A novel time dependent Prandtl-Ishlinskii model for sensorless hysteresis compensation in piezoelectric actuators

Piezoelectric actuators are widely used for micromanipulation processes. High natural frequency, fine resolution and also response time are piezoelectric special properties. But the main problem is with the hysteresis nonlinear behavior which degrades its performance. Several hysteresis models have been proposed for hysteresis identification and compensation. The necessity of precise and high cost position sensors is the main drawback in hysteresis estimation. In this paper, it is analytically shown that the hysteresis compensation in mechanical domain (Voltage-Position) can be concurrently achieved by hysteresis compensation in electrical domain (Voltage-Charge). But hysteresis in electrical domain can be more complicated rather than mechanical one due to the time dependent behavior which is called "Active Hysteresis". In fact, the output charge includes the main hysteresis compounded with an increasing behavior. As a result, conventional models cannot identify the hysteresis behavior. In this paper, a new active Prandtl-Ishlinskii model is proposed for active hysteresis estimation. This model can estimate the increasing output trend with the main hysteresis behavior, simultaneously. Experimental results confirm that the proposed model successfully estimate the time dependent hysteresis and also compensate it. It is shown that hysteresis in mechanical domain would also be compensated by this approach.