Proportional-Integral-Derivative Gain-Scheduling Control of a Magnetic Levitation System

Authors

  • Claudia-Adina Bojan-Dragos Politehnica University of Timisoara Department of Automation and Applied Informatics, Bd. V. Parvan 2, 300223 Timisoara
  • Radu-Emil Precup Politehnica University of Timisoara Department of Automation and Applied Informatics, Bd. V. Parvan 2, 300223 Timisoara
  • Marius L. Tomescu Aurel Vlaicu University of Arad Romania, 310330 Arad, Elena Dragoi, 2
  • Stefan Preitl Politehnica University of Timisoara Department of Automation and Applied Informatics, Bd. V. Parvan 2, 300223 Timisoara
  • Oana-Maria Tanasoiu Politehnica University of Timisoara Department of Automation and Applied Informatics, Bd. V. Parvan 2, 300223 Timisoara
  • Stefania Hergane Politehnica University of Timisoara Department of Automation and Applied Informatics Bd. V. Parvan 2, 300223 Timisoara, Romania

Keywords:

gain-scheduling, magnetic levitation system, Proportional-Integral-Derivative control, real-time experiments

Abstract

The paper presents a gain-scheduling control design procedure for classical Proportional-Integral-Derivative controllers (PID-GS-C) for positioning system. The method is applied to a Magnetic Levitation System with Two Electromagnets (MLS2EM) laboratory equipment, which allows several experimental verifications of the proposed solution. The nonlinear model of MLS2EM is linearized at seven operating points. A state feedback control structure is first designed to stabilize the process. PID control and PID-GS-C structures are next designed to ensure zero steady-state control error and bumpless switching between PID controllers for the linearized models. Real-time experimental results are presented for validation. 

References

An S., Ma Y., Cao Z. (2009); Applying simple adaptive control to magnetic levitation system, Proceedings of 2nd International Conference on Intelligent Computation Technology and Automation, Changsha, Hunan, China, 1, 746-749, 2009. https://doi.org/10.1109/ICICTA.2009.186

Angelov P., Yager R. (2012); A new type of simplified fuzzy rule-based systems, International Journal of General Systems, 41(2), 163-185, 2012. https://doi.org/10.1080/03081079.2011.634807

Azar D., Fayad K., Daoud C. (2016); A combined ant colony optimization and simulated annealing algorithm to assess stability and fault-proneness of classes based on internal software quality attributes, International Journal of Artificial Intelligence, 14(2), 137-156, 2016.

Baranyi P., Tikk D., Yam Y., Patton R.J. (2003); From differential equations to PDC controller design via numerical transformation, Computers in Industry, 51(3), 281-297, 2003. https://doi.org/10.1016/S0166-3615(03)00058-7

Bianchi F.D., Sánchez Pe-a R.S. (2011); Interpolation for gain-scheduled control with guarantees, Automatica, 47(1), 239-243, 2011. https://doi.org/10.1016/j.automatica.2010.10.028

Bianchi F.D.; Sánchez-Pena R.S., Guadayol M. (2012); Gain scheduled control based on high fidelity local wind turbine models, Renewable Energy, 37(1), 233-240, 2012. https://doi.org/10.1016/j.renene.2011.06.024

Bedoud K., Ali-rachedi M., Bahid T., Lakel R. (2015); Adaptive fuzzy gain scheduling of PI controller for control of the wind energy conversion systems, Energy Procedia, 74, 211-225, 2015. https://doi.org/10.1016/j.egypro.2015.07.580

Bojan-Dragos C.-A., Preitl S., Precup R.-E., Hergane S., Hughiet E.G., Szedlak-Stinean A.-I. (2016); State feedback and proportional-integral-derivative control of a magnetic levitation system, Proceedings of IEEE 14th International Symposium on Intelligent Systems and Informatics, Subotica, Serbia, 111-116, 2016.

