Robust reliable control in vibration suppression of sandwich circular plates

• A new formulation is proposed to extract the dynamics of the piezolaminated sandwich circular plate.
• An analytical solution is presented for the simply supported boundary condition that satisfies the Maxwell static electricity equation and the sensor/actuator boundary conditions.
• The conservatism of the control system is addressed by reformatting the dynamic equation of motion and the associated uncertain elements.
• The robust non-fragile H∞H∞ controller is designed in an LMI framework to handle both the modeling uncertainties and uncertainties of the controller gain.

The wide real life applications of circular plates under dynamic loading such as laminate saw blades and accurate slitting narrow industrial cutters require special attention to smart structural design that optimally handles the dynamic behavior of these configurations. The purpose of this paper is to investigate the vibration regulation of a sandwich circular plate using a non-fragile robust control strategy. A new dynamic modeling of the piezolaminated structure is proposed based on satisfying the Maxwell static electricity equation and on assuring the full coupling effects of the piezoelectric layers on the host structure. The Eigen functions are chosen optimally such that the boundary conditions for the piezoelectric sensor/actuator are satisfied without additional complexities. In order to reach to the desired performance in vibration attenuation, a robust controller is designed by considering the uncertainties that exist in the system matrices and controller itself. The proposed controller is obtained by solving a system of linear matrix inequalities (LMIs) that are based on the Bounded Real Lemma (BRL). Simulations show that the controller is capable of suppressing the vibration in existence of both the structured uncertainty in the system matrices and the feedback controller gain.