Adaptive Control of Nonlinear Free Vibration of Shallow Shell Using Piezoelectric Actuators
A coupled structural-electrical nonlinear modal finite-element multiple-mode formulation for laminated composite shallow shells with embedded piezoelectric sensors and actuators is presented for the suppression of large-amplitude undamped free vibrations. Composite shells exhibiting both softening and hardening behavior are investigated. The linear quadratic regulator combined with an extended Kalman filter is employed as an active controller for the suppression of nonlinear free vibrations. However, when the frequency of limit-cycle oscillations is suddenly changed from the softening to the hardening response characteristics or vice versa, active controller has difficulties to adjust the control parameters to cope with the changed structural response. To mitigate this issue, the currently developed controller is adaptively designed using the system identification which has the ability to identify the frequency of limit-cycle oscillations. It is shown that the adaptive controller constructed of the linear quadratic regulator and extended Kalman filter with system identification is suitable for suppression of the sudden change of shallow-shell response characteristics. The norm of optimal feedback control gain method for actuators and the norm of Kalman filter estimator gain method for sensors are employed to determine their optimal locations, respectively. Two different self-sensing actuator types, PZT5A and macrofiber composite, are used and their control performance for the suppression of the oscillations is compared. The numerical results illustrate that the adaptive controller can successfully suppress the nonlinear free vibrations, even with unknown sudden changes in the multimode response characteristic.