Bojan-Dragos C.-A., Preitl S., Precup R.-E., Hergane S., Hughiet E.G., Szedlak-Stinean A.-I. (2016); Proportional-integral gain-scheduling control of a magnetic levitation system, Proceedings of 20th International Conference on System Theory, Control and Computing, Sinaia, Romania, 1-6, 2016.

Chadli M., Akhenak A., Ragot J., Maquin D. (2009); State and unknown input estimation for discrete time multiple model, Journal of the Franklin Institute, 346(6), 593-610, 2009. https://doi.org/10.1016/j.jfranklin.2009.02.011

Chauhan S., Nigam M.J. (2014); Model predictive controller design and perturbation study for magnetic levitation system, Proceedings of 2014 IEEE Recent Advances in Engineering and Computational Sciences, Chandigarh, India, 1-6, 2014.

Colhon M., Danciulescu, D. (2010); Semantic schemas for natural language generation in multilingual systems, Journal of Knowledge,Communications and Computing Technologies, 2(1), 10-17, 2010.

Danciulescu D. (2015); Formal languages generation in systems of knowledge representation based on stratified graphs, Informatica, 26(3), 407-417, 2015. https://doi.org/10.15388/Informatica.2015.55

Deliparaschos K., Michail K., Zolotas A., Tzafestas S. (2016); FPGA-based efficient hardware/ software co-design for industrial systems with systematic sensor selection, Journal of Electrical Engineering, 67(3), 150-159, 2016.

Derr K.W., Manic M. (2015); Wireless sensor networks - node localization for various industry problems, IEEE Transactions on Industrial Informatics, 11(3), 752-762, 2015. https://doi.org/10.1109/TII.2015.2396007

Dragos C.-A., Precup R.-E., David R.-C., Preitl S., Stinean A.-I., Petriu E.M. (2013); Simulated annealing-based optimization of fuzzy models for magnetic levitation systems, Proceedings of 2013 Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, AB, Canada, 286-29, 2013.

Dounis A.I., Kofinas P., Alafodimos C., Tseles D. (2013); Adaptive fuzzy gain scheduling PID controller for maximum power point tracking of photovoltaic system, Renewable Energy, 60, 202-214, 2013. https://doi.org/10.1016/j.renene.2013.04.014

Dzitac I. (2015); The fuzzification of classical structures: A general view, International Journal of Computers Communications & Control, 10(6), 772-788, 2015. https://doi.org/10.15837/ijccc.2015.6.2069

Elsodany N.M., Rezeka S.F., Maharem N.A. (2011); Adaptive PID control of a stepper motor driving a flexible rotor, Alexandria Engineering Journal, 50(2), 127-136, 2011. https://doi.org/10.1016/j.aej.2010.08.002

Filip F.G. (2008); Decision support and control for large-scale complex systems, Annual Reviews in Control, 32(1), 61-70, 2008. https://doi.org/10.1016/j.arcontrol.2008.03.002

Gaxiola F., Melin P., Valdez F., Castro J.R., Castillo O. (2016); Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO, Applied Soft Computing, 38, 860-871, 2016. https://doi.org/10.1016/j.asoc.2015.10.027

Haber R.E., Alique J.R. (2007); Fuzzy logic-based torque control system for milling process optimization, IEEE Transactions on Systems, Man and Cybernetics, Part C: Applications and Reviews, 37(5), 941-950, 2007. https://doi.org/10.1109/TSMCC.2007.900654

Huang Y.-W., Tung P.-C. (2009); Design of a fuzzy gain scheduling controller having input saturation: a comparative study, Journal of Marine Science and Technology, 17(4), 249-256, 2009.

Inteco. (2008); Magnetic Levitation System 2EM (MLS2EM), User's Manual (Laboratory Set), Inteco Ltd., Krakow, Poland, 2008.

Johanyák Z.C. (2013); Fuzzy modeling of thermoplastic composites' melt volume rate, Computing and Informatics, 32(4), 845-857, 2013.

