Fractional Order Fixed-time Nonsingular Terminal Sliding Mode Control for Chaotic Oscillation in Power System
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- 英文论文题名：Fractional Order Fixed-time Nonsingular Terminal Sliding Mode Control for Chaotic Oscillation in Power System
- 论文作者：Junkang Ni ; Ling Liu ; Chongxin Liu ; Xiaoyu Hu ; Lin Cheng
- 英文论文作者：Junkang Ni ; Ling Liu ; Chongxin Liu ; Xiaoyu Hu ; Lin Cheng ; State Key Laboratory of Electrical Insulation and Power Equipment ; School of Electrical Engineering ; Xi'an Jiaotong University ; State Grid Shaanxi Electric Power Research Institute
- 年：2017
- 作者机构：State Key Laboratory of Electrical Insulation and Power Equipment,School of Electrical Engineering,Xi'an Jiaotong University;State Grid Shaanxi Electric Power Research Institute;
- 英文论文关键词：Chaos suppression ; Power system ; Fixed-time control ; Nonsingular terminal sliding mode control ; Fractional order control
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：TM712
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：6
- 文件大小：254k
- 原文格式：D
- 会议级别：全国
摘要
Chaotic oscillation is a harmful phenomenon for power system and it threatens the safe and stable operation of power system. This paper presents fractional order fixed-time nonsingular terminal sliding mode control to suppress chaos in power system. A novel fractional order terminal sliding mode surface is first proposed to guarantee the fixed-time convergence of system states along the sliding surface, and then a nonsingular terminal sliding mode controller is designed to force the system states to reach the sliding surface within fixed-time and stay on it forever. Furthermore, the fixed-time stability and the robustness of the proposed control scheme are proved using the fractional Lyapunov stability theory. Finally, the proposed control scheme is applied to suppress chaos in fractional order power system and simulation results demonstrate the effectiveness of the proposed control scheme.
Chaotic oscillation is a harmful phenomenon for power system and it threatens the safe and stable operation of power system. This paper presents fractional order fixed-time nonsingular terminal sliding mode control to suppress chaos in power system. A novel fractional order terminal sliding mode surface is first proposed to guarantee the fixed-time convergence of system states along the sliding surface, and then a nonsingular terminal sliding mode controller is designed to force the system states to reach the sliding surface within fixed-time and stay on it forever. Furthermore, the fixed-time stability and the robustness of the proposed control scheme are proved using the fractional Lyapunov stability theory. Finally, the proposed control scheme is applied to suppress chaos in fractional order power system and simulation results demonstrate the effectiveness of the proposed control scheme.
Chaotic oscillation is a harmful phenomenon for power system and it threatens the safe and stable operation of power system. This paper presents fractional order fixed-time nonsingular terminal sliding mode control to suppress chaos in power system. A novel fractional order terminal sliding mode surface is first proposed to guarantee the fixed-time convergence of system states along the sliding surface, and then a nonsingular terminal sliding mode controller is designed to force the system states to reach the sliding surface within fixed-time and stay on it forever. Furthermore, the fixed-time stability and the robustness of the proposed control scheme are proved using the fractional Lyapunov stability theory. Finally, the proposed control scheme is applied to suppress chaos in fractional order power system and simulation results demonstrate the effectiveness of the proposed control scheme.
引文
[1]D.Q.Wei and X.S.Luo,Noise-induced chaos in singlemachine infinite-bus power systems,EPL,86(5):50008,2009.
[2]H.D.Chiang,C.W.Liu,P.P.Varaiya,F.F.Wu and M.G.Lauby,Chaos in a simple power system,IEEE Trans.Power Syst.,8(4):1407-1417,1993
[3]M.L.Ma and F.H.Min,Bifurcation behavior and coexisting motions in a time-delayed power system,Chin.Phys.B,24(3):030501,2015.
[4]W.Ji and V.Venkatasubramanian,Hard-limit induced chaos in a fundamental power system model,Int.J.Electr.Power Energy Syst.,18(5):279-295,1996.
[5]Y.X.Yu,H.J.Jia,P.Li and J.F.Su,Power system instability and chaos.Electr.Power Syst.Res.,65(3):187-195,2003
[6]D.Q.Wei and X.S.Luo,Passivity-based adaptive control of chaotic oscillations in power system,Chaos Solitons Fractals,31(3):665-671,2007.
