Bouc-Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators

A new approach to compensate the strong hysteresis nonlinearity in piezoelectric materials is proposed. Based on the inverse multiplicative scheme, the approach avoids models inversion as employed in existing works. The compensator is therefore simple to implement and does not require additional computation as soon as the direct model is available. The proposed compensation technique is valuable for hysteresis that are modeled with the Bouc-Wen set of equations. Note to Practitioners— Since many years, the hysteresis nonlinearity in piezoelectric micro/nanoactuators (AFM, microgrippers, etc.) has been moving many researchers. Despite the high resolution and the high speed of these materials, the hysteresis strongly compromises the accuracy. If feedback control laws could easily improve the performances, their use in micro/nanoactuators and small systems are constrained by the luck of convenient sensors. On the one hand, accurate and high bandwidth sensors are very expensive and bulky (accelerometers, optical sensors). On the other hand, integrable sensors are highly sensitive to noises and are very fragile (strain gage). To surpass the use of sensors, feedforward control techniques have been used. These techniques represent a great interest in an integration/package point of view but the existing methods show a complexity in term of computation and implementation. Three points have motivated the works presented in this article: 1) the need of high performances in micro/nanoactuation, 2) the shunning of the use of bulky sensors, 3) and the need of easily computable and implementable control techniques. The content of the article focuses therefore on the design of a feedforward controller (compensator) with a special concern on the ease of computation and implementation. Of course, even if we present an application to a specific piezoelectric actuator, the proposed approach is also applicable to other systems whose the hysteresis is modeled with the Bouc-Wen expression.