Continuous dynamic modelling of bimorph piezoelectric cantilevered actuators considering hysteresis effect and dynamic behaviour analysis

Journal of Vibration and Control

Taghvaeipour

2020

Piezoelectric bending actuators have been widely used in a variety of micro- and nano-applications, including atomic force microscopy, micro assembly, cell manipulation, and in general, micro electromechanical systems. However, their control algorithms at low frequencies suffer from nonlinearities such as hysteