A Study On An Explicit Time-domain Formulation Based Optimal Control Algorithms For Linear Vibration Of Structures

In this paper,the active control algorithm is used as the entry point,and the related research on the problems of classical linear quadratic optimal control is carried out.The optimal control problem can be divided into three parts: control evolution rule,physical movement evolution rule and system observation.The theoretical innovation and main work of this paper are as follows:(1)Under the Ideal-Excitation-Situation which means the load time history is known,the optimal control problem is converted into a differential algebraic equation problem,an efficient and accurate algorithm based on Lobatto IIIA configuration method is proposed,and a new control effect evaluation index is proposed accordingly.(2)In this paper,we using an explicit time-domain formulation of the structural dynamic response to consider the constraint of the structural motion equation to the control performance functional.In this way,we can avoid to introduction of the Lagrangian multiplier and fundamentally simplifying the solution of the optimal control problem.(3)Under the Ideal-Excitation-Situation,we can derive the calculation formula of the ideal optimal control force based on the explicit time-domain formulation.And the calculation result is consistent with Lobatto IIIA algorithm.(4)Aiming at the Ggeneral-Excitation-ituation with unknown load duration,Combining the linear quadratic optimal control algorithm and the instantaneous optimal control algorithm,a time-varying control performance function is proposed.This new control performance function fully considered the current time seismic load,the current time control force effect,and the successor state.Using the explicit time-domain formulation,we derive the optimal control force calculation formula under feedforward and feedback control.(5)Structural state estimation is an important part of the active control algorithm.On the basis of the known random earthquake model,a real time earthquake recognition and prediction algorithm based on bayesian estimation is proposed to improve the deficiency of traditional active control algorithm in filtering and estimating the structural state.(6)A predictive dynamic performance functional that considers the identification and prediction of ground motion is proposed to establish the predictive optimal control strategy for the linear system.The predictive dynamic performance functional concerned about the effects of current ground motions,control forces,predicted ground motions,predicted control forces and the subsequent structural states.It is proved that the predictive optimal control which base on the finint time seismic motions prediction can improve the control effect.