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

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.

Stay cable vibration mitigation: A review

“…Using the active stiffness control scheme and based on displacement and velocity measurements, Wang and Xu (2008) developed optimal control algorithm targeting RWIVs. Zhao and Zhu (2011) formulated a stochastic optimal control using axial cable support motion. Zhu and Li (2009) and Zhu (2010) considered bending stiffness of cables in active stiffness control, and compared the performances of different control algorithms, i.e., Linear Quadratic Regulator (LQR) and Bang-Bang, and found that the peak of control force of using the latter algorithm is smaller.…”