This article deals with the problem of robust fractional-order fixed-structure controller design for commensurate and non-commensurate fractional-order interval systems using fractional Kharitonov theorem. The contribution of this study is to develop a simple control methodology to stabilize the fractional-order Kharitonov-defined vortex polynomials. Using the idea of robust stability testing function and extending it to the systems under study, the straightforward graphical and systematic procedures are proposed to investigate the robust stability of the system by searching for a non-conservative fractional-order Kharitonov region in the controller parameters plane. This region can establish all the fractional-order controllers that make the uncertain fractional-order systems stable. The relation between the fractional-order Kharitonov region and the parameters of the stabilizing controller is also found. Finally, comparison results with three relevant works are given to illustrate the feasibility of the proposed method.
HcheichiKBouaniF.Comparison between commensurate and non-commensurate fractional systems. Int J Adv Comput Sci Appl2018; 9: 11.
2.
OustaloupASabatierJLanusseP, et al. An overview of the CRONE approach in system analysis, modeling and identification, observation and control. IFAC Proc Vol2008; 41: 14254–14265.
3.
AytenKKÇiplakMHDumluA.Implementation a fractional-order adaptive model-based PID-type sliding mode speed control for wheeled mobile robot. Proc IMechE, Part I: J Systems and Control Engineering2019; 233: 1067–1084.
4.
YaghootiBSalariehH.Robust adaptive fractional order proportional integral derivative controller design for uncertain fractional order nonlinear systems using sliding mode control. Proc IMechE, Part I: J Systems and Control Engineering2018; 232: 550–557.
5.
MonjeCAChenYVinagreBM, et al. Fractional-order systems and controls: fundamentals and applications. New York: Springer, 2010.
6.
PetrášI.Fractional-order nonlinear systems: modeling, analysis and simulation. New York: Springer, 2011.
7.
LiangSWuRChenL.BIBO stability of fractional-order controlled nonlinear systems. Int J Syst Sci2017; 48: 1507–1514.
8.
GhorbaniMTavakoli-KakhkiMEstaramiAA.Robust FOPID stabilization of retarded type fractional order plants with interval uncertainties and interval time delay. J Franklin Inst2019; 356: 9302–9329.
9.
Guel-CortezAJMéndez-BarriosCFGonzález-GalvánEJ, et al. Geometrical design of fractional PDμ controllers for linear time-invariant fractional-order systems with time delay. Proc IMechE, Part I: J Systems and Control Engineering2019; 233: 815–829.
10.
MaheswariCPriyankaEBMeenakshipriyaB.Fractional-order PIλDµ controller tuned by coefficient diagram method and particle swarm optimization algorithms for SO2 emission control process. Proc IMechE, Part I: J Systems and Control Engineering2017; 231: 587–599.
11.
PetrášIChenYVinagreBM. A robust stability test procedure for a class of uncertain LTI fractional order systems. In: Proceedings of the international Carpathian control conference, Malenovice, Czech Republic, 27–30 May 2002, pp.27–30.
12.
AsgariMKhaloozadehH.Robust extended Kalman filtering for non-linear systems with unknown input: a UBB model approach. IET Radar Sonar Navigat2020; 14: 1837–1844.
13.
AhnHSChenYPodlubnyI.Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality. Appl Math Comput2007; 187: 27–34.
14.
TavazoeiMSHaeriM.A note on the stability of fractional order systems. Math Comput Simul2009; 79: 1566–1576.
15.
LuJGChenG.Robust stability and stabilization of fractional-order interval systems: an LMI approach. IEEE T Automat Control2009; 54: 1294–1299.
16.
TanNÖzgüvenÖFÖzyetkinMM.Robust stability analysis of fractional order interval polynomials. ISA Trans2009; 48: 166–172.
17.
YerogluCTanN.Classical controller design techniques for fractional order case. ISA Trans2011; 50: 461–472.
18.
KangHILeeHSBaeJW. Robust stability analysis of commensurate fractional order interval polynomials. In: 2009 ISECS international colloquium on computing, communication, control, and management, Sanya, China, 8–9 August 2009, pp. 384–387. New York: IEEE.
19.
MoornaniKAHaeriM.Robust stability testing function and Kharitonov-like theorem for fractional order interval systems. IET Control Theory Appl2010; 4: 2097–2108.
20.
LuJGChenYQ.Robust stability and stabilization of fractional-order interval systems with the fractional order α: the case. IEEE Trans Automat Control2009; 55: 152–158.
21.
GaoZLiaoX.Robust stability criterion of fractional-order functions for interval fractional-order systems. IET Control Theory Appl2013; 7: 60–67.
22.
SondhiSHoteYV.Fractional order PID controller for perturbed load frequency control using Kharitonov’s theorem. Int J Electr Power Energ Syst2016; 78: 884–896.
23.
ZamaniMKarimi-GhartemaniMSadatiN, et al. Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Eng Pract2009; 17: 1380–1387.
24.
ZhengSTangXSongB.Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust-stability. Int J Robust Nonlin Control2016; 26: 1112–1142.
25.
Akbari MoornaniKHaeriM. Robust stability check for fractional PID-based control systems. Trans Inst Meas Control2013; 35: 236–246.
26.
HuangYJWangYJ.Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem. ISA Trans2000; 39: 419–431.
27.
LambaRSinglaSKSondhiS.Fractional order PID controller for power control in perturbed pressurized heavy water reactor. Nuclear Eng Design2017; 323: 84–94.
28.
KennedyJEberhartR.Particle swarm optimization. Int Conf Neural Netw1995; 4: 1942–1948.
29.
PiresESMachadoJTde Moura OliveiraPB, et al. Particle swarm optimization with fractional-order velocity. Nonlin Dynam2010; 61: 295–301.
30.
ZhangXDuanH.Comments on ‘Particle swarm optimization with fractional-order velocity’. Nonlin Dynam2014; 77: 427–429.
