Balkan Journal of Electrical and Computer Engineering 2147-284X 2147-284X MUSA YILMAZ 10.17694/bajece.492482 Engineering Mühendislik Fuzzy Variable Order Extremum-Seeking Controller Design for Mobile Robots https://orcid.org/0000-0001-6443-9600 Atan Ozkan MÜHENDİSLİK FAKÜLTESİ 01 31 2019 7 1 81 87 12 08 2018 01 31 2019 Copyright © 2013, Balkan Journal of Electrical and Computer Engineering 2013 Balkan Journal of Electrical and Computer Engineering

In this paper, we aredesigned a fuzzy variable order extremum-seeking control (FVO-ESC) system for amobile robot. Fractional order controllers have advantages in the control ofnonlinear systems such as a wider area of stability and performance enhancementin the presence of noise. The main proposal of the paper is to increase theperformance of the fractional order controller. So a variable order controllerwas designed for a mobile robot, and a fuzzy logic controller was designedaccording to user experiences to tune the controller order. The proposedFVO-ESC approach has been validated the effects on nonlinear systems such asthe mobile robot system. It has been put forward in the preliminaryinvestigation that the order of the fractional order ESC controller affects theovershoot and time to reach the target. The results suggested that avariable-level controller would have better performance. The results show thatthe proposed FVO-ESC control approach provides optimum performance for mobile robotsystems.

 Mobile robots Variable Order Systems Extremum-Seeking Control. [1] D. Carnevale, A. Astolfi, C. Centioli, S. Podda, V. Vitale, and L. Zaccarian, “A new extremum seeking technique and its application to maximize RF heating on FTU,” Fusion Eng. Des., vol. 84, no. 2–6, pp. 554–558, Jun. 2009. [2] Y. Ou et al., “Design and simulation of extremum-seeking open-loop optimal control of current profile in the DIII-D tokamak,” Plasma Phys. Control. Fusion, vol. 50, no. 11, p. 115001, Nov. 2008. [3] U. Ciri, M. A. Rotea, and S. Leonardi, “Model-free control of wind farms: A comparative study between individual and coordinated extremum seeking,” Renew. Energy, vol. 113, pp. 1033–1045, 2017. [4] B. Hu, Y. Li, B. Mu, S. Wang, J. E. Seem, and F. Cao, “Extremum seeking control for efficient operation of hybrid ground source heat pump system,” Renew. Energy, vol. 86, pp. 332–346, 2016. [5] N. Bizon, “Global Maximum Power Point Tracking (GMPPT) of Photovoltaic array using the Extremum Seeking Control (ESC): A review and a new GMPPT ESC scheme,” Renew. Sustain. Energy Rev., vol. 57, pp. 524–539, 2016. [6] H. C. Lee, S. Kim, J. P. Heo, D. H. Kim, and J. Lee, “Wiener Model and Extremum Seeking Control for a CO Preferential Oxidation Reactor with the CuO-CeO2 catalyst,” IFAC-PapersOnLine, vol. 48, no. 8, pp. 574–579, 2015. [7] G. Lara-Cisneros, R. Aguilar-López, and R. Femat, “On the dynamic optimization of methane production in anaerobic digestion via extremum-seeking control approach,” Comput. Chem. Eng., vol. 75, pp. 49–59, 2015. [8] D. Krishnamoorthy, A. Pavlov, and Q. Li, “Robust Extremum Seeking Control with application to Gas Lifted Oil Wells,” IFAC-PapersOnLine, vol. 49, no. 13, pp. 205–210, 2016. [9] P. Cougnon, D. Dochain, M. Guay, and M. Perrier, “On-line optimization of fed-batch bioreactors by adaptive extremum seeking control,” IFAC Proc. Vol., vol. 43, no. 6, pp. 108–113, 2010. [10] M. Titica, D. Dochain, and M. Guay, “Real-Time Optimization of Fed-Batch Bioreactors via Adaptive Extremum-Seeking Control,” Chem. Eng. Res. Des., vol. 81, no. 9, pp. 1289–1295, 2003. [11] P. Cougnon, D. Dochain, M. Guay, and M. Perrier, “On-line optimization of fedbatch bioreactors by