Robust active vibration control of FGMs plate with uncertainties and jump in mechanical properties under disturbed conditions using piezoelectric layers

In this study, the time response control of a sandwich plate with functionally graded core and piezoelectric side layers under external excitation, parametric uncertainty and jump in mechanical properties has been investigated. To express the displacement field, using Hamilton's principle, the structural equations were obtained in displacement terms and were spatially discretized by the Differential Quadrature Method (DQM) and converted into time differential equations. Subsequently, to achieve the control goal, a Markov jump state space model of the composite plate coupling system with a piezoelectric sensor and actuator was extracted and presented under the influence of an external disturbance. The H ∞ stability index was obtained based on the Lyapunov function, which resulted in a set of linear matrix inequalities for each region. The simulation results showed that the use of smart layers with robust control method and matrix inequalities in the presence of external disturbance, in addition to ensuring stochastic stability, can have satisfactory effects on reducing plate oscillations in the presence of parametric uncertainty and jumps in mechanical properties. Also, compared to the conventional PID controller, the control effort is reduced by 60%. In addition, the proposed method converges to zero at a much better speed. On the other hand, the PID method has many high-frequency oscillations, especially at the initial moments (more than 1 second), which indicates its weakness in respect to the simultaneous uncertainty, disturbance, and jump. Lastly, the validity of the model and the presented results have been compared with the results in previous articles and the appropriate convergence of the results has been demonstrated.