| The dynamic behavior of the PZT-5H Bimorph bender actuator is studied by applying driving waveforms with higher harmonics. Due to the large dynamic displacement the actuator providing at its tip, the trajectory of the actuator response is emphasized instead of stroke of the response. The mathematical model of the actuator (combined the mechanical cantilever bin and electrical model of the actuator) is derived and a computer simulation is used to describe the dynamic behavior of the actuator under different frequencies. Since both significant delay and hysteresis effect of the actuator are induced by its large capacitance and dynamic ferroelectric property, how to reduce the undesired deformation and handle the coupling between delay and hysteresis is emphasized in our research. To acquire a precise hysteresis model of the actuator independent of the system delay, the major loop and minor loop of the actuator is studied both statically and dynamically. Experimentally, an optical interferometer is employed to sense both the static and dynamic displacement of the actuator and the results are compared with the mathematical simulations. Once the precise model is acquired, an inversion-based adaptive control algorithm is employed. Since the operation system is varying with time, the plant model used in control needs to be detected continuously. The recursive Least Square method is used in dynamic system identification. A FIR filter is designed to decouple the linear and nonlinear noise and bring the response of the actuator to desired trajectory. After fundamental frequency adaptation and disturbance suppression, great improvement has been detected in the waveform tracking. Finally, the controlled piezo actuator is applied to a one-dimensional vibratory feeding system and the precision of the actuating system is analyzed. It is proved experimentally that the feeding speed of decoupled vibratory feeder can be adjusted dynamically and no hopping and backsliding are detected in the feeding process. The successful control of the narrow bandwidth actuator makes the regular piezoelectric actuator suitable in the horizontal direction vibration and therefore introduced in an economic way of design. |
