Stochastic Vibration Control Based On Piezoelectric Stack Inertial Actuator

Piezoelectric stack actuators have been widely used in vibration control of mechanical structures due to the advantages of fast response,high precision,etc..A piezoeleetric stack actuator is usually fixed at one end and the other end generates a force to control structure's vibration.For this kind of direct action,the control law can be easily acquired,however,the disadvantage is that it will introduce a new excitation source to the structure.In recent years,a novel piezoelectric stack inertial actuator has been proposed,which can effectively overcome the above limitations.Previous studies on piezoelectric stack inertial actuators have been mostly limited to the dynamic characteristics of the actuator itself,and researchs on active control based on this type of actuator are rarely involved.This paper aims to study the random vibration control of the main structure using piezoelectric stack inertial actuator.The details are as follows:For the linear structure,according to the constitutive relation of the piezoelectric stack,the expression of the inertial force is derived,and the differential vibration equation of the main structure considering the actuator's dynamics is established.Based on the linear vibration control theory,the linear-quadratic-Gaussian(LQG)control strategy is designed.The random responses of the main structure and the actuator before and after the control are obtained.The influence of systems,parameters(the inertial mass and stiffness of the actuator,mass and stiffness of main structure,etc.)on the control effectiveness is discussed.The influence of the time delay on the control is also investigated,and a method of optimizing the control strategy by adjusting time delay is proposed.For the nonlinear structural system,the partial average Ito equation of the actuator and main structure coupling system is obtained by stochastic averaging method.The dynamic programming equation is established based on the dynamic programming principle.By solving the dynamic programming equation,the nonlinear stochastic optimal control law is determined.The control effectiveness of the proposed control is then estimated.The results show that the proposed control strategy of piezoelectric stack inertial actuator is quite effective for the reduction of random vibration of the linear and nonlinear structures.The theoretical method is verified by comparing the theoretical calculation results with the direct simulation ones.