Direct model reference adaptive control (MRAC) design and simulation for the vibration suppression of piezoelectric smart structures

The paper presents control system design based on a non-linear model reference adaptive control law (MRAC) used for the vibration suppression of a smart piezoelectric mechanical structure. Numerical simulation of the proposed control system is performed based on the finite element (FE) model of the structure, modally reduced in order to meet the requirements of the control system design. First the MRAC problem is defined and a direct control algorithm described in the paper is suggested as a solution to the control problem. The basic MRAC algorithm is modified by augmenting the integral term of the control law in order to provide the robustness of the control system with respect to the stability. This approach provides preserving the boundness of the system states and adaptive gains, with small trackings error over large ranges of non-ideal conditions and uncertainties. The efficiency of the suggested control for the vibration suppression is tested and shown through a numerical simulation of the funnel-shaped piezoelectric structure.