This paper presents an implementation of a robust control LQG-Kalman model applied to composite Kirchhoff plate dynamics. A reduced model of a finite element method and control procedure is considered in the modeling of a structure because of the important number of piezoelectric patches used in control. Replacing the full model with a short model reduces the computational and time costs, especially when the number of degrees of freedom is significant. In robust control, the measurement of all states is not necessary and the observability and estimability criteria can be exploited, while conventional LQR control assumes that the data accessibility of all states is available. For this reason, robust control is proposed to control the random external disturbances and is compared to LQR control to illustrate its practicability and efficiency. The sensors and actuators in the thermo-piezoelectric material are randomly distributed on both sides of the plate to establish the control procedure. A Monte Carlo simulation is used in the selection of the degrees of freedom of sensors presenting high electrical outputs. Numerical simulations are performed to demonstrate the effectiveness of the proposed control procedure in a reduced model and under mechanical and thermal disturbances in comparison with the LQR control.

Considerable attention has been given to the study of the propagation of surface waves in order to improve the efficiency and lifetime of the surface acoustic wave devices such as transducers. In this paper, an investigation of the Rayleigh waves in functionally graded piezoelectric material is presented. The Rayleigh surface wave propagation is assumed to take place in a transversely isotropic graded piezoelectric half-space with material properties varying continuously along the thickness direction. The obtained results have shown that dispersive Rayleigh waves can propagate on the surface of the FGPM half-space with characteristics that depend on the graded variation of the material parameters. Based on the dispersion relations, the phase velocity for both the electrically open and shorted cases at the free surface is deduced. The displacement magnitudes and the corresponding decay variations are plotted and discussed.

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The present contribution presents a comparison between two types of controls, namely, the optimal linear quadratic regulator (LQR) and the Kalman-LQG controller using the model order reduction process. Due to numerical constraints, the models of structures have been reduced so that the design of controllers and/or estimators could be performed. The proposed method results in a significant reduction in computational costs for dynamic analysis without compromising on accuracy. Transforming the full order state-space resulting from finite element space to a lower model reduces the simulation time with a few degrees of freedom and helps to implement easily the control without changes in the dynamics of the structure. The estimator Kalman is used here in order to estimate the modal states of the system that are used in modal analysis. In this context, a one-side cantilever Timoshenko beam is chosen with perfectly bonded piezoelectric layers of actuators and sensors to apply this comparison. The Monte Carlo simulation was used to improve the number and location selection of piezoelectric sensors on the chosen beam model. Neglecting environmental effects, numerical results relating to this comparison without and with model order reduction are established. Simulation results are presented to illustrate the effectiveness of the proposed vibration control algorithm for the studied beam.

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