Inverse Rate-Dependent Prandtl-Ishlinskii Model for Feedforward Compensation of Hysteresis in a Piezomicropositioning Actuator

• Published in: IEEE/ASME transactions on mechatronics Vol. 18; no. 5; pp. 1498 - 1507
• Main Authors: Al Janaideh, M., Krejci, P.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2013; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Control systems; Control theory; Excitation; Feedback control; Feedforward; Feedforward neural networks; Frequency control; Hysteresis; inverse control; Mathematical model; Nanostructure; Nonlinearity; Numerical models; piezomicropositioning actuator; Prandtl-Ishlinskii; rate dependent
• ISSN: 1083-4435; 1941-014X
• DOI: 10.1109/TMECH.2012.2205265

Piezomicropositioning actuators, which are widely used in micropositioning applications, exhibit strong rate-dependent hysteresis nonlinearities that affect the accuracy of these micropositioning systems when used in open-loop control systems, and may also even lead to system instability of closed-loop control systems. Feedback control techniques could compensate for the rate-dependent hysteresis in piezomicropositioning actuators. However, accurate sensors over a wide range of excitation frequencies and the feedback control techniques inserted in the closed-loop control systems may limit the use of the piezomicropositioning and nanopositioning systems in different micropositioning and nanopositioning applications. We show that open-loop control techniques, also called feedforward techniques, can compensate for rate-dependent hysteresis nonlinearities over different excitation frequencies. An inverse rate-dependent Prandtl-Ishlinskii model is utilized for feedforward compensation of the rate-dependent hysteresis nonlinearities in a piezomicropositioning stage. The exact inversion of the rate-dependent model holds under the condition that the distances between the thresholds do not decrease in time. The inverse of the rate-dependent model is applied as a feedforward compensator to compensate for the rate-dependent hysteresis nonlinearities of a piezomicropositioning actuator at a range of different excitation frequencies between 0.05-100 Hz. The results show that the inverse compensator suppresses the rate-dependent hysteresis nonlinearities, and the maximum positioning error in the output displacement at different excitation frequencies.