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Volume 6 Issue 5
Sep.  2019

IEEE/CAA Journal of Automatica Sinica

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Vahid Badri and Mohammad Saleh Tavazoei, "On Time-Constant Robust Tuning of Fractional Order [Proportional Derivative] Controllers," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1179-1186, Sept. 2019. doi: 10.1109/JAS.2017.7510667
Citation: Vahid Badri and Mohammad Saleh Tavazoei, "On Time-Constant Robust Tuning of Fractional Order [Proportional Derivative] Controllers," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1179-1186, Sept. 2019. doi: 10.1109/JAS.2017.7510667

On Time-Constant Robust Tuning of Fractional Order [Proportional Derivative] Controllers

doi: 10.1109/JAS.2017.7510667
Funds:  This work was supported by the Iran National Science Foundation (INSF)
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  • This paper deals with analyzing a newly introduced method for tuning of fractional order [proportional derivative] (FO[PD]) controllers to be used in motion control. By using this tuning method, not only the phase margin and gain crossover frequency are adjustable, but also robustness to variations in the plant time-constant is guaranteed. Conditions on the values of control specifications (desired phase margin and gain crossover frequency) for solution existence in this tuning method are found. Also, the number of solutions is analytically determined in this study. Moreover, experimental verifications are presented to indicate the applicability of the obtained results.

     

