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

  • 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


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. 


[1] 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.

[2] Angelov P., Yager R. (2012); A new type of simplified fuzzy rule-based systems, International Journal of General Systems, 41(2), 163-185, 2012.

[3] 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.

[4] 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.

[5] Bianchi F.D., Sánchez Pe-a R.S. (2011); Interpolation for gain-scheduled control with guarantees, Automatica, 47(1), 239-243, 2011.

[6] 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.

[7] 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.

[8] 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.

[9] 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.

[10] 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.

[11] 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.

[12] 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.

[13] Danciulescu D. (2015); Formal languages generation in systems of knowledge representation based on stratified graphs, Informatica, 26(3), 407-417, 2015.

[14] 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.

[15] 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.

[16] 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.

[17] 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.

[18] Dzitac I. (2015); The fuzzification of classical structures: A general view, International Journal of Computers Communications & Control, 10(6), 772-788, 2015.

[19] 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.

[20] Filip F.G. (2008); Decision support and control for large-scale complex systems, Annual Reviews in Control, 32(1), 61-70, 2008.

[21] 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.

[22] 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.

[23] 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.

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

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

[26] 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.

[27] 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.

[28] 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.

[29] 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.

[30] 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.

[31] 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.

[32] 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.

[33] 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.

[34] 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.

[35] 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.

[36] 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.

[37] 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.

[38] 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.

[39] Precup R.-E., Preitl S. (2007); PI-fuzzy controllers for integral plants to ensure robust stability, Information Sciences, 177(20), 4410-4429, 2007.

[40] 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.

[41] 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.

[42] 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.

[43] 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.

[44] 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.

[45] 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.

[46] 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.

[47] 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.

[48] 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.

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

[50] 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.

[51] 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.

[52] 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.

[53] 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.

[54] 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.

[55] Zhao Z.Y., Tomizuka M. (1993); Fuzzy gain scheduling of PID controllers, IEEE Transactions on Systems, Man, and Cybernetics, 23(5), 1392-1398, 1993.

[56] 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.
How to Cite
BOJAN-DRAGOS, Claudia-Adina et al. Proportional-Integral-Derivative Gain-Scheduling Control of a Magnetic Levitation System. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 12, n. 5, p. 599-611, sep. 2017. ISSN 1841-9844. Available at: <>. Date accessed: 30 nov. 2020. doi:


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