Data-Driven Model-Free Sliding Mode and Fuzzy Control with Experimental Validation


The paper presents the combination of the model-free control technique with two popular nonlinear control techniques, sliding mode control and fuzzy control. Two data-driven model-free sliding mode control structures and one data-driven model-free fuzzy control structure are given. The data-driven model-free sliding mode control structures are built upon a model-free intelligent Proportional-Integral (iPI) control system structure, where an augmented control signal is inserted in the iPI control law to deal with the error dynamics in terms of sliding mode control. The data-driven model-free fuzzy control structure is developed by fuzzifying the PI component of the continuous-time iPI control law. The design approaches of the data-driven model-free control algorithms are offered. The data-driven model-free control algorithms are validated as controllers by real-time experiments conducted on 3D crane system laboratory equipment.


[1] Abed-alguni, B.H. (2019). Island-based cuckoo search with highly disruptive polynomial mutation, International Journal of Artificial Intelligence, 17(1), 57-82, 2019.

[2] Andoga, R.; Fozo, L. (2017). Near magnetic field of a small turbojet engine, Acta Physica Polonica A, 131(4), 1117-1119, 2017.

[3] Angelov, P.; Škrjanc, I.; Blažic, S. (2013). Robust evolving cloud-based controller for a hydraulic plant, Proceedings of 2013 IEEE Conference on Evolving and Adaptive Intelligent Systems, Singapore, 1-8, 2013.

[4] Baranyi, P.; Korondi, P.; Patton, R.J.; Hashimoto, H. (2004). Trade-off between approximation accuracy and complexity for TS fuzzy models, Asian Journal of Control, 6(1), 21-33, 2004.

[5] Bashir, A.O.; Rui, X.-T.; Zhang, J.-S. (2019). Ride comfort improvement of a semi-active vehicle suspension based on hybrid fuzzy and fuzzy-PID controller, Studies in Informatics and Control, 28(4), 421-430, 2019.

[6] Bejinariu, S.-I.; Saramandu, N.; Nevaci, M.; Apopei, V.; Teodorescu, H.-N. (2020). Recovery of old dialectal materials and maps through image processing, Romanian Journal of Information Science and Technology, 23(3), 223-237, 2020.

[7] Bouteraa, Y.; Abdallah, I.B.; Elmogy, A.; Ibrahim, A.; Tariq, U.; Ahmad, T. (2020). A fuzzy logic architecture for rehabilitation robotic systems, International Journal of Computers Communications & Control, 15(4), 3814, 2020.

[8] Campi, M.C.; Lecchini, A.; Savaresi, S.M. (2002). Virtual reference feedback tuning: a direct method for the design of feedback controllers, Automatica, 38(8), 1337-1346, 2002.

[9] Cao, L.; Gao, S.-L.; Zhao, D.-Y. (2020). Data-driven model-free sliding mode learning control for a class of discrete-time nonlinear systems, Transactions of the Institute of Measurement and Control, DOI: 10.1177/0142331220921022, 2020.

[10] Chen, M.-R.; Zeng, G.-Q.; Lu, K.-D. (2019). A many-objective population extremal optimization algorithm with an adaptive hybrid mutation operation, Information Sciences, 498, 62-90, 2019.

[11] Costin, H.; Rotariu, C.; Alexa, I.; Constantinescu, G.; Cehan, V.; Dionisie, B.; Andruseac, G.; Felea, V.; Crauciuc, E.; Scutariu, M. (2009). TELEMON - A complex system for real time medical telemonitoring, Proceedings of 11th International Congress of the IUPESM/World Congress on Medical Physics and Biomedical Engineering, Munich, Germany, 92-95, 2009.

[12] da Silva Moreira, J.; Acioli Júnior, G.; Rezende Barros, G. (2018). Time and frequency domain data-driven PID iterative tuning, IFAC-PapersOnLine, 51(15), 1056-1061, 2018.

[13] Deliparaschos, K.M.; Michail, K.; Zolotas, A.C. (2020). Facilitating autonomous systems with AI-based fault tolerance and computational resource economy, Electronics, 9(5), 788, 2020.

[14] Dombi, J.; Hussain, A. (2019). Data-driven arithmetic fuzzy control using the distending function, in Ahram, T.; Taiar, R.; Colson, S.; Choplin, A. (eds.), IHIET: Human Interaction and Emerging Technologies, Springer, Cham, Advances in Intelligent Systems and Computing, 1018, 215-221, 2019.

[15] Dzitac, I.; Filip, F.-G.; Manolescu, M.-J. (2017). Fuzzy logic is not fuzzy: World-renowned computer scientist Lotfi A. Zadeh, International Journal of Computers Communications & Control, 12(6), 748-789, 2017.

