Recently, a robust controller has been proposed to be used in control of plants with large uncertainty in location of one of their poles. By using this controller, not only the phase margin and gain crossover frequency are adjustable for the nominal case but also the phase margin remains constant, notwithstanding the variations in location of the uncertain pole of the plant. In this paper, the tuning rule of the aforementioned controller is extended such that it can be applied in control of plants modeled by fractional order models. Numerical examples are provided to show the effectiveness of the tuned controller.
Issue Section:
Technical Brief
Keywords:
Stability
References
1.
Monje
, C. A.
, Chen
, Y. Q.
, Vinagre
, B. M.
, Xue
, D.
, and Feliu
, V.
, 2010
, Fractional-order Systems and Controls–Fundamentals and Applications (Advanced Industrial Control Series)
, Springer-Verlag
, London, UK.2.
Caponetto
, R.
, Dongola
, G.
, Fortuna
, L.
, and Petras
, I.
, 2010
, Fractional Order Systems: Modeling and Control Applications
, World Scientific
, Singapore.3.
Rekanos
, I. T.
, and Yioultsis
, T. V.
, 2014
, “Approximation of Grünwald–Letnikov Fractional Derivative for FDTD Modeling of Cole–Cole Media
,” IEEE Trans. Magn.
, 50
(2
), pp. 181
–184
.10.1109/TMAG.2013.22819984.
Mescia
, L.
, Bia
, P.
, and Caratelli
, D.
, 2014
, “Fractional Derivative Based FDTD Modeling of Transient Wave Propagation in Havriliak–Negami Media
,” IEEE Trans. Microwave Theory Tech.
, 62
(9
), pp. 1920
–1929
.10.1109/TMTT.2014.23272025.
Beaulieu
, A.
, Bosse
, D.
, Micheau
, P.
, Avoine
, O.
, Praud
, J.
, and Walti
, H.
, 2012
, “Measurement of Fractional Order Model Parameters of Respiratory Mechanical Impedance in Total Liquid Ventilation
,” IEEE Trans. Biomed. Eng.
, 59
(2
), pp. 323
–331
.10.1109/TBME.2011.21692576.
Podlubny
, I.
, 1999
, “Fractional-Order Systems and PIλDμ-Controllers
,” IEEE Trans. Autom. Control
, 44
(1
), pp. 208
–214
.10.1109/9.7391447.
Tavazoei
, M. S.
, and Tavakoli-Kakhki
, M.
, 2014
, “Compensation by Fractional-Order Phase-Lead/Lag Compensators
,” IET Control Theory Appl.
, 8
(5
), pp. 319
–329
.10.1049/iet-cta.2013.01388.
Oustaloup
, A.
, 2006
, “The CRONE Approach: Theoretical Developments and Major Applications
,” Proceedings of the Second IFAC Workshop on Fractional Differentiation and Its Applications
, Porto, Portugal
, pp. 39
–69
.9.
Vinagre
, B. M.
, and Feliu
, V.
, 2007
, “Optimal Fractional Controllers for Rational Order Systems: A Special Case of the Wiener-Hopf Spectral Factorization Method
,” IEEE Trans. Autom. Control
, 52
(12
), pp. 2385
–2389
.10.1109/TAC.2007.91072810.
Djennoune
, S.
, and Bettayeb
, M.
, 2013
, “Optimal Synergetic Control for Fractional-Order Systems
,” Automatica
, 49
(7
), pp. 2243
–2249
.10.1016/j.automatica.2013.04.00711.
Yin
, C.
, Chen
, Y.
, and Zhong
, S. M.
, 2014, “Fractional-Order Sliding Mode Based Extremum Seeking Control of a Class of Nonlinear Systems
,” Automatica, 50
(12
), pp. 3173
–3181
.12.
Pisano
, A.
, Rapaić
, M. R.
, Jeličić
, Z. D.
, and Usai
, E.
, 2010
, “Sliding Mode Control Approaches to the Robust Regulation of Linear Multivariable Fractional-Order Dynamics
,” Int. J. Rob. Nonlinear Control
, 20
(18
), pp. 2045
–2056
.10.1002/rnc.156513.
Charef
, A.
, Assabaa
, M.
, Ladaci
, S.
, and Loiseau
, J. J.
, 2013
, “Fractional Order Adaptive Controller for Stabilised Systems Via High-Gain Feedback
,” IET Control Theory Appl.
, 7
(6
), pp. 822
–828
.10.1049/iet-cta.2012.030914.
Monje
, C. A.
, Vinagre
, B. M.
