Abstract
In this paper, a design method is proposed for a robust stabilizing fractional order proportional integral derivative (FOPID) controller for One Non-Integer Order Plus Time Delay plant (NIOPTD-I). The NIOPTD-I model is obtained after reducing the higher order continuous time process model. The FOPID controller is designed by using stability boundary locus method, which satisfies user defined frequency domain specifications phase margin and the gain crossover frequency. A robust control system is designed against gain variations by achieving flat phase condition which is due to zero slope at the gain crossover frequency of the phase plot. Thus robust stabilizing FOPID controller for NIOPTD-I fractional order plant is designed. The applicability of the proposed method is illustrated with simulation example and experimental validation with the liquid level control system.
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References
Tepljakov A (2011) Fractional-order calculus based identification and control of linear dynamic systems. Department of Computer Control, Tallinn University of Technology, Tallinn
Malek H, Luo Y, Chen Y (2011) Tuning fractional order proportional integral controllers for time delayed systems with a fractional pole. In: ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, p 311–321. American Society of Mechanical Engineers
Valério D, Sá da Costa J (2005) Levys identification method extended to commensurate fractional order transfer functions. In: Fifth EUROMECH Nonlinear Dynamics Conference, p 1357–1366
Ma C, Hori Y (2004) An introduction of fractional order control and its applications in motion control. In: Proceedings of 23rd Chinese Control Conference, p 10–13. Wuxi, China
Tan N (2005) Computation of stabilizing PI and PID controllers for processes with time delay. ISA Trans 44:213–223
Monje CA, Vinagre BM, Chen Y, Feliu V, Lanusse P, Sabatier J (2009) Optimal tunings for fractional PI\(^\lambda \) D\(^\mu \) controllers. Fract Differ Appl 675–686
Podlubny I (1999) Fractional differential equations. Academic Press, San Diego
Podlubny I (1999) Fractional-order systems and \({P} {I}^\lambda {D}^\mu \)-controllers. IEEE Trans Autom Control 44(1):208–214
Petras I (1999) The fractional-order controllers: methods for their synthesis and application. J Electr Eng 50(9/10):284–288
Vinagre BM, Podlubny I, Dorcak L, Feliu V (2000) On fractional PID controllers: a frequency domain approach. In: Proceedings of IFAC Workshop on Digital Control, Past, Present and Future of PID Control. Terrasa, Spain
Das S, Saha S, Das S, Gupta A (2011) On the selection of tuning methodology of FOPID controllers for the control of higher order processes. ISA Trans 50(3):376–388
Monje CA, Calderon AJ, Vinagre BM (2004) On fractional \({P}{I}^\lambda \) controllers: some tuning rules for robustness to plant uncertainties. Nonlinear Dyn 38(1/4):369–381
Amoura K, Mansouri R, Bettayeb M, Al-Saggaf UM (2016) Closed-loop step response for tuning PID-fractional-order-filter controllers. ISA Trans. doi:10.1016/j.isatra.2016.04.017)
Hamamci SE, Tan N (2006) Design of PI controllers for achieving time and frequency domain specifications simultaneously. ISA Trans 45(4):529–543
Luo Y, Chen Y (2012) Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems. Automatica 48:2159–2167
Wang DJ, Li W, Guo ML (2013) Tuning of \({P}{I}^\lambda {D}^\mu \) controllers based on sensitivity constraint. J Process Control 23(6):861–867
Maiti D, Acharya A, Chakraborty M, Konar A, Janarthanan R (2008) Tuning PID and \(PI^\lambda D^\delta \) controllers using the integral time absolute error criterion. In: Information and Automation for Sustainability, 2008. ICIAFS 2008. 4th International Conference on, p 457–462. IEEE
Leu JF, Tsay SY, Hwang C et al (2002) Design of optimal fractional-order pid controllers. J Chin Inst Chem Eng 33(2):193–202
MATLAB: version 7.10.0 (R2010a). The MathWorks Inc., Natick, Massachusetts (2010)
Monje CA, Chen YQ, Vinagre BM, Xue D (2010) Fractional-order systems and controls. Springer, New York
Hamanci SE (2008) Stbilization using fractional-order PI and PID controllers. Nonlinear Dyn 51(1):329–343
Tan N, Kaya I, Yeroglu C, Atherton DP (2006) Computation of stabilizing PI and PID controllers using the stability boundary locus. Energy Convers Manag 47(18):3045–3058
Vu TNL, Lee M (2013) Analytical design of fractional order proportional integral controllers for time delay processes. ISA Trans 52:583–591
Yeroglu C, Tan N (2011) Classical controller design techniques for fractional order case. ISA Trans 50:461–472
Hamamci SE (2007) An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers. IEEE Trans Autom Control 52(10):1964–1969
Maione G, Lino P (2007) New tuning rules for fractional \(PI^\alpha \) controllers. Nonlinear Dyn 49(1–2):251–257
Shah P, Agashe S (2016) Review of fractional PID controller. Mechatronics 38:29–41
Hwang C, Cheng YC (2006) A numerical algorithm for stability testing of fractional delay systems. Automatica 42(5):825–831
Bongulwar MR, Patre BM (2015) Stability regions of closed loop system with one non-integer plus time delay plant by fractional order PID controller. Int J Dyn Control doi:10.1007/s40435-015-0191-0
Astrom KJ, Panagopoulos H, Hagglund T (1998) Design of PI controllers based on non-convex optimization. Automatica 34(5):585–601
Chen YQ, Tripti B, Xue D (2008) Practical tuning rule development for fractional order proportional and integral controllers. J Comput Nonlinear Dyn 3(2):021403
Panagopoulos H, Astrom KJ (2002) Design of PID controllers based on constrained optimization. IEE Proc Control Theory Appl 149:32–40
Shen JC (2002) New tuning method for PID controller. ISA Trans 41(4):473–484
Bhase SS, Patre BM (2014) Robust FOPI controller design for power control of PHWR under step-back condition. Nucl Eng Des 274:20–29
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Bongulwar, M.R., Patre, B.M. Design of FOPID controller for fractional-order plants with experimental verification. Int. J. Dynam. Control 6, 213–223 (2018). https://doi.org/10.1007/s40435-017-0305-y
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DOI: https://doi.org/10.1007/s40435-017-0305-y