inducción”, Trabajo de grado (Ingeniero Electrónico). Universidad Industrial de Santander, Bucaramanga, 2020