The Application Of Mr Damper Hysteretic System Of Nonlinear Stochastic Optimal Semi-active Control

In chapter 1, the present status of the stochastic control theory is briefly reviewed, and many methods for predicting the stochastic response of the hysteretic system are introduced. In chapter 2, the working principle of the MR damper and its mathematical models are expatiated, and the control strategies for using MR dampers are enumerated. In chapter 3, the stochastic averaging method of energy envelope and stochastic optimal control strategy are introduced. In chapter 4, based on the basic principles described in chapter 3, MR damper is used to semi-actively control the hysteretic system. First, the system is converted into an equivalent non-hysteretic nonlinear stochastic system, from which a partially averaged It(?) stochastic equation is derived by using the stochastic averaging method of energy envelope. For the ergodic control problem, a dynamical programming equation is established based on the stochastic dynamical programming principle and solved to yield the optimal control law. The fully averaged It(?) equation is obtained by substituting the optimal control force into partially averaged It(?) equation and completing the average. Finally, the response of the controlled system is obtained by solving the final dynamical programming equation and the Fokker-Planck-Kolmogorov equation associated with the fully averaged It(?) equation. Simultaneously, LQG control strategy is also used to control the same system. The numerical result indicates that both the effectiveness and efficiency of the former control strategy are better than those of the latter.