Kazakov A.L., Lempert A.A. (2015); On mathematical models for optimization problem of logistics infrastructure, International Journal of Artificial Intelligence, 13(1), 200-210, 2010.

King R., Stathaki A. (2000); Fuzzy gain scheduling control of nonlinear processes, Research Report, Department of Electrical and Computer Engineering, University of Patras, Patras, Greece, 2000.

Lashin M., Elgammal A.T., Ramadan A., Abouelsoud A.A., Assal S.F.M., Abo-Ismail A. (2014); Fuzzy-based gain scheduling of exact feedforward linearization control and SMC for magnetic ball levitation system: A comparative study, Proceedings of 2014 IEEE International Conference on Automation, Quality and Testing, Robotics, Cluj-Napoca, Romania, 1-6, 2014.

Michino R., Tanaka H., Mizumoto I. (2009); Application of high gain adaptive output feedback control to a magnetic levitation system, Proceedings of ICROS-SICE International Joint Conference, Fukuoka, Japan, 970-975, 2009.

Moharam A., El-Hosseini M.A., Ali H.A. (2015); Design of optimal PID controller using NSGA-II algorithm and level diagram, Studies in Informatics and Control, 24(3), 301-308, 2015.

Negru V., Grigoras G., Danciulescu D. (2015); Natural language agreement in the generation mechanism based on stratified graphs, Proceedings of 7th Balkan Conference in Informatics, Craiova, Romania, 36:1-36:8, 2015.

Obe O., Dumitrache I. (2012); Adaptive neuro-fuzzy controller with genetic training for mobile robot control, International Journal of Computers Communications & Control, 7(1), 135-146, 2012. https://doi.org/10.15837/ijccc.2012.1.1429

Osaba E., Onieva E., Dia F., Carballedo R., Lopez P., Perallos A. (2015); A migration strategy for distributed evolutionary algorithms based on stopping non-promising subpopulations: A case study on routing problems, International Journal of Artificial Intelligence, 13(2), 46-56, 2015.

Osaba E., Yang X.-S., Diaz F., Lopez P., Carballedo R. (2016); An improved discrete bat algorithm for symmetric and asymmetric traveling salesman problems, Engineering Applications of Artificial Intelligence, 48, 59-71, 2016. https://doi.org/10.1016/j.engappai.2015.10.006

Pallav S., Pandey K., Laxmi V. (2014); PID control of magnetic levitation system based on derivative filter, Proceedings of 2014 Annual International Conference on Emerging Research Areas: Magnetics, Machines and Drives, Kottayam, India, 1-5, 2014.

Precup R.-E., Angelov P., Costa B.S.J., Sayed-Mouchaweh M. (2015); An overview on fault diagnosis and nature-inspired optimal control of industrial process applications, Computers in Industry, 74, 75-94, 2015. https://doi.org/10.1016/j.compind.2015.03.001

Precup R.-E., David R.-C., Petriu E.M., Preitl S., Radac M.-B. (2014); Novel adaptive charged system search algorithm for optimal tuning of fuzzy controllers, Expert Systems with Applications, 41(4), 1168-1175, 2014. https://doi.org/10.1016/j.eswa.2013.07.110

Precup R.-E., Preitl S. (1997); Popov-type stability analysis method for fuzzy control systems, Proceedings of Fifth European Congress on Intelligent Technologies and Soft Computing, Aachen, Germany, 2, 1306-1310, 1997.