[7]I.M.Ginarsa,A.Soeprijanto and M.H.Purnomo,Controlling chaos and voltage collapse using an ANFIS-based composite controller-static var compensator in power systems.Int.J.Electr.Power Energy Syst.,46:79-88,2013.
[8]Q.Y.Sun,Y.G.Wang,J.Yang,Y.Qiu and H.G.Zhang,Chaotic dynamics in smart grid and suppression scheme via generalized fuzzy hyperbolic model,Math.Problems Eng.,2014,Article ID 761271,2014
[9]J.K.Ni,C.X.Liu and X.Pang,Fuzzy fast terminal sliding mode controller using an equivalent control for chaotic oscillation in power system,Acta Phys.Sin.,62(19):190507,2013(in Chinese)
[10]J.K.Ni,C.X.Liu,K.Liu and X.Pang,Variable speed synergetic control for chaotic oscillation in power system,Nonlinear Dyn.,78(1):681-690,2014
[11]J.K.Ni,L.Liu,C.X.Liu,X.Y.Hu and A.A.Li,Chaos suppression for a four-dimensional fundamental power system model using adaptive feedback control,Trans.Inst.Meas.Control,39(2):194-207,2017
[12]J.K.Ni,L.Liu,C.X.Liu and X.Y.Hu,Chattering-Free time scale separation sliding mode control design with application to power system chaos suppression,Math.Problems Eng.,2016,Article ID 5943934,2016
[13]J.K.Ni,L.Liu,C.X.Liu,X.Y.Hu and S.L.Li,Fast fixedtime nonsingular terminal sliding mode control and its application to chaos suppression in power system,IEEE Trans.Circuits Syst.II,Exp.Briefs,64(2):151-155,2017
[14]J.K.Ni,L.Liu,C.X.Liu,X.Y.Hu and T.S.Shen,Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system,Nonlinear Dyn.,86(1):401-420,2016
[15]I.Schafer and K.Kruger,Modelling of lossy coils using fractional derivatives,J.Phys.D,Appl.Phys.,41(4):1-8,2008
[16]S.Westerlund and L.Ekstam,Capacitor theory,IEEE Trans.Dielectr.Elect.Insul.,1(5):826-839,1994.
[17]C.J.Wu,G.Q.Si and Y.B.Zhang,The fractional-order statespace averaging modeling of the Buck Boost DC/DC converter in discontinuous conduction mode and the performance analysis,Nonlinear Dyn.,79(1):689-703,2015.
[18]W.Zheng,Y.Luo,Y.Q.Chen and Y.G.Pi,Fractional-order modeling of permanent magnet synchronous motor speed servo system,J.Vib.Control,22(9):2255-2280,2016.
[19]H.S.Li,Y.Luo and Y.Q.Chen,A fractional order proportional and derivative(FOPD)motion controller:tuning rule and experiments,IEEE Trans.Control Syst.Technol.,18(2):516-520,2010.
[20]T.C.Lin and C.H.Kuo,H-inf synchronization of uncertain fractional order chaotic systems:Adaptive fuzzy approach,ISA Trans,50(4):548-556,2011.
[21]B.Wang,J.Y.Xue,F.J.Wu and D.L.Zhu,Stabilization conditions for fuzzy control of uncertain fractional order nonlinear systems with random disturbances,IET Contr.Theory Appl.,10(6):637-647,2016.
[22]X.J.Tang,Z.B.Liu and X.Wang,Integral fractional pseudospectral methods for solving fractional optimal control problems,Automatica,62:304-311,2015.
[23]M.P.Aghababa,Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic(hyperchaotic)systems using fractional nonsingular terminal sliding mode technique.Nonlinear Dyn,69(1):247-261,2012
[24]H.T.Song and T.Zhang,Fast robust integrated guidance and control design of interceptors,IEEE Trans.Control Syst.Technol.,24(1):349-356,2016
[25]B.Wang,J.L.Ding,F.J.Wu and D.L.Zhu,Robust finitetime control of fractional-order nonlinear systems via frequency distributed model,Nonlinear Dyn,85(4):2133-2142,2016
[26]A.Polyakov,Nonlinear feedback design for fixed-time stabilization of linear control systems,IEEE Trans.Autom.Contr.,57(8):2106-2110,2012.