, Feliu
, V.
, and Chen
, Y. Q.
, 2008
, “Tuning and Auto-Tuning of Fractional Order Controllers for Industry Applications
,” Control Eng. Pract.
, 16
(7
), pp. 798
–812
.10.1016/j.conengprac.2007.08.00615.
Yeroglu
, C.
, and Tan
, N.
, 2011
, “Note on Fractional-Order Proportional-Integral-Differential Controller Design
,” IET Control Theory Appl.
, 5
(17
), pp. 1978
–1989
.10.1049/iet-cta.2010.074616.
Monje
, C. A.
, Calderon
, A. J.
, Vinagre
, B. M.
, Chen
, Y.
, and Feliu
, V.
, 2004
, “On Fractional PIλ Controllers: Some Tuning Rules for Robustness to Plant Uncertainties
,” Nonlinear Dyn.
, 38
(1–4
), pp. 369
–381
.10.1007/s11071-004-3767-317.
Chen
, Y.
, Bhaskaran
, T.
, and Xue
, D.
, 2008
, “Practical Tuning Rule Development for Fractional Order Proportional and Integral Controllers
,” ASME J. Comput. Nonlinear Dyn.
, 3
(2
), p. 021403
.10.1115/1.283393418.
Chao
, H.
, Luo
, Y.
, Di
, L.
, and Chen
, Y. Q.
, 2010
, “Roll-Channel Fractional Order Controller Design for a Small Fixed-Wing Unmanned Aerial Vehicle
,” Control Eng. Pract.
, 18
(7
), pp. 761
–772
.10.1016/j.conengprac.2010.02.00319.
Li
, H.
, Luo
, Y.
, and Chen
, Y. Q.
, 2010
, “A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments
,” Control Syst. Technol., IEEE Trans.
, 18
(2
), pp. 516
–520
.10.1109/TCST.2009.201912020.
Tavazoei
, M. S.
, Haeri
, M.
, Jafari
, S.
, Bolouki
, S.
, and Siami
, M.
, 2008
, “Some Applications of Fractional Calculus in Suppression of Chaotic Oscillations
,” IEEE Trans. Ind. Electron.
, 55
(11
), pp. 4094
–4101
.10.1109/TIE.2008.92577421.
Calderon
, A. J.
, Vinagre
, B. M.
, and Feliu
, V.
, 2006
, “Fractional Order Control Strategies for Power Electronic Buck Converters
,” Signal Process.
, 86
(10
), pp. 2803
–2819
.10.1016/j.sigpro.2006.02.02222.
Efe
, M. O.
, 2008
, “Fractional Fuzzy Adaptive Sliding-Mode Control of a 2-DOF Direct-Drive Robot Arm
,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern.
, 38
(6
), pp. 1561
–1570
.10.1109/TSMCB.2008.92822723.
Efe
, M. O.
, 2011
, “Fractional Order Systems in Industrial Automation—A Survey
,” IEEE Trans. Ind. Inf.
, 7
(4
), pp. 582
–591
.10.1109/TII.2011.216677524.
Corradini
, M. L.
, Giambò
, R.
, and Pettinari
, S.
, 2014
, “On the Adoption of a Fractional-Order Sliding Surface for the Robust Control of Integer-Order LTI Plants
,” Automatica
, 51
, pp. 364
–371
.25.
Lan
, Y. H.
, and Zhou
, Y.
, 2013
, “Non-Fragile Observer-Based Robust Control for a Class of Fractional-Order Nonlinear Systems
,” Syst. Control Lett.
, 62
(12
), pp. 1143
–1150
.10.1016/j.sysconle.2013.09.00726.
Luo
, Y.
, Chen
, Y.
, Ahn
, H. S.
, and Pi
, Y.
, 2010
, “Fractional Order Robust Control for Cogging Effect Compensation in PMSM Position Servo Systems: Stability Analysis and Experiments
,” Control Eng. Pract.
, 18
(9
), pp. 1022
–1036
.10.1016/j.conengprac.2010.05.00527.
Badri
, V.
, and Tavazoei
, M. S.
, 2013
, “On Tuning Fractional Order [Proportional–Derivative] Controllers for a Class of Fractional Order Systems
,” Automatica
, 49
(7
), pp. 2297
–2301
.10.1016/j.automatica.2013.04.02628.
Luo
, Y.
, and Chen
, Y. Q.
, 2009
, “Fractional Order [Proportional Derivative] Controller for a Class of Fractional Order Systems
,” Automatica
, 45
(10
), pp. 2446
–2450
.10.1016/j.automatica.2009.06.02229.
