İbrahim EKSİN, Müjde GÜZELKAYA, Erhan YUMUK

Application of fractional order PI controllers on a magnetic levitation system

Fractional order PI controllers based on two different analytical design methods are applied to a magnetic levitation system in this paper. The controller parameters are specified in order to fulfill specific frequency criteria. The first design method utilizes a unity feedback reference model whose forward path includes Bode’s ideal loop transfer function. The second method uses the reference model that has been obtained via delayed Bode’s ideal loop transfer function. The achievement of these two controllers are contrasted with each other on the magnetic levitation system using various criteria.

PDF

___

[1] Azarmi R, Tavakoli-Kakhki M, Sedigh, AK, Fatehi, A. Analytical design of fractional order PID controllers based on the fractional set-point weighted structure: Case study in twin rotor helicopter. Mechatronics 2015; 31: 376-388.
[2] Yumuk E, Guzelkaya M, Eksin I. Design of an integer order proportional–integral/proportional–integral–derivative controller based on model parameters of a certain class of fractional order systems. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 2019; 233; 3: 320-334.
[3] Saleem A, Soliman H, Al-Ratrout S, Mesbah M. Design of a fractional order PID controller with application to an induction motor drive. Turkish Journal of Electrical Engineering & Computer Sciences 2018; 26; 5: 2768-2778.
[4] Visioli A, Padula F. Tuning rules for optimal PID and fractional order PID controllers. Journal of Process Control 2011; 21: 69-81.
[5] Kurucu MC, Yumuk E, Güzelkaya M, Eksin İ. Investigation of the effects of fractional and integer order fuzzy logic PID controllers on system performances. In: IEEE 10th International Conference on Electrical and Electronics Engineering (ELECO); 2017; Bursa, Turkey. pp. 775-779.
[6] Kumar MR, Deepak V, Ghosh S. Fractional-order controller design in frequency domain using an improved nonlinear adaptive seeker optimization algorithm. Turkish Journal of Electrical Engineering & Computer Sciences 2017; 25; 5: 4299-4310.
[7] Titouche K, Mansouri R, Bettayeb M, Al-Saggaf UM. Internal model control–proportional integral derivative– Fractional-order filter controllers design for unstable delay systems. Journal of Dynamic Systems, Measurement, and Control 2016; 138; 2: 021006.
[8] Bettayeb M, Mansouri R. Fractional IMC-PID-filter controllers design for non-integer order systems. Journal of Process Control 2014; 24: 261-271.
[9] Yumuk E, Güzelkaya M, Eksin İ. Analytical fractional PID controller design based on Bode’s ideal transfer function plus time delay. ISA Transactions 2019; 91: 196-206.
10] Skogestad S. Simple analytic rules for model reduction and PID controller tuning. Journal of Process Control 2003; 13; 4: 291-309.
[11] Malek H, Luo Y, Chen YQ. Identification and tuning fractional order proportional integral controllers for time delayed system with a fractional pole. Mechatronics 2013; 23: 746-754.
[12] Yumuk E, Güzelkaya M, Eksin İ. Fractional and integer models of a ball balancing table system based on its frequency domain response. In: 8th International Conference on Advanced Technologies (ICAT’19); Sarajevo, Bosnia Herzegovina; 2019. pp. 1-6.
[13] Das S, Saha S, Das S, Gupta A. On the selection of tuning methodology of FOPID controllers for the control of higher order processes. ISA Transactions 2011; 50; 3: 376-388.
[14] Monje CA, Vinagre BM, Feliu V, Chen YQ. Tuning and auto-tuning of fractional order controllers for industry applications. Control Engineering Practice 2008; 16: 798-812.
[15] Luo Y, Chen Y. Fractional order [proportional derivative] controller for a class of fractional order systems. Auto- matica 2009; 45; 10: 2446-2450.
[16] Muresan CI, Ionescu C, Folea S, De Keyser, R. Fractional order control of unstable processes: the magnetic levitation study case. Nonlinear Dynamics 2015; 80; 4: 1761-1772.
[17] Kim KB, Im SH, Um DY, Park GS. Comparison of magnetic levitation systems using ring-shaped permanent magnets. IEEE Transactions on Magnetics, 2019; 55; 7: 1-4.
[18] de Jesús Rubio J, Zhang L, Lughofer E, Cruz P, Alsaedi A, Hayat T. Modeling and control with neural networks for a magnetic levitation system. Neurocomputing 2017; 227: 113-121.
[19] Maji D, Biswas M, Bhattacharya A, Sarkar G, Mondal TK et al. Maglev system modeling and LQR controller design in real time simulation. In: 2016 International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET); New York, USA; 2016. pp. 1562-1567.
[20] Stettinger G, Benedikt M, Horn M, Zehetner J, Giebenhain C. Control of a magnetic levitation system with communication imperfections: A model-based coupling approach. Control Engineering Practice 2017; 58: 161-170.
[21] He G, Li J, Cui P. Nonlinear control scheme for the levitation module of maglev train. Journal of Dynamic Systems, Measurement, and Control 2016; 138; 7: 074503.
[22] Bode HW. Network analysis and feedback amplifier design. United States of America: van Nostrand, 1945.
[23] Barbosa RS, Machado JT, Ferreira IM. Tuning of PID controllers based on Bode’s ideal transfer function. Nonlinear Dynamics 2004; 38; 1-4: 305-321.
[24] Quanser Inc. Magnetic levitation experiment (User manual). 2008.
[25] Tepljakov A, Petlenkov E, Belikov J. FOMCOM: a MATLAB toolbox for fractional-order system identification and control. International Journal of Microelectronics and Computer Science 2011; 2; 2: 51-62