Active Control of Nonlinear Free Vibrations of a Beam and a Composite Plate Using Piezoelectric Self-Sensing Actuators

Abstract

This paper employs a coupled structural-electrical finite element modal formulation for the control of nonlinear free vibrations of beams and composite plates. Multiple modes of the nonlinear free vibration are considered in the closed loop simulations. Two different controllers are designed and investigated for the suppression of nonlinear free vibrations. The first one is the position output feedback controller comprised of a linear quadratic regulator (LQR) and an extended Kalman Filter (EKF). Unlike the standard Kalman Filter based on linearized system equations, EKF considers the nonlinear state space matrix and has a gain sequence evaluated on-line. Thus the LQR/EKF nonlinear controller has more accurate state estimation over linear quadratic Gaussian controller for the nonlinear dynamics. The second controller is the output feedback adaptive LQR/EKF controller. This adaptive controller includes an adaptive modal frequency identification and state estimation algorithm. Numerical simulations show that the adaptive LQR/EKF controller with system identification is effective to suppress nonlinear free vibrations of a beam and a composite plate with unknown sudden frequency changes. The placement of piezoelectric self-sensing actuators is based on two approaches: one is the norm of optimal feedback control gain matrix (NFCG) method and another is the H2 norm.