Proc. SPIE. 8418, 6th International Symposium on Advanced Optical Manufacturing and Testing Technologies: Design, Manufacturing, and Testing of Smart Structures, Micro- and Nano-Optical Devices, and Systems
KEYWORDS: Mathematical modeling, Actuators, Data modeling, Error analysis, Adaptive optics, Control systems, Data acquisition, Dynamical systems, Feedback control, Optics manufacturing
Piezo-electric actuators with advantage of fast responsiveness, large force output, low power consumption, negligible
friction and no backlash are widely used in precision positioning, adaptive optics and vibration conduction. However its inherent hysteresis brings difficulty to high precision positioning. To describe the hysteresis, a mathematical model based on experimental data is used. And the inverse of the model is connected to the piezo-electric actuator as a controller to compensating the hysteresis. In this paper KP operator is used to model the hysteresis of piezo-electric actuators and a numerical algorithm is proposed to compute the inverse. Experiments data of major hysteresis loop and minor loop collected on a nano-positioning stage are used to identify the model Γ based on which the inverse model Γ-1 is developed. Experiments show that given a voltage series the model Γ can give displacement prediction which has an error of 6% relative to experimental results and Γ-1 can give voltage prediction with the error of 5% relative to the experimental data.