Control and Anti-control of Chaotic Motion for a Under-actuated Planar Five-bar Mechanism
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摘要: 对于欠驱动连杆机构,混沌的控制和反控制研究是避免或利用其混沌运动的关键问题。在欠驱动平面五杆机构中加装一个线性弹簧,改变了机构的受力状况,从而实现了对机构混沌运动的控制与反控制。以弹簧安装位置为参数的分叉图显示,不同的弹簧安装位置可以使机构呈现出混沌运动、周期运动等多种运动形式,弹簧的安装位置可以通过螺旋机构进行调节,这样就形成了一种简单、有效的机构混沌运动控制和反控制的方法。机构运动的相图和最大Lyapunov指数验证了方法的有效性。
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关键词:
- 混沌控制 /
- 混沌反控制 /
- 欠驱动机构 /
- Lyapunov指数
Abstract: For the under-actuated linkage mechanism,techniques to control and anti-control chaos are the crucialproblem for the prevention or utilization of chaos. In this paper,by adding a linear spring to an under-actuated pla-nar five-bar mechanism,the force applied to the mechanism was changed,therefore,the control and anti-control ofchaotic motion of the mechanism was implemented. In the bifurcation diagram with the location of spring as the pa-rameter,it is indicated that the different locations of the spring lead to different motions of the mechanism,such aschaotic and periodic motions. A helical pair was used to adjust the location of the spring. In this way,a simple butefficient technique to control and anti-control chaos was created,which was proved by the phase diagram and thelargest Lyapunov exponent.-
Key words:
- chaos control /
- chaos anti-control /
- under-actuated mechanism /
- Lyapunov exponent
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[1] Baker G,McRobie F A. Implication of chaos theory for engineer-ing science[J]. Proceedings of the Institution of MechanicalEngineers,Part C: Journal of Mechanical Engineering Sci-ence,1997,211(5):349~363 [2] Fradkov A L,Evans R J. Control of chaos: methods and applica-tions in engineering[J]. Annual Reviews in Control,2005,29(1):33~56 [3] 陈学森,董海军,刘晓宁. 含时变啮合刚度的间隙非线性齿轮系统的混沌控制[J]. 机械科学与技术,2006,25(9):1035~1037 [4] 李立,李开富. 双杆摆机构混沌运动的控制[J]. 机械科学与技术,2003,22(3):249~253 [5] Cao H,Chi X,Chen G. Suppressing or inducing chaos in amodel of robot arms and mechanical manipulators[J]. Journalof Sound and Vibration,2004,271(3-5):705~724 [6] Chen G. Chaos: its control and generation for engineering appli-cations[J]. Discrete and Impulsive Systems Series B,2003,10:235~245 [7] Chen H,Lee C. Anti-control of chaos in rigid body motion[J].Chaos,Solitons & Fractals,2004,21(4):957~965 [8] 吴然超,郭玉祥. 含一个非线性项混沌系统的线性控制及反控制[J]. 物理学报,2010,59(8):5293~5298 [9] Wang X,Chen G. Anticontrol of chaos in continuous-time sys-tems via time-delay feedback[J]. Chaos,2000,10:771~779 [10] Chen J H. Controlling chaos and chaotification in the Chen-Leesystem by multiple time delays[J]. Chaos,Solitons & Frac-tals,2008,36(4):843~852 [11] Tavazoei M S,Haeri M. Chaos generation via a switching frac-tional multi-model system [J]. Nonlinear Analysis: RealWorld Applications,2010,11(1):332~340 [12] Liu Z Z,Tian Y T,Zhang P J,Zhou C J. The analysis on bifur-cation and chaos in the compass-gait biped[A]. Proceedings ofthe 2007 IEEE International Conference on Robotics andBiomimetics[C],2007 [13] Seneviratne L E,Earles S W E. Chaotic behavior exhibited dur-ing contact loss in a clearance joint of a four bar mechanism[J].Mechanism and Machine Theory,1992,27(3):307~321 [14] 王国庆,刘宏昭,何长安. 非线性接触模型在多间隙机构混沌分析中的应用[J]. 机械科学与技术,2005,24(6):636~638 [15] Li Z. Chaotic vibration sieve[J]. Mechanism and MachineTheory,1995,30(4):613~618 [16] Herder J L. Design of spring force compensation systems[J].Mechanism and Machine Theory,1998,33(1-2):151~161
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