[16] Ebrahimi, N.; Ozgoli, S.; Ramezani, A. (2018). Model-free sliding mode control, theory and application, Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering, 232(10), 095965181878059, 2018.

[17] Ebrahimi, N.; Ozgoli, S.; Ramezani, A. (2020). Model free sliding mode controller for blood glucose control: Towards artificial pancreas without need to mathematical model of the system, Computer Methods and Programs in Biomedicine, DOI: 10.1016/j.cmpb.2020.105663, 2020.

[18] Fan, Q.-Y.; Yang, G.-H. (2016). Adaptive actor-critic design-based integral sliding-mode control for partially unknown nonlinear systems with input disturbances, IEEE Transactions on Neural Networks and Learning Systems, 27(1), 165-177, 2016.

[19] Fliess, M.; Join, C. (2009). Model-free control and intelligent PID controllers: Towards a possible trivialization of nonlinear control?, IFAC Proceedings Volumes, 42(10), 1531-1550, 2009.

[20] Fliess, M.; Join, C. (2013). Model-free control, International Journal of Control, 86(12), 2228- 2252, 2013.

[21] Fliess, M.; Join, C.; Mboup, M.; Sira-Ramirez, H. (2006). Vers une commande multivariable sans modele, Proceedings of Conférence Internationale Francophone d'Automatique, Bordeaux, France, 1-7, 2006.

[22] Formentin, S.; Campi, M.C.; Caré, A.; Savaresi, S.M. (2019). Deterministic continuous-time Virtual Reference Feedback Tuning (VRFT) with application to PID design, Systems and Control Letters, 127, 25-34, 2019.

[23] Gajate, A.; Haber, R.E.; Vega, P.I.; Alique, J.R. (2010). A transductive neuro-fuzzy controller: Application to a drilling process, IEEE Transactions on Neural Networks, 21(7), 1158-1167, 2010.

[24] Galluppi, O.; Formentin, S.; Novara, C.; Savaresi, S.M. (2019). Multivariable D2-IBC and application to vehicle stability control, ASME Journal of Dynamic Systems, Measurement and Control, 141(10), 1-12, 2019.

[25] Gao, Z. (2006). Active disturbance rejection control: a paradigm shift in feedback control system design, Proceedings of 2006 American Control Conference, Minneapolis, MN, USA, 2399-2405, 2006.

[26] Gu, Z.-M.; Wang, G.-G. (2020). Improving NSGA-III algorithms with information feedback models for large-scale many-objective optimization, Future Generation Computer Systems, 107, 49-69, 2020.

[27] Guerra, T.M.; Sala, A.; Tanaka, K. (2015). Fuzzy control turns 50: 10 years later, Fuzzy Sets and Systems, 281, 168-182, 2015.

[28] Hjalmarsson, H. (2002). Iterative feedback tuning - an overview, International Journal of Adaptive Control and Signal Processing, 16(5), 373−395, 2002.

[29] Hou, Z.-S.; Wang, Z. (2013). From Model-based control to data-driven control: Survey, classification and perspective, Information Sciences, 235, 3-35, 2013.

[30] Huang, J.-W.; Gao, J.-W. (2020). How could data integrate with control? A review on data-based control strategy, International Journal of Dynamics and Control, DOI: 10.1007/s40435-020-00688- x, 2020.

[31] Inteco Ltd. (2008). 3D Crane, User's Manual, Inteco Ltd., Krakow, Poland, 2008.

[32] Jiang, P.; Cheng, Y.-Q.; Wang, X.-N.; Feng, Z. (2016). Unfalsified visual servoing for simultaneous object recognition and pose tracking, IEEE Transactions on Cybernetics, 46(12), 3032-3046, 2016.

[33] Johanyák, Z.C. (2015). A simple fuzzy logic based power control for a series hybrid electric vehicle, Proceedings of 9th IEEE European Modelling Symposium on Mathematical Modelling and Computer Simulation, Madrid, Spain, 207-212, 2015.

[34] Juang, C.-F.; Chang, Y.-C. (2016). Data-driven interpretable fuzzy controller design through multi-objective genetic algorithm, Proceedings of 2016 IEEE International Conference on Systems, Man, and Cybernetics, Budapest, Hungary, 2403-2408, 2016.

[35] Jung, H.; Jeon, K.; Kang, J.-G.; Oh, S. (2021). Iterative feedback tuning of cascade control of two-inertia system, IEEE Control Systems Letters, 5(3), 785−790, 2021.

