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Structural Engineering and Mechanics Volume 43, Number 2, July25 2012 , pages 163-177 DOI: https://doi.org/10.12989/sem.2012.43.2.163 |
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Fuzzy control for geometrically nonlinear vibration of piezoelectric flexible plates |
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Yalan Xu and Jianjun Chen
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| Abstract | ||
| This paper presents a LMI(linear matrix inequality)-based fuzzy approach of modeling and active vibration control of geometrically nonlinear flexible plates with piezoelectric materials as actuators and sensors. The large-amplitude vibration characteristics and dynamic partial differential equation of a piezoelectric flexible rectangular thin plate structure are obtained by using generalized Fourier series and numerical integral. Takagi-Sugeno (T-S) fuzzy model is employed to approximate the nonlinear structural system, which combines the fuzzy inference rule with the local linear state space model. A robust fuzzy dynamic output feedback control law based on the T-S fuzzy model is designed by the parallel distributed compensation (PDC) technique, and stability analysis and disturbance rejection problems are guaranteed by LMI method. The simulation result shows that the fuzzy dynamic output feedback controller based on a two-rule T-S fuzzy model performs well, and the vibration of plate structure with geometrical nonlinearity is suppressed, which is less complex in computation and can be practically implemented. | ||
| Key Words | ||
| geometrical nonlinearity; piezoelectric flexible plate; T-S fuzzy model; output feedback control; LMI | ||
| Address | ||
| Yalan Xu and Jianjun Chen: School of Electronic & Mechanical Engineering, Xidian University, Xi | ||