Luo
, Y.
, Chen
, Y. Q.
, Wang
, C. Y.
, and Pi
, Y. G.
, 2010
, “Tuning Fractional Order Proportional Integral Controllers for Fractional Order Systems
,” J. Process Control
, 20
(7
), pp. 823
–831
.10.1016/j.jprocont.2010.04.01130.
Luo
, Y.
, and Chen
, Y. Q.
, 2012
, “Stabilizing and Robust Fractional Order PI Controller Synthesis for First Order Plus Time Delay Systems
,” Automatica
, 48
(9
), pp. 2159
–2167
.10.1016/j.automatica.2012.05.07231.
Luo
, Y.
, Zhang
, T.
, Lee
, B.
, Kang
, C.
, and Chen
, Y.
, 2014
, “Fractional-Order Proportional Derivative Controller Synthesis and Implementation for Hard-Disk-Drive Servo System
,” IEEE Trans. Control Syst. Technol.
, 22
(1
), pp. 281
–289
.10.1109/TCST.2013.223911132.
Chen
, Y. Q.
, and Moore
, K. L.
, 2005
, “Relay Feedback Tuning of Robust PID Controllers With Iso-Damping Property
,” IEEE Trans. Syst., Man, Cybern.-Part B: Cybern.
, 35
(1
), pp. 23
–31
.10.1109/TSMCB.2004.83795033.
Barbosa
, R. S.
, Tenreiro Machado
, J. A.
, and Ferreira
, I. M.
, 2004
, “Tuning of PID Controllers Based on Bode's Ideal Transfer Function
,” Nonlinear Dyn.
, 38
(1–4
), pp. 305
–321
.10.1007/s11071-004-3763-734.
Jin
, Y.
, Chen
, Y. Q.
, and Xue
, D.
, 2011
, “Time-Constant Robust Analysis of a Fractional Order [Proportional Derivative] Controller
,” IET Control Theory Appl.
, 5
(1
), pp. 164
–172
.10.1049/iet-cta.2009.054335.
Feliu-Batlle
, V.
, and Castillo-García
, F. J.
, 2014
, “On the Robust Control of Stable Minimum Phase Plants With Large Uncertainty in a Time Constant, A Fractional-Order Control Approach
,” Automatica
, 50
(1
), pp. 218
–224
.10.1016/j.automatica.2013.10.00236.
Petras
, I.
, Chen
, Y. Q.
, Vinagre
, B. M.
, and Podlubny
, I.
, 2004
, “Stability of Linear Time Invariant Systems With Interval Fractional Orders and Interval Coefficients
,” IEEE International Conference on Computational Cybernetics (ICCC)
, pp. 341
–346
.37.
Galvão
, R. K. H.
, Hadjiloucas
, S.
, Kienitz
, K. H.
, Paiva
, H. M.
, and Afonso
, R. J. M.
, 2013
, “Fractional Order Modeling of Large Three-Dimensional RC Networks
,” IEEE Trans. Circuits Syst. I: Regular Papers
, 60
(3
), pp. 624
–637
.10.1109/TCSI.2012.220973338.
Gabano
, J. D.
, and Poinot
, T.
, 2011
, “Fractional Modeling and Identification of Thermal Systems
,” Signal Process.
, 91
(3
), pp. 531
–541
.10.1016/j.sigpro.2010.02.00539.
Narayanaswamy
, P. N.
, Kanthabhabha
, P.
, and Hamamci
, S. E.
, 2010
, “Fractional Order PIλ Control Strategy for a Liquid Level System
,” IEEE Second World Congress on Nature and Biologically Inspired Computing (NaBIC)
, pp. 121
–126
.10.1109/NABIC.2010.571634540.
Bonnet
, C.
, and Partington
, J. R.
, 2000
, “Coprime Factorizations and Stability of Fractional Differential Systems
,” Syst. Control Lett.
, 41
(3
), pp. 167
–174
.10.1016/S0167-6911(00)00050-541.
Tavazoei
, M. S.
, 2013
, “On Type Number Concept in Fractional-Order Systems
,” Automatica
, 49
(1
), pp. 301
–304
.10.1016/j.automatica.2012.09.02242.
Mansouri
, R.
, Bettayeb
, M.
, Djamah
, T.
, and Djennoune
, S.
, 2008
, “Vector Fitting Fractional System Identification Using Particle Swarm Optimization
,” Appl. Math. Comput.
, 206
(2
), pp. 510
–520
.10.1016/j.amc.2008.05.146Copyright © 2015 by ASME
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