Robust Control of Periodic Bifurcation Solutions
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摘要: 根据C-L方法,可以得到非线性动力系统的分岔方程和拓扑分岔图.根据得到的分岔图,结合控制理论,提出了周期解的鲁棒控制方法.该方法将运动模式控制到目标模式.由于该方法对控制器的参数没有严格的控制,所以在设计和制造控制器方面是很方便的.数值研究验证了该方法的有效性.Abstract: The topological bifurcation diagrams and the coefficients of bifurcation equation were obtained by C-L method. According to obtained bifurcation diagrams and combining control theory, the method of robust control of periodic bifurcation was presented, which differs from generic methods of bifurcation control. It can make the existing motion pattern into the goal motion pattern. Because the method does not make strict requirement about parametric values of the controller, it is convenient to design and make it. Numerical simulations verify validity of the method.
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Key words:
- bifurcation /
- topological structure /
- bifurcation control /
- C-L method
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[1] Krylov N,Bogoliubov N.Les methods de la mecarique nonlinear[J].Monographie.Chaire de la Phys and Math of Academic Science.U K,1934,8:44—51. [2] CHEN Yu-shu,Langford W F.The subharmonic bifurcation solution of nonlinear Mathieu's equation and Euler dynamically bucking problem[J].Acta Mech Sinica,1988,20(4):522—532. [3] Yu P,Huseyin K.Parametrically exited nonlinear systems:a comparison of certain methods[J].Int J Non-Linear Mechanics,1998,33(6):967—978. doi: 10.1016/S0020-7462(97)00061-9 [4] Chow S Y,Hale J K.Methods of Bifurcation Theory[M].New York:Springer,1982. [5] Golubisky M,Schaeffer D G.Singularities and Groups in Bifurcan'on Theory(Vol.[STHZ]. 1[STBZ]. )[M].New York:Springer,1985. [6] Bogoliubov N,Mitropolsky Y A.Asymptotic Methods in the Theory of Nonlinear Oscillations[M].New York:Gordon & Breach,1961. [7] Nayfeh A H,Mook D T.Nonlinear Osci Uations[M].New York:Wiley,1979. [8] Abed E H,Wang H O,Chen R C.Stabilization of period doubling bifurcation and implications for control of chaos[J].Physica D,1994,70(1):154—164. doi: 10.1016/0167-2789(94)90062-0 [9] Wang H O,Abed E H.Bifurcation control of a chaotic system[J].Automatica,1995,31(9):1213—1226. doi: 10.1016/0005-1098(94)00146-A [10] Kang W.Bifurcation and normal form of nonlinear control systems—Parts Ⅰand Ⅱ[J].SIAM J Contr Optim,1998.36(1):193—232. [11] Chen G,Dong X.From Chaos to Order:Methodologies,Perspectives and Applications[M].Singapore:World Scientific Pub Co,1998. [12] Abed E H.Bifurcation-theoretic issues in the control of voltage collapse[A].In:Chow J H,Kokotovic P V,Thomas R J Eds.Proc IMA Workshop on Systems and Control Theory for Power Sys[C].New York:Springer,1995,1—21. [13] Chen G,Lu J,Yap K C.Controlling Hopf bifurcation[A].In:Ueta T,Chen G Eds.Proc Int Symp Circ Sys[C].3.USA:Monterey, C A,1998,693—642. [14] Basso M,Evangelisti A,Genesio R,et al.On bifurcation control in time delay feedback systems[J].Int J Bifur Chaos,1998,8(4):713—721. doi: 10.1142/S0218127498000504 [15] Chen G.Controlling Chaos and Bifurcation in Engineering Systems[M].Boca Raton,FL:CRC Press,1999. [16] Chen G,Moiola J L,Wang H O.Bifurcation control:theories,methods and applications[J].Int J Bifur Chaos,2000,10(3):511—548. [17] CHEN Yu-shu,Leung Andrew Y T.Bifurcation and Chaos in Engineering[M].London:Springer,1998. [18] 陈予恕,杨彩霞,吴志强,等.具有平方、立方非线性项的耦合动力学系统1:2内共振分岔[J].应用数学和力学,2001,22(8):817—824. [19] LI Xin-ye,CHEN Yu-shu,WU Zhi-qiang,et al.Bifurcation of nonlinear normal modes of M-DOF systems with internal resonance[J].Acta Mechanica Sinica,2002,34(3):104—407. [20] Sundararajan P,Noah S.Dynamics of forced nonlinear systems using shooting arc length continuation method[J].ASME J Vib Acoustics,1995,119(1):9—20.
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