Precup R.-E., Preitl S. (2007); PI-fuzzy controllers for integral plants to ensure robust stability, Information Sciences, 177(20), 4410-4429, 2007. https://doi.org/10.1016/j.ins.2007.05.005

Precup R.-E., Sabau, M.-C., Petriu E.M. (2015); Nature-inspired optimal tuning of input membership functions of Takagi-Sugeno-Kang fuzzy models for anti-lock braking systems, Applied Soft Computing, 27, 575-589, 2015. https://doi.org/10.1016/j.asoc.2014.07.004

Precup R.-E., Radac M.-B., Tomescu M.L., Petriu E.M., Preitl S. (2013); Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems, Expert Systems with Applications, 40(1), 188-199, 2013. https://doi.org/10.1016/j.eswa.2012.07.023

Precup R.-E., Tomescu M.L., Preitl S. (2009); Fuzzy logic control system stability analysis based on Lyapunov's direct method, International Journal of Computers Communications & Control, 4(4), 415-426, 2009. https://doi.org/10.15837/ijccc.2009.4.2457

Preitl S., Precup R.-E.(1996); On the algorithmic design of a class of control systems based on providing the symmetry of open-loop Bode plots, Scientific Bulletin of UPT, Transactions on Automatic Control and Computer Science, 41(55)(2), 47-55, 1996.

Puig V., Bolea Y., Blesa J. (2012); Robust gain-scheduled Smith PID controllers for second order LPV systems with time varying delay, IFAC Proceedings Volumes, 45(3), 199-204, 2012.

Rebai A., Guesmi K., Hemici B. (2015); Design of an optimized fractional order fuzzy PID controller for a piezoelectric actuator, Control Engineering and Applied Informatics, 17(3), 41-49, 2015.

Qin Q., Cheng S., Zhang, Q., Qin Q., Cheng S., Zhang Q., Li L., Shi Y. (2016); Particle swarm optimization with interswarm interactive learning strategy, IEEE Transactions on Cybernetics, 46(10), 2238-2251, 2016. https://doi.org/10.1109/TCYB.2015.2474153

Sakalli A., Kumbasar T., Yesil E., Hagras H. (2014); Analysis of the performances of type- 1, self-tuning type-1 and interval type-2 fuzzy PID controllers on the magnetic levitation system, Proceedings of 2014 IEEE International Conference on Fuzzy Systems, Beijing, China, 1859-1866, 2014.

Sedaghati A. (2006); A PI controller based on gain-scheduling for synchronous generator, Turkish Journal of Electrical Engineering and Computer Sciences, 14(2), 241-251, 2006.

Shameli E., Khamesee M.B., Huissoon J.P. (2007); Nonlinear controller design for a magnetic levitation device, Microsystem Technologies, 13(8), 831-835, 2007.

Škrjanc I., Blažic S., Agamennoni O.E. (2005); Interval fuzzy model identification using l1-norm, IEEE Transactions on Fuzzy Systems, 13(5), 561-568, 2005. https://doi.org/10.1109/TFUZZ.2005.856567

Vašcák J. (2010); Approaches in adaptation of fuzzy cognitive maps for navigation purposes, Proceedings of 8th International Symposium on Applied Machine Intelligence and Informatics, Heržany, Slovakia, 31-36, 2010.

Wang B.; Liu G.-P.; Rees D.(2009); Networked predictive control of magnetic levitation system, Proceedings of 2009 IEEE International Conference on Systems, Man and Cybernetics, San Antonio, TX, USA, 4100-4105, 2009.

Xie Y.-M., Shi H., Alleyne A., Yang B.-G. (2016); Feedback shape control for deployable mesh reflectors using gain scheduling method, Acta Astronautica, 121, 241-255, 2016. https://doi.org/10.1016/j.actaastro.2016.01.005

Yang Y.-N., Yan Y. (2016); Attitude regulation for unmanned quadrotors using adaptive fuzzy gain-scheduling sliding mode control, Aerospace Science and Technology, 54, 208-217, 2016. https://doi.org/10.1016/j.ast.2016.04.005

Zhao Z.Y., Tomizuka M. (1993); Fuzzy gain scheduling of PID controllers, IEEE Transactions on Systems, Man, and Cybernetics, 23(5), 1392-1398, 1993. https://doi.org/10.1109/21.260670

Zietkiewicz J. (2011); Constrained predictive control of a levitation system, Proceedings of 16th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, 278-283, 2011.

Published

2017-09-10

Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.