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  • [1]
    D. Cafagna, "Fractional calculus: a mathematical tool from the past for present engineers, " IEEE Industrial Electronics Magazine, pp. 35-40, 2007.
    [2]
    C. Ma, Y. Hori, "Fractional-order control: theory and applications in motion control, " IEEE Industrial Electronics Magazine, vol. 1, no. 4, pp. 6-16, 2007. doi: 10.1109/MIE.2007.909703
    [3]
    M. Cugnet, J. Sabatier, S. Laruelle, S. Grugeon, B. Sahut, A. Oustaloup, J.M. Tarascon, "On lead-acid-battery resistance and cranking-capability estimation, " IEEE Transactions on Industrial Electronics, vol. 57, no. 3, pp. 909-917, 2010. doi: 10.1109/TIE.2009.2036643
    [4]
    M. Branciforte, A. Meli, G. Muscato, D. Porto, "ANN and non-integer order modeling of ABS solenoid valves, " IEEE Transactions on Control Systems Technology, vol. 19, no. 3, pp. 628-635, 2011. doi: 10.1109/TCST.2010.2049999
    [5]
    A. Narang, S.L. Shah, T. Chen: "Continuous-time model identification of fractional-order models with time delays, " IET Control Theory & Applications, vol. 5, no. 7, pp. 900-912, 2010.
    [6]
    M. R. Rapaic, A. Pisano, "Variable-order fractional operators for adaptive order and parameter estimation, " IEEE Transactions on Automatic Control, vol. 59, no. 3, pp. 798-803, 2014. doi: 10.1109/TAC.2013.2278136
    [7]
    M. S. Tavazoei, "From traditional to fractional PI control: a key for generalization, " IEEE Industrial Electronics Magazine, vol. 6, no. 3, pp. 41-51, 2012. doi: 10.1109/MIE.2012.2207818
    [8]
    M. O. Efe, "Fractional order systems in industrial automation-a survey, " IEEE Transactions on Industrial Informatics, vol. 7, no. 4, pp. 582-591, 2011. doi: 10.1109/TII.2011.2166775
    [9]
    Y. Luo, T. Zhang, B. Lee, V. Kang, Y. Q. Chen, "Fractional-order proportional derivative controller synthesis and implementation for hard-disk-drive servo system, " IEEE Transactions on Control Systems Technology, vol. 22, no. 1, pp. 281-289, 2014. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=324f0da88edac4578d502230f52ecd0d
    [10]
    M. S. Tavazoei, M. Haeri, S. Jafari, S. Bolouki, M. Siami, "Some applications of fractional calculus in suppression of chaotic oscillations, " IEEE Transactions on Industrial Electronics, vol. 55, no. 11, pp. 4094-4101, 2008. doi: 10.1109/TIE.2008.925774
    [11]
    Z. X. Zou, K. Zhou, Z. Wang, M. Cheng, "Frequency-Adaptive fractional-order repetitive control of shunt active power filters, " IEEE Transactions on Industrial Electronics, vol. 62, no. 3, pp. 1659-1668, 2015. doi: 10.1109/TIE.2014.2363442
    [12]
    C. Yeroglu, N. Tan, "Note on fractional-order proportional-integral-differential controller design, " IET Control Theory & Applications, vol. 5, no. 17, pp. 1978-1989, 2011. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=dca22b013498d739cbde7dff1f22de9d
    [13]
    M. S. Tavazoei, M. Tavakoli-Kakhki, "Compensation by fractional-order phase-lead/lag compensators, " IET Control Theory & Applications, vol. 8, no. 5, pp. 319-329, 2014.
    [14]
    M. O. Efe, "Fractional fuzzy adaptive sliding-mode control of a 2-DoF direct-drive robot arm, " IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 38, no. 6, pp. 1561-1570, 2008. doi: 10.1109/TSMCB.2008.928227
    [15]
    A. Dumlu, K. Erenturk, "Trajectory tracking control for a 3-DoF parallel manipulator using fractional-order PIλDμ control, " IEEE Transactions on Industrial Electronics, vol. 61, no. 7, pp. 3417-3426, 2014. doi: 10.1109/TIE.2013.2278964
    [16]
    K. Erenturk, "Fractional-order and active disturbance rejection control of nonlinear two-mass drive system, " IEEE Transactions on Industrial Electronics, vol. 60, no. 9, pp. 3806-3813, 2013. doi: 10.1109/TIE.2012.2207660
    [17]
    Y. Jin, Y. Q. Chen, D. Xue, "Time-Constant robust analysis of a fractional order[proportional derivative] controller, " IET Control Theory & Applications, vol. 5, no. 1, pp. 164-172, 2011. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=163dd44620202a6f919ffa9393544e7a
    [18]
    H. Li, Y. Luo, Y. Q. Chen, "A fractional order proportional and derivative (FOPD) motion controller: tuning rule and experiments, " IEEE Transactions on Control Systems Technology, vol. 18, no. 2, pp. 516-520, 2010. doi: 10.1109/TCST.2009.2019120
    [19]
    Y. Luo, Y. Q. Chen, C.Y. Wang, Y.G. Pi, "Tuning fractional order proportional integral controllers for fractional order systems, " Journal of Process Control, vol. 20, no. 7, pp. 823-831, 2010. doi: 10.1016/j.jprocont.2010.04.011
    [20]
    Y. Luo, Y. Q. Chen, "Fractional order[proportional derivative] controller for a class of fractional order systems, " Automatica, vol. 45, pp. 2446-2450, 2009. doi: 10.1016/j.automatica.2009.06.022
    [21]
    V. Badri, M. S. Tavazoei, "On tuning fractional order [proportional--derivative] controllers for a class of fractional order systems, " Automatica, vol. 49, no. 7, pp. 2297-2301, 2013. doi: 10.1016/j.automatica.2013.04.026
    [22]
    V. Badri, M. S. Tavazoei, "On tuning FO[PI] controllers for FOPDT processes, " Electronics Letters, vol. 49, no. 21, pp. 1326-1328, 2013. doi: 10.1049/el.2013.2457
    [23]
    V. Badri, M. S. Tavazoei, "Fractional order control of thermal systems: achievability of frequency-domain requirements, " Nonlinear Dynamics, vol. 8, no. 4, pp. 1773-1783, 2014.
    [24]
    V. Badri, M. S. Tavazoei, "Achievable performance region for a fractional order proportional and derivative motion controller, " IEEE Transactions on Industrial Electronics, vol. 62, no. 11, pp. 7171-7180, 2015. doi: 10.1109/TIE.2015.2448691
    [25]
    V. Badri, M. S. Tavazoei, "Some analytical results on tuning fractional-order[proportional-integral] controllers for fractional-order systems, " IEEE Transactions on Control Systems Technology, vol. 24, no. 3, pp. 1059-1066, 2016. doi: 10.1109/TCST.2015.2462739
    [26]
    V. Badri, M. S. Tavazoei, "Simultaneous compensation of the gain, phase, and phase-slope, " Journal of Dynamic Systems, Measurement, and Control, vol. 138, no. 12, pp. 121002, 2016. doi: 10.1115/1.4034073
    [27]
    N. Sayyaf, M. S. Tavazoei, "Frequency Data Based Procedure to Adjust Gain and Phase Margins and Guarantee the Uniqueness of Crossover Frequencies, " IEEE Transactions on Industrial Electronics, DOI: 10.1109/TIE.2019.2905814, 2019.
    [28]
    A. A. Dastjerdi, B. M. Vinagre, Y. Q. Chen, S. H. HosseinNia, "Linear fractional order controllers; A survey in the frequency domain, " Annual Reviews in Control, vol. 47, pp. 51-70, 2019.
    [29]
    A. A. Dastjerdi, N. Saikumar, S. H. HosseinNia, "Tuning guidelines for fractional order PID controllers: Rules of thumb, " Mechatronics, vol. 56, pp. 26-36, 2018. doi: 10.1016/j.mechatronics.2018.10.004
    [30]
    V. Feliu-Batlle, F. J. Castillo-García, "On the robust control of stable minimum phase plants with large uncertainty in a time constant. A fractional-order control approach, " Automatica, vol. 50, no. 1, pp. 218-224, 2014. doi: 10.1016/j.automatica.2013.10.002
    [31]
    H. Anton, Calculus: A New Horizon, 6th ed. New York: Wiley, 1999.
    [32]
    Quanser. (2015). "Industrial mechatronic drives unit."[Online]. Available: http://www.quanser.com/products/imdu
    [33]
    Y. Q. Chen (2008). "Impulse response invariant discretization of fractional order low-pass filters."[Online]. Available: http://www.mathworks.com/matlabcentral/fileexchange/21365-impulse-response-invariant-discretization-of-fractional-order-low-pass-filters
    [34]
    Y. Wei, Q. Gao, C. Peng, Y. Wang, "A rational approximate method to fractional order systems, " International Journal of Control, Automation and Systems, vol. 12, no. 6, pp. 1180-1186, 2014. doi: 10.1007/s12555-013-0109-6
    [35]
    Y. Wei, W. T. Peter, B. Du, Y. Wang, "An innovative fixed-pole numerical approximation for fractional order systems, " ISA Transactions, vol. 62, pp. 94-102, 2016. doi: 10.1016/j.isatra.2016.01.010

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    Highlights

    • Solution existence of a recently proposed tuning method of fractional order [proportional derivative](FO[PD]) controllers is investigated.
    • The number of the solutions of the tuning method is analytically found.
    • It is shown that the tuning method can result in two distinct feasible solutions.
    • The obtained results are applied in motion control.

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