[27]M.Defoort,A.Polyakov,G.Demesure,M.Djemai and K.Veluvolu,Leader-follower fixed-time consensus for multiagent systems with unknown non-linear inherent dynamics,IET Contr.Theory Appl.,9(14):2165-2170,2015
[28]Z.Y.Zuo,Nonsingular fixed-time consensus tracking for second-order multi-agent networks,Automatica,54:305-309,2015
[29]J.J.Fu and J.Z.Wang,Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties,Syst.and Contr.Lett.,93:1-12,2016
[30]Z.Y.Zuo and L.Tie,Distributed robust finite-time nonlinear consensus protocols for multi-agent systems,Int.J.Syst.Sci.,47(6):1366-1375,2016.
[31]I.Podlubny,Fractional Differential Equations,Academic Press,New York,NY,USA,1999.
[32]Y.Li,Y.Q.Chen and I.Podlubny,Mittag-Leffler stability of fractional order nonlinear dynamic systems,Automatica,45(8):1965-1969,2009
[33]S.P.Bhat and D.S.Bernstein,Finite-time stability of continuous autonomous systems,SIAM J.Contr.Optim.,38(3):751-766,2000
[34]G.Hardy,J.Littlewood and G.Polya,Inequalities.London,U.K.:Cambridge Univ.Press,1951
[35]Y.Wang,L.Gu,Y.Xu and X.Cao,Practical tracking control of robot manipulators with continuous fractional-order nonsingular terminal sliding mode,IEEE Trans.Ind.Electron.,63(10):6194-6204,2016.
[2]H.D.Chiang,C.W.Liu,P.P.Varaiya,F.F.Wu and M.G.Lauby,Chaos in a simple power system,IEEE Trans.Power Syst.,8(4):1407-1417,1993
[3]M.L.Ma and F.H.Min,Bifurcation behavior and coexisting motions in a time-delayed power system,Chin.Phys.B,24(3):030501,2015.
[4]W.Ji and V.Venkatasubramanian,Hard-limit induced chaos in a fundamental power system model,Int.J.Electr.Power Energy Syst.,18(5):279-295,1996.
[5]Y.X.Yu,H.J.Jia,P.Li and J.F.Su,Power system instability and chaos.Electr.Power Syst.Res.,65(3):187-195,2003
[6]D.Q.Wei and X.S.Luo,Passivity-based adaptive control of chaotic oscillations in power system,Chaos Solitons Fractals,31(3):665-671,2007.
[7]I.M.Ginarsa,A.Soeprijanto and M.H.Purnomo,Controlling chaos and voltage collapse using an ANFIS-based composite controller-static var compensator in power systems.Int.J.Electr.Power Energy Syst.,46:79-88,2013.
[8]Q.Y.Sun,Y.G.Wang,J.Yang,Y.Qiu and H.G.Zhang,Chaotic dynamics in smart grid and suppression scheme via generalized fuzzy hyperbolic model,Math.Problems Eng.,2014,Article ID 761271,2014
[9]J.K.Ni,C.X.Liu and X.Pang,Fuzzy fast terminal sliding mode controller using an equivalent control for chaotic oscillation in power system,Acta Phys.Sin.,62(19):190507,2013(in Chinese)
[10]J.K.Ni,C.X.Liu,K.Liu and X.Pang,Variable speed synergetic control for chaotic oscillation in power system,Nonlinear Dyn.,78(1):681-690,2014
[11]J.K.Ni,L.Liu,C.X.Liu,X.Y.Hu and A.A.Li,Chaos suppression for a four-dimensional fundamental power system model using adaptive feedback control,Trans.Inst.Meas.Control,39(2):194-207,2017
[12]J.K.Ni,L.Liu,C.X.Liu and X.Y.Hu,Chattering-Free time scale separation sliding mode control design with application to power system chaos suppression,Math.Problems Eng.,2016,Article ID 5943934,2016
[13]J.K.Ni,L.Liu,C.X.Liu,X.Y.Hu and S.L.Li,Fast fixedtime nonsingular terminal sliding mode control and its application to chaos suppression in power system,IEEE Trans.Circuits Syst.II,Exp.Briefs,64(2):151-155,2017
[14]J.K.Ni,L.Liu,C.X.Liu,X.Y.Hu and T.S.Shen,Fixed-time dynamic surface high-order sliding mode control for chaotic oscillation in power system,Nonlinear Dyn.,86(1):401-420,2016
[15]I.Schafer and K.Kruger,Modelling of lossy coils using fractional derivatives,J.Phys.D,Appl.Phys.,41(4):1-8,2008
[16]S.Westerlund and L.Ekstam,Capacitor theory,IEEE Trans.Dielectr.Elect.Insul.,1(5):826-839,1994.