adaptive extremum seeking control,” J. Process Control, vol. 21, no. 10, pp. 1526–1532, 2011. [12] A. Vargas, J. A. Moreno, and A. Vande Wouwer, “Super-twisting estimation of a virtual output for extremum-seeking output feedback control of bioreactors,” J. Process Control, vol. 35, pp. 41–49, 2015. [13] O. Trollberg and E. W. Jacobsen, “Greedy Extremum Seeking Control with Applications to Biochemical Processes,” IFAC-PapersOnLine, vol. 49, no. 7, pp. 109–114, 2016. [14] Y. Zhang, O. Makarenkov, and N. Gans, “Extremum seeking control of a nonholonomic system with sensor constraints,” 2016. [15] V. Koropouli, A. Gusrialdi, S. Hirche, and D. Lee, “An extremum-seeking control approach for constrained robotic motion tasks,” Control Eng. Pract., vol. 52, pp. 1–14, 2016. [16] A. S. Matveev, M. C. Hoy, and A. V. Savkin, “3D environmental extremum seeking navigation of a nonholonomic mobile robot,” Automatica, vol. 50, no. 7, pp. 1802–1815, 2014. [17] Y. Tian, N. Sarkar, Y. Tian, and N. Sarkar, “Control of a Mobile Robot Subject to Wheel Slip,” J Intell Robot Syst, vol. 74, pp. 915–929, 2014. [18] C. Li, Z. Qu, and M. A. Weitnauer, “Distributed extremum seeking and formation control for nonholonomic mobile network,” Syst. Control Lett., vol. 75, pp. 27–34, 2015. [19] K. T. Atta, A. Johansson, and T. Gustafsson, “On the stability analysis of phasor and classic extremum seeking control,” Syst. Control Lett., vol. 91, pp. 55–62, 2016. [20] P. Thounthong, M. Raducu, and L. M. Constantinescu, “Designing and modelling of the asymptotic perturbed extremum seeking control scheme for tracking the global extreme,” Int. J. Hydrogen Energy, vol. 42, no. 28, pp. 17632–17644, 2017. [21] L. Wang, S. Chen, and K. Ma, “On stability and application of extremum seeking control without steady-state oscillation,” Automatica, vol. 68, pp. 18–26, 2016. [22] M. Guay and D. Dochain, “A time-varying extremum-seeking control approach,” Automatica, vol. 51, pp. 356–363, Jan. 2015. [23] D. Nešić, “Extremum Seeking Control: Convergence Analysis,” Eur. J. Control, vol. 15, no. 3–4, pp. 331–347, Jan. 2009. [24] C. Hong and K. Li, “Swarm intelligence-based extremum seeking control,” Expert Syst. Appl., vol. 38, no. 12, pp. 14852–14860, Nov. 2011. [25] M. Haring, N. van de Wouw, and D. Nešić, “Extremum-seeking control for nonlinear systems with periodic steady-state outputs,” 2013. [26] C. Yin, B. Stark, and S. Zhong, “Adaptive minimum energy cognitive lighting control: Integer order vs fractional order strategies in sliding mode based extremum seeking,” Mechatronics, vol. 23, no. 7, pp. 863–872, 2013. [27] K. T. Atta, A. Johansson, and T. Gustafsson, “Extremum seeking control based on phasor estimation,” Syst. Control Lett., vol. 85, pp. 37–45, 2015. [28] S. Z. Khong, D. Nešić, and M. Krstić, “Iterative learning control based on extremum seeking,” 2016. [29] B. Mu, Y. Li, J. M. House, and T. I. Salsbury, “Experimental evaluation of anti-windup extremum seeking control for airside economizers,” Control Eng. Pract., vol. 50, pp. 37–47, 2016. [30] C. Yin, S. Dadras, X. Huang, J. Mei, H. Malek, and Y. Cheng, “Energy-saving control strategy for lighting system based on multivariate extremum seeking with Newton algorithm,” Energy Convers. Manag., vol. 142, pp. 504–522, 2017. [31] H. Malek and Y. Chen, “Fractional Order Extremum Seeking Control: Performance and Stability Analysis,” IEEE/ASME Trans. Mechatronics, vol. 21, no. 3, pp. 1620–1628, Jun. 2016. [32] H. Malek, S. Dadras, and Y. Chen, “Performance analysis of fractional order extremum seeking control,” ISA Trans., vol. 63, pp. 281–287, 2016. [33] C. A. Monje, Y. Chen, B. M. Vinagre, D. Xue, and