In this paper, large amplitude vibration control of functionally graded material (FGM) plates under thermal gradient and transverse mechanical loads using integrated piezoelectric sensor/actuator layers is investigated. In this regard, finite element formulation based on higher order shear deformation plate theory is developed. The von Karman nonlinear strain-displacement relationship is used to account for the large deflection of the plate. The material properties of FGM are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The temperature field is assumed to be constant in the plane and varied only in the thickness direction of the plate. In order to control the large amplitude vibration of the plate, two control algorithms are employed: classical displacement-velocity feedback control and robust H2 control. Also, the uncertainty which arises from external disturbances (low-frequency sine-wave sensor noise and high-frequency Gaussian white sensor noise) is considered. Active control of both the static deflection due to thermal gradient and dynamic oscillation is studied. Numerical results are presented to investigate the effectiveness of the mentioned control algorithms to control nonlinear vibration and thermally induced deflection of the FGM plate. Also, robustness of the controllers in the face of sensor noise is investigated. Effects of the design parameters on performance of each controller are studied and finally, the two control methods are compared.

In this study, the effectiveness of an active engine mount in vibration suppression of a four-cylinder engine is evaluated. Two robust control algorithms, namely H2 and H∞ schemes, are employed to provide control input using accelerations of the engine body in the position of the mounts. In this regard, an accurate engine model is presented and the exciting active engine mount model is employed to design robust controllers. Derivation of equations of motion for an engine on the mounts is performed using Lagrange's and Newton–Euler equations. This derivation of equations has not been presented in any other study. In addition, unstructured uncertainties due to the unmodeled dynamics of the plant, actuator and sensors are considered. Using appropriate weighting functions, two robust control algorithms are designed. Robust stability and robust performance of the proposed controllers are evaluated using µ-analysis. The effectiveness of the proposed controllers, in the presence of sensor noise, in vibration suppression of the engine is evaluated. Results show that active mount with the designed robust controllers can improve the vibration behavior of the engine in the presence of sensor noise.

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In this study, a robust adaptive control method is employed for an active engine mount in a six-degree-of-freedom model of the engine on the mounts to improve vibration behavior of the engine. The vibration isolation performance and robustness of the employed robust adaptive controller are compared with a robust and an adaptive control technique. In addition, effectiveness of the robust adaptive control is evaluated in transient conditions (accelerating and gear change conditions). In this regard, a dynamic model for the engine supported by rubber and active mounts and its governing equations are presented. Then, a robust adaptive control, namely the robust Model Reference Adaptive Control (robust MRAC) technique, based on the gradient method with σ-modification, is designed by selecting a proper reference model. Moreover, a robust control, namely the H∞ control scheme and an adaptive control, namely MRAC, are employed for the active mount. Simulation results show that the robust MRAC has a better control performance (in reducing the transmitted force to the chassis) as compared with the H∞ scheme. In addition, in the face of large uncertainties, MRAC may diverge and become unstable. However, the robust MRAC is robust in the presence of large uncertainties. Also, robust MRAC is effective not only in constant engine speeds, but also in transient conditions.