[17]C.J.Wu,G.Q.Si and Y.B.Zhang,The fractional-order statespace averaging modeling of the Buck Boost DC/DC converter in discontinuous conduction mode and the performance analysis,Nonlinear Dyn.,79(1):689-703,2015.
[18]W.Zheng,Y.Luo,Y.Q.Chen and Y.G.Pi,Fractional-order modeling of permanent magnet synchronous motor speed servo system,J.Vib.Control,22(9):2255-2280,2016.
[19]H.S.Li,Y.Luo and Y.Q.Chen,A fractional order proportional and derivative(FOPD)motion controller:tuning rule and experiments,IEEE Trans.Control Syst.Technol.,18(2):516-520,2010.
[20]T.C.Lin and C.H.Kuo,H-inf synchronization of uncertain fractional order chaotic systems:Adaptive fuzzy approach,ISA Trans,50(4):548-556,2011.
[21]B.Wang,J.Y.Xue,F.J.Wu and D.L.Zhu,Stabilization conditions for fuzzy control of uncertain fractional order nonlinear systems with random disturbances,IET Contr.Theory Appl.,10(6):637-647,2016.
[22]X.J.Tang,Z.B.Liu and X.Wang,Integral fractional pseudospectral methods for solving fractional optimal control problems,Automatica,62:304-311,2015.
[23]M.P.Aghababa,Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic(hyperchaotic)systems using fractional nonsingular terminal sliding mode technique.Nonlinear Dyn,69(1):247-261,2012
[24]H.T.Song and T.Zhang,Fast robust integrated guidance and control design of interceptors,IEEE Trans.Control Syst.Technol.,24(1):349-356,2016
[25]B.Wang,J.L.Ding,F.J.Wu and D.L.Zhu,Robust finitetime control of fractional-order nonlinear systems via frequency distributed model,Nonlinear Dyn,85(4):2133-2142,2016
[26]A.Polyakov,Nonlinear feedback design for fixed-time stabilization of linear control systems,IEEE Trans.Autom.Contr.,57(8):2106-2110,2012.
[27]M.Defoort,A.Polyakov,G.Demesure,M.Djemai and K.Veluvolu,Leader-follower fixed-time consensus for multiagent systems with unknown non-linear inherent dynamics,IET Contr.Theory Appl.,9(14):2165-2170,2015
[28]Z.Y.Zuo,Nonsingular fixed-time consensus tracking for second-order multi-agent networks,Automatica,54:305-309,2015
[29]J.J.Fu and J.Z.Wang,Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties,Syst.and Contr.Lett.,93:1-12,2016
[30]Z.Y.Zuo and L.Tie,Distributed robust finite-time nonlinear consensus protocols for multi-agent systems,Int.J.Syst.Sci.,47(6):1366-1375,2016.
[31]I.Podlubny,Fractional Differential Equations,Academic Press,New York,NY,USA,1999.
[32]Y.Li,Y.Q.Chen and I.Podlubny,Mittag-Leffler stability of fractional order nonlinear dynamic systems,Automatica,45(8):1965-1969,2009
[33]S.P.Bhat and D.S.Bernstein,Finite-time stability of continuous autonomous systems,SIAM J.Contr.Optim.,38(3):751-766,2000
[34]G.Hardy,J.Littlewood and G.Polya,Inequalities.London,U.K.:Cambridge Univ.Press,1951
[35]Y.Wang,L.Gu,Y.Xu and X.Cao,Practical tracking control of robot manipulators with continuous fractional-order nonsingular terminal sliding mode,IEEE Trans.Ind.Electron.,63(10):6194-6204,2016.