Controller design for the Vector Control of Piezoelectric transducers

Abstract:
The Vector Control Method applied to piezoelectric transducers is a promising way to track the resonance frequency as well as to control the vibration speed. Similar to the modulation-demodulation techniques, the (d,q) transformation applied here takes advantage of the recent advances in microcontrollers. Moreover, engineers can make a bridge between the control of brushless DC motors and piezoelectric actuators and two simple PI controllers, one for each axis are tuned in order to precisely control the vibration amplitude components in axis d and axis q. This paper presents the procedure to tune the PI controllers. First, the model in the rotating reference frame is given. A procedure, based on the LQR approach, is used to calculate the parameters of the PI controllers based on the desired closed loop response time. In the (d,q) reference frame, the second order type response of the system becomes two first order systems, coupled if the system is operated outside its resonance. By taking into account these couplings, the closed loop system can be accelerated, yet ensuring stable operation. In addition to the control, environment’s acoustic impedance can be derived, on line. Finally, we present experimental results, obtained on a haptic display. The model and the measures are consistent, and confirms the approach: the vibration amplitude can be tuned with a response time less than 10ms.