It has been popular for decades that the vibrations of space structures are suppressed with smart actuators. However, the higher mode vibrations are often motivated when a control strategy is applied to attenuate the vibration for the smart structures. Moreover, if the multi-mode vibration of a smart structure is suppressed with multi-actuators, a proper multivariable control law will be adopted to solve the coupling problem caused by the multi-actuators of the smart structure. Therefore, in the paper, a decoupling technique for two modal vibrations of a smart flexible beam with two piezoelectric patches is adopted by adaptive control. The proposed control law is designed with a multivariable minimum variance self-tuning control. Considering the first two orders of modal vibrations, two piezoelectric patches are configured on the flexible beam according to the strain of the first two orders of modal vibrations along the longitudinal direction of the beam. A dynamical model for the flexible beam with two piezoelectric actuators is constructed by the mode superposition method. With the dynamical model, simulations are implemented to suppress the free vibration of the flexible beam. Moreover, experiments are carried out to verify the effectiveness of the multivariable minimum variance self-tuning control for vibration suppression of the flexible structure. The control results clearly show that the free vibration amplitude of the cantilevered beam with two control voltages applied to the two piezoelectric patches is less than that with one control voltage applied to the first piezoelectric actuator. Thus, multivariable minimum variance self-tuning control is a more efficient approach for suppressing multimodal vibration for a smart flexible beam with two piezoelectric actuators compared with the conventional velocity feedback control.

中文翻译：

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带有两个压电执行器的智能挠性梁的自适应模态振动控制

几十年来，使用智能致动器抑制空间结构的振动已经很普遍。但是，当应用控制策略来衰减智能结构的振动时，通常会激发较高模式的振动。此外，如果用多执行器抑制智能结构的多模振动，则将采用适当的多变量控制律来解决由智能结构的多执行器引起的耦合问题。因此，在本文中，通过自适应控制采用具有两个压电片的智能柔性梁的两种模态振动的解耦技术。所提出的控制律采用多变量最小方差自整定控制进行设计。考虑到模态振动的前两个阶，根据沿梁的纵向的前两个模态振动的应变，在柔性梁上配置两个压电贴片。通过模式叠加法建立了带有两个压电致动器的柔性梁的动力学模型。使用动力学模型，可以执行仿真来抑制柔性梁的自由振动。此外，进行了实验以验证多变量最小方差自整定控制对于抑制柔性结构的有效性。控制结果清楚地表明，向两个压电片施加两个控制电压的悬臂梁的自由振动幅度小于向第一压电致动器施加一个控制电压的悬臂梁的自由振动幅度。从而，