V. Feliu, Fractional-order Systems and Controls. London: Springer London, 2010. [34] S. E. Hamamci, “An Algorithm for Stabilization of Fractional-Order Time Delay Systems Using Fractional-Order PID Controllers,” IEEE Trans. Automat. Contr., vol. 52, no. 10, pp. 1964–1969, Oct. 2007. [35] Y. Chen, I. Petras, and D. Xue, “Fractional order control - A tutorial,” in 2009 American Control Conference, 2009, pp. 1397–1411. [36] M. Beschi, F. Padula, and A. Visioli, “The generalised isodamping approach for robust fractional PID controllers design,” Int. J. Control, vol. 90, no. 6, pp. 1157–1164, Jun. 2017. [37] A. Biswas, S. Das, A. Abraham, and S. Dasgupta, “Design of fractional-order PIλDμ controllers with an improved differential evolution,” Eng. Appl. Artif. Intell., vol. 22, no. 2, pp. 343–350, Mar. 2009. [38] O. Atan, M. Turk, and R. Tuntas, “Fractional Order Controller Design for Fractional Order Chaotic Synchronization,” Int. J. Nat. Eng. Sci., vol. 7, no. 1, pp. 71–77, 2013. [39] V. Haji Haji and C. A. Monje, “Fractional order fuzzy-PID control of a combined cycle power plant using Particle Swarm Optimization algorithm with an improved dynamic parameters selection,” Appl. Soft Comput., vol. 58, pp. 256–264, Sep. 2017. [40] I. Pan and S. Das, “Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO,” ISA Trans., vol. 62, pp. 19–29, May 2016. [41] H. Senberber and A. Bagis, “Fractional PID controller design for fractional order systems using ABC algorithm,” in 2017 Electronics, 2017, pp. 1–7. [42] L. Liu, F. Pan, and D. Xue, “Variable-order fuzzy fractional PID controller,” ISA Trans., vol. 55, pp. 227–233, Mar. 2015. [43] S. Ma, Y. Xu, and W. Yue, “Numerical Solutions of a Variable-Order Fractional Financial System,” J. Appl. Math., vol. 2012, pp. 1–14, Sep. 2012. [44] I. Podlubny, Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Academic Press, 1999. [45] S. M. Miller and R. Bertram, An Introduction to the Fractional Calculus and Fractional Differential EquationsNo Title. USA: Wiley, 1993. [46] S. Ma, Y. Xu, and W. Yue, “Numerical Solutions of a Variable-Order Fractional Financial System,” J. Appl. Math., vol. 2012, pp. 1–14, 2012. [47] D. Sierociuk and M. Macias, “Comparison of variable fractional order PID controller for different types of variable order derivatives,” in Proceedings of the 14th International Carpathian Control Conference (ICCC), 2013, pp. 334–339. [48] P. Ostalczyk, D. Brzezinski, P. Duch, M. Łaski, and D. Sankowski, “The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control,” Open Phys., vol. 11, no. 6, pp. 750–759, Jan. 2013. [49] P. Ostalczyk, “Variable-, fractional-order discrete PID controllers,” in 2012 17th International Conference on Methods & Models in Automation & Robotics (MMAR), 2012, pp. 534–539. [50] A. Razminia, A. F. Dizaji, and V. J. Majd, “Solution existence for non-autonomous variable-order fractional differential equations,” Math. Comput. Model., vol. 55, no. 3–4, pp. 1106–1117, Feb. 2012. [51] Q. Zheng and Z. Gao, 2010 29th Chinese Control Conference. I E E E, 2010. [52] K. B. Ariyur and M. Krstić, Real-Time Optimization by Extremum-Seeking Control, vol. 0, no. 0. 2003. [53] M. Krstiã, “Performance improvement and limitations in extremum seeking control,” Syst. Control Lett., vol. 39, pp. 313–326, 2000. [54] Y. Li, S. Sui, and S. Tong, “Adaptive Fuzzy Control Design for Stochastic Nonlinear Switched Systems With Arbitrary Switchings and Unmodeled Dynamics,” IEEE Trans. Cybern., pp. 1–12, 2016. [55] A. Boulkroune, “A fuzzy adaptive control approach for nonlinear systems with unknown control gain sign,” Neurocomputing, vol. 179, pp. 318–325, Feb. 2016.