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

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Abstract

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 Itô 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.

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Authors and Affiliations

  1. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, 310027, Hangzhou, China

    Ming Zhao & Wei-Qiu Zhu

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  1. Ming Zhao
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  2. Wei-Qiu Zhu
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Correspondence to Wei-Qiu Zhu.

Additional information

The project was supported by the National Natural Science Foundation of China (11072212, 10932009) and the Zhejiang Natural Science Foundation of China (7080070).

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Zhao, M., Zhu, WQ. Stochastic optimal control of cable vibration in plane by using axial support motion. Acta Mech Sin 27, 578–586 (2011). https://doi.org/10.1007/s10409-011-0456-6

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  • DOI: https://doi.org/10.1007/s10409-011-0456-6

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