[36] Kadali, R.; Huang, B.; Rossiter, A. (2003). A data driven subspace approach to predictive controller design, Control Engineering Practice, 11(3), 261-278, 2003.

[37] Kamesh, R.; Rani, K.Y. (2016). Parameterized data-driven fuzzy model based optimal control of a semi-batch reactor, ISA Transactions, 64, 418-430, 2016.

[38] Kammer, L.C.; Bitmead, R.R.; Bartlett, P.L. (2000). Direct iterative tuning via spectral analysis, Automatica, 36(9), 1301-1307, 2000.

[39] Karimi, A.; Miskovic, L.; Bonvin, D. (2004). Iterative correlation-based controller tuning, International Journal of Adaptive Control and Signal Processing, 18(8), 645-664, 2004.

[40] Li, L.-M.; Lu, K.-D.; Zeng, G.-Q.; Wu, L.; Chen, M.-R. (2016). A novel real-coded populationbased extremal optimization algorithm with polynomial mutation: A non-parametric statistical study on continuous optimization problems, Neurocomputing, 174, 577-587, 2016.

[41] Li, S.; Ahn, C.K.; Xiang, Z.-R. (2019). Adaptive fuzzy control of switched nonlinear time-varying delay systems with prescribed performance and unmodeled dynamics, Fuzzy Sets and Systems, 371, 40-60, 2019.

[42] Lucchini, A.; Formentin, S.; Corno, M.; Piga, D.; Savaresi, S.M. (2020). Torque vectoring for high-performance electric vehicles: a data-driven MPC approach, IEEE Control Systems Letters, 4(3), 725-730, 2020.

[43] McDaid, A.J.; Aw, K.C.; Haemmerle, E.; Xie, S.Q. (2012). Control of IPMC actuators for microfluidics with adaptive "online" iterative feedback tuning, IEEE/ASME Transactions on Mechatronics, 17(4), 789-797, 2012.

[44] Mls, K.; Cimler, R.; Vašcák, J.; Puheim, M. (2017). Interactive evolutionary optimization of fuzzy cognitive maps, Neurocomputing, 232, 58-68, 2017.

[45] Nguyen, A.-T.; Taniguchi, T.; Eciolaza, L.; Campos, V.; Palhares, R.; Sugeno, M. (2019). Fuzzy control systems: past, present and future, IEEE Computational Intelligence Magazine, 14(1), 56-68, 2019.

[46] Novara, C.; Formentin, S.; Savaresi, S.M.; Milanese, M. (2015). A data-driven approach to nonlinear braking control, Proceedings of 54th IEEE Conference on Decision and Control, Osaka, Japan, 1-6, 2015.

[47] Ontiveros-Robles, E.; Melin, P.; Castillo, O. (2018). Comparative analysis of noise robustness of type 2 fuzzy logic controllers, Kybernetika, 54(1), 175-201, 2018.

[48] Osaba, E.; Yang, X.S.; Fister Jr, I.; Del Ser, J.; Lopez-Garcia, P.; Vazquez-Pardavila, A.J. (2019). A discrete and improved bat algorithm for solving a medical goods distribution problem with pharmacological waste collection, Swarm and Evolutionary Computation, 44, 273-286, 2019.

[49] Precup R.-E.; Enache, F.-C.; Radac, M.-B.; Petriu, E. M.; Preitl, S; Dragos, C.-A. (2013). Leadlag controller-based iterative learning control algorithms for 3D crane systems, in Madarász, L.; Živcák J. (eds.), Aspects of Computational Intelligence: Theory and Applications, Springer, Berlin, Heidelberg, 2, 25-38, 2013.

[50] 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.

[51] Precup, R.-E.; David, R.-C.; Petriu, E.M.; Szedlak-Stinean, A.-I.; Bojan-Dragos, C.-A. (2016). Grey wolf optimizer-based approach to the tuning of PI-fuzzy controllers with a reduced process parametric sensitivity, IFAC-PapersOnLine, 49(5), 55-60, 2016.

[52] Precup, R.-E.; Preitl, S. (2003). Development of fuzzy controllers with non-homogeneous dynamics for integral-type plants, Electrical Engineering, 85(3), 155-168, 2003.

[53] Precup, R.-E.; Preitl, S. (2004). Sensitivity analysis of a class of fuzzy controlled mobile robots, IFAC Proceedings Volumes, 37(16), 115-120, 2004.

[54] Precup, R.-E.; Preitl, S. (2006). Stability and sensitivity analysis of fuzzy control systems. Mechatronics applications, Acta Polytechnica Hungarica, 3(1), 61-76, 2006.

