Nonlinear Systems Applications Of Mr Damper Semi-active Stochastic Optimal Control,

A semi-active stochastic optimal control strategy for nonlinear hysteretic system using magneto-rheological (MR) damper is proposed. The dynamic behavior of a MR damper is characterized by using Bouc-Wen hysteretic model The control force produced by the MR damper is split into a passive part and a semi-active part. The passive part is incorporated with the uncontrolled system to form a passive control system. Then the system is converted into an equivalent nonlinear non-hysteretic stochastic control system, from which an lto stochastic differential equation for total energy is derived by using the stochastic averaging method of energy envelope. For the ergodic control problem, a dynamical programming equation for the controlled total energy process is established based on the stochastic dynamical programming principle. The optimal control law is obtained by minimizing the dynamical programming equation, and implemented by the MR damper without clipping. Then the fully completed averaged lto equation is obtained from the partially completed averaged equation for the controlled total energy process by replacing the control forces with the optimal control forces. Finally, the response of semi-actively controlled system is obtained from solving the final dynamical programming equation and the Fokker-Planck-Kolmogorov equation associated with the fully completed averaged lto equation. The efficacy of the proposed semi-active stochastic optimal control strategy is illustrated by using the numerical simulation, which shows that the proposed semi-active stochastic optimal control strategy holds the better performance at the reduction of vibration.