Analytical Investigation on Elastodynamic Vibration Suppression of a Flexible Four-Bar Mechanism System Featuring a Smart Coupler Link and Multivariable Optimal Regulator

Abstract

Abstract This paper presents an analytical investigation on active control of the elastodynamic response of a four-bar (4R) mechanism system using “smart” materials featuring piezoelectric sensor/actuator (S/A) pairs and multivariable optimal control. The 4R mechanism consists of a flexible coupler link, relatively flexible follower link, and a relatively rigid crank. Two thin plate-type piezoceramic S/A pairs are bonded to the flanks of the coupler link at high strain locations corresponding to the first and second vibration modes. Based on the optimal multivariable control theory, a controller which consists of a linear quadratic regulator (LQR) and a Luenberger observer as a state estimator is designed and implemented. As the mechanism changes configuration, its modal characteristics are recalculated, and the controller is redesigned. The dynamic model used for the controller design includes the second and fourth vibration modes of the mechanism system. These modes are predominated by the first two bending modes of the mechanism’s coupler link. The results showed that while the proposed active control strategy is successful in reducing the amplitudes of vibrations about the quasistatic response, it has no effect on the quasistatic deflections due to steady state loading.