[55] Precup, R.-E.; Preitl, S.; Petriu, E.M.; Roman, R.-C.; Bojan-Dragos, C.-A.; Hedrea, E.-L.; Szedlak-Stinean, A.-I. (2020). A center manifold theory-based approach to the stability analysis of state feedback Takagi-Sugeno-Kang fuzzy control systems, Facta Universitatis, Series: Mechanical Engineering, 18(2), 189-204, 2020.

[56] Precup, R.-E.; Radac, M.-B.; Petriu, E.M.; Dragos, C.-A.; Preitl, S. (2014). Model-free tuning solution for sliding mode control of servo systems, Proceedings of 8th Annual IEEE International Systems Conference, Ottawa, ON, Canada, 30-35, 2014.

[57] Precup, R.-E.; Radac, M.-B.; Roman, R.-C.; Petriu, E.M. (2017). Model-free sliding mode control of nonlinear systems: Algorithms and experiments, Information Sciences, 381, 176-192, 2017.

[58] Precup, R.-E.; Tomescu, M.L. (2015). Stable fuzzy logic control of a general class of chaotic systems, Neural Computing and Applications, 26(3), 541-550, 2015.

[59] Precup, R.-E.; Voisan, E.-I.; Petriu, E.M.; Tomescu, M.L.; David, R.-C.; Szedlak-Stinean, A.-I.; Roman, R.-C. (2020). Grey wolf optimizer-based approaches to path planning and fuzzy logicbased tracking control for mobile robots, International Journal of Computers Communications

& Control, 15(3), 3844, 2020.

[60] Preitl, S.; Precup, R.-E.; Preitl, Z. (2005). Sensitivity analysis of low cost fuzzy controlled servo systems, IFAC Proceedings Volumes, 38(1), 342-347, 2005.

[61] Preitl, S.; Precup, R.-E.; Preitl, Z.; Vaivoda, S.; Kilyeni, S.; Tar, J.K. (2007). Iterative feedback and learning control. Servo systems applications, IFAC Proceedings Volumes, 40(8), 16-27, 2007.

[62] Roman, R.-C.; Precup, R.-E.; Bojan-Dragos, C.-A.; Szedlak-Stinean, A.-I. (2019). Combined model-free adaptive control with fuzzy component by virtual reference feedback tuning for tower crane systems, Procedia Computer Science, 162, 267-274, 2019.

[63] Roman, R.-C.; Precup, R.-E.; David, R.-C. (2018). Second order intelligent proportional-integral fuzzy control of twin rotor aerodynamic systems, Procedia Computer Science, 139, 372-380, 2018.

[64] Roman, R.-C.; Precup, R.-E.; Petriu, E.M. (2020). Hybrid data-driven fuzzy active disturbance rejection control for tower crane systems, European Journal of Control, DOI: 10.1016/j.ejcon.2020.08.001, 2020.

[65] Roman, R.-C.; Precup, R.-E.; Petriu, E.M.; Dragan, F. (2019). Combination of data-driven active disturbance rejection and Takagi-Sugeno fuzzy control with experimental validation on tower crane systems, Energies, 12(8), 1-19, 2019.

[66] Roman, R.-C.; Precup, R.-E.; Petriu, E.M.; Hedrea, E.-L.; Bojan-Dragos, C.-A.; Radac, M.-B. (2019). Model-free adaptive control with fuzzy component for tower crane systems, Proceedings of 2019 IEEE International Conference on Systems, Man and Cybernetics, Bari, Italy, 1384-1389, 2019.

[67] Roman, R.-C.; Precup, R.-E.; Radac, M.-B. (2017). Model-free fuzzy control of twin rotor aerodynamic systems, Proceedings of 25th Mediterranean Conference on Control and Automation, Valletta, Malta, 559-564, 2017.

[68] Safonov, M.G.; Tsao, T.-C. (1997). The unfalsified control concept and learning, IEEE Transactions on Automatic Control, 42(6), 843-847, 1997.

[69] Sato, T.; Kusakabe, T.; Himi, K.; Arakim N.; Konishi, Y. (2020). Ripple-free data-driven dualrate controller using lifting technique: Application to a physical rotation system, IEEE Transactions on Control Systems Technology, DOI: 10.1109/TCST.2020.2988613, 2020.

[70] Schulken, E.; Crassidis, A. (2018). Model-free sliding mode control algorithms including application to a real-world quadrotor, Proceedings of 5th International Conference of Control, Dynamic Systems, and Robotics, Niagara Falls, Canada, 112-1-112-9, 2018.

[71] Shamloo, N.F.; Kalat, A.A.; Chisci, L. (2020). Indirect adaptive fuzzy control of nonlinear descriptor systems, European Journal of Control, 51, 30-38, 2020.

[72] Simani, S.; Alvisi, S.; Venturini, M. (2015). Data-driven design of a fault tolerant fuzzy controller for a simulated hydroelectric system, IFAC-PapersOnLine, 48(21), 1090-1095, 2015.

[73] Spall, J.C.; Cristion, J.A. (1998). Model-free control of nonlinear stochastic systems with discretetime measurements, IEEE Transactions on Automatic Control, 43(9), 1198-1210, 1998.

[74] Teodorescu, H.-N. (2012). Characterization of nonlinear dynamic systems for engineering purposes - a partial review, International Journal of General Systems, 41(8), 805-825, 2012.

[75] Touhami, M.; Hazzab, A.; Mokhtari, F.; Sicard, P. (2019). Active disturbance rejection controller with ADRC-fuzzy for MAS control, Electrotehnica, Electronica, Automatica (EEA), 67(2), 89-97, 2019.

[76] Van Waarde, H.J.; Eising, J.; Trentelman, H.L.; Camlibel, M.K. (2020). Data informativity: a new perspective on data-driven analysis and control, IEEE Transactions on Automatic Control, DOI: 10.1109/TAC.2020.2966717, 2020.

[77] Vrkalovic, S.; Lunca, E.-C.; Borlea, I.-D. (2018). Model-free sliding mode and fuzzy controllers for reverse osmosis desalination plants, International Journal of Artificial Intelligence, 16(2), 208-222, 2018.

[78] Wang, G.-G.; Tan, Y. (2019). Improving metaheuristic algorithms with information feedback models, IEEE Transactions on Cybernetics, 49(2), 542-555, 2019.

[79] Wang, H.-P.; Ye, X.-F.; Tian, Y.; Christov, N. (2015). Attitude control of a quadrotor using model free based sliding model controller, Proceedings of 2015 20th International Conference on Control Systems and Science, Bucharest, Romania, 149-154, 2015.

[80] Wang, X.-F.; Li, X.; Wang, J.-H.; Fang, X.-K.; Zhu, X.-F. (2016). Data-driven model-free adaptive sliding mode control for the multi degree-of-freedom robotic exoskeleton, Information Sciences, 327, 246-257, 2016.

[81] Wang, Z.H.; Liu, Z.; Chen, C.L.P.; Zhang, Y. (2019). Fuzzy adaptive compensation control of uncertain stochastic nonlinear systems with actuator failures and input hysteresis, IEEE Transactions on Cybernetics, 49(1), 2-13, 2019.

[82] Wu, H.-N.; Wang, J.-W.; Li, H.-X. (2012). Design of distributed H fuzzy controllers with constraint for nonlinear hyperbolic PDE systems, Automatica, 48(10), 2535-2543, 2012.

[83] Yang, X.Z.; Lam, H.-K.; Wu, L.G. (2019). Membership-dependent stability conditions for type-1 and interval type-2 T-S fuzzy systems, Fuzzy Sets and Systems, 356, 44-62, 2019.

[84] Yu, W.; Wang, R.; Bu, X.-H.; Hou, Z.-S. (2020). Model free adaptive control for a class of nonlinear systems with fading measurements, Journal of The Franklin Institute, 357(12), 7743- 7760, 2020.

[85] Zamanipour, M. (2020). A novelty in Blahut-Arimoto type algorithms: Optimal control over noisy communication channels, IEEE Transactions on Vehicular Technology, 69(6), 6348-6358, 2020.

[86] Zapata, H.; Perozo, N.; Angulo, W.; Contreras, J. (2020). A hybrid swarm algorithm for collective construction of 3D structures, International Journal of Artificial Intelligence, 18(1), 1-18, 2020.

[87] Zeng, G.-Q.; Xie, X.-Q.; Chen, M.-R.; Weng, J. (2019). Adaptive population extremal optimization-based PID neural network for multivariable nonlinear control systems, Swarm and Evolutionary Computation, 44, 320-334, 2019.

[88] Zhang, Y.; Wang, G.-G.; Li, K.-Q.; Yeh, W.-C., Jian, M.-W.; Dong, J.-Y. (2020). Enhancing MOEA/D with information feedback models for large-scale many-objective optimization, Information Sciences, 522, 1-16, 2020.
How to Cite
PRECUP, Radu-Emil et al. Data-Driven Model-Free Sliding Mode and Fuzzy Control with Experimental Validation. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 16, n. 1, oct. 2020. ISSN 1841-9844. Available at: <>. Date accessed: 04 mar. 2021. doi: