Stochastic optimal semi-active control of hysteretic systems by using a magneto-rheologicaldamper

Abstract

A stochastic optimal semi-active control strategy for stochastically excited hystereticsystems by using a magneto-rheological (MR) damper is proposed. The dynamics ofboth the hysteretic system and the MR damper is characterized by using theBouc–Wen hysteretic model. The control force produced by the damper is split intoa passive part and a semi-active part. The passive part is combined with theuncontrolled system to form a passively controlled system. Then the system isconverted into an equivalent nonlinear non-hysteretic stochastic system, fromwhich a partially averaged Itô stochastic differential equation is derived by usingthe stochastic averaging method of the energy envelope. For the ergodic controlproblem, a dynamical programming equation is established based on the stochasticdynamical programming principle and solved to yield the optimal semi-activecontrol law. The fully averaged Itô equation is obtained by substituting the optimalsemi-active control force into the partially averaged Itô equation and completing theaveraging. Finally, the response of the semi-actively controlled system is obtainedfrom solving the Fokker–Planck–Kolmogorov equation associated with the fullyaveraged Itô equation. The efficacy of the proposed control strategy is illustrated bythe numerical results and comparison with clipped LQG control for an example.