Analytical development of a robust controller for smart structural systems

This paper aims at demonstrating the feasibility of active control of beams with a multiobjective state-feedback control technique. The multiobjective state-feedback controller is designed on a linear matrix inequality (LMI) approach for the multiobjective synthesis. The design objectives are to achieve a mix ofH _∞ performance andH ₂ performance satisfying constraints on the closed-loop pole locations in the face of model uncertainties. The controller is also designed to reject the effects of the noise and external of disturbances. For the theoretical analysis, the governing equation of motion is derived by Hamilton’s principle to describe the dynamics of a smart structural system. Numerical examples are presented to demonstrate the effectiveness of the integrated robust controller in damping out the multiple vibration modes of the piezo/beam system.