Stochastic optimal control of cable vibration in plane by using axial support motion

• Published in: Acta mechanica Sinica Vol. 27; no. 4; pp. 578 - 586
• Main Authors: Zhao, Ming, Zhu, Wei-Qiu
• Format: Journal Article
• Language: English
• Published: Heidelberg The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences 01.08.2011
• Subjects: Cables; Classical and Continuum Physics; Computational Intelligence; Dynamical systems; Engineering; Engineering Fluid Dynamics; Galerkin方法; Lyapunov直接方法; Mathematical analysis; Optimal control; Programming; Research Paper; Stochasticity; Strategy; Theoretical and Applied Mechanics; Vibration; 平面运动; 振动模式; 最优控制策略; 移动电缆; 轴向; 随机最优控制; Stochastic optimal control; Active control; Dynamical programming principle; Stay cable
• ISSN: 0567-7718; 1614-3116
• DOI: 10.1007/s10409-011-0456-6

A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is introduced. The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.