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Structural Engineering and Mechanics
  Volume 29, Number 5, July30 2008 , pages 489-504

Modal-based model reduction and vibration control for uncertain piezoelectric flexible structures
Xu Yalan and Chen Jianjun

    In piezoelectric flexible structures, the contribution of vibration modes to the dynamic response of system may change with the location of piezoelectric actuator patches, which means that the
ability of actuators to control vibration modes should be taken into account in the development of modal reduction model. The spatial H2 norm of modes, which serves as a measure of the intensity of modes to
system dynamical response, is used to pick up the modes included in the reduction model. Based on the reduction model, the paper develops the state-space representation for uncertain flexible structures with
piezoelectric material as non-collocated actuators/sensors in the modal space, taking into account uncertainties due to modal parameters variation and unmodeled residual modes. In order to suppress the vibration of the structure, a dynamic output feedback control law is designed by simultaneously considering the conflicting performance specifications, such as robust stability, transient response requirement, disturbance rejection, actuator saturation constraints. Based on linear matrix inequality, the vibration control design is converted into a linear convex optimization problem. The simulation results show how the influence of vibration modes on the dynamical response of structure varies with the location of piezoelectric actuators, why the uncertainties should be considered in the reductiom model to avoid exciting high-frequency modes in the non-collcated vibration control, and the possiblity that the conflicting performance specifications are dealt with simultaneously.
Key Words
    spatial norm of modes; uncertain flexible structures; vibration control.
Xu Yalan and Chen Jianjun: School of Electronic & Mechanical Engineering, Xidian University, Xi?an 710071, P.R. China

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