Stochastic optimal semi-active control of stay cables by using magneto-rheological damper

Stochastic optimal semi-active control for stay cable multi-mode vibration attenuation by using magneto-rheological (MR) damper is developed. The Bingham model for an MR damper is used. The force produced by an MR damper is split into passive and active parts. The passive part is combined with structural damping forces into effective damping forces. The partially averaged Ito stochastic differential equations for controlled modal energies are derived by applying the stochastic averaging method for quasi-integrable Hamiltonian systems. Then the dynamical programming equation for controlled modal energies with an index involving control force is established by applying the stochastic dynamical programming principle, and a stochastic optimal semi-active control law is obtained by solving the dynamical programming equation. For controlled modal energies with an index not involving control force, bang-bang control law is obtained without solving a dynamical programming equation. A comparison between the two control laws shows that the stochastic optimal semi-active control strategy is superior to the bang-bang control strategy in the sense of higher control effectiveness and efficiency and less chattering.