Nonlinear Stochastic Optimal Control Using Piezoelectric Stack Inertial Actuator

Abstract

An optimal control strategy for the random vibration reduction of nonlinear structures using piezoelectric stack inertial actuator is proposed. First, the dynamic model of the nonlinear structure considering the dynamics of a piezoelectric stack inertial actuator is established, and the motion equation of the coupled system is described by a quasi-non-integrable-Hamiltonian system. Then, using the stochastic averaging method, this quasi-non-integrable-Hamiltonian system is reduced to a one-dimensional averaged system for total energy. The optimal control law is determined by establishing and solving the dynamic programming equation. The proposed control law is analytical and can be fully executed by a piezoelectric stack inertial actuator. The responses of optimally controlled and uncontrolled systems are obtained by solving the Fokker–Planck–Kolmogorov (FPK) equation to evaluate the control effectiveness of the proposed strategy. Numerical results show that our proposed control strategy is effective for random vibration reduction of the nonlinear structures using piezoelectric stack inertial actuator, and the theoretical method is verified by comparing with the simulation results.

Experimental Validation of Two Types of Force Actuators: A Performance Comparison

“…While piezoelectric stack actuators are capable of directly actuating structures, auxiliary preloading devices are often necessary to ensure effective output of the driving force. The inertial mass has commonly been employed in the development of inertial-type actuators to achieve larger output forces [ 11 , 12 ]. Tianyue Pan et al contributed to the development of an inertial piezoelectric actuator and investigated its dynamic characteristics [ 13 ].…”

Effects of Strain Node on the Actuation Performance of Multilayer Cantilevered Piezoactuator with Segmented Electrodes

“…Piezoactuators are widely used in microelectromechanical systems (MEMS) because of the characteristics of small size, thinness, and high displacement, such as atomic force microscopes [1], biosensors [2], microelectromechanical switches [3], and micropositioning platforms [4], etc. e actuation performance improvement and design optimization of such devices have always been the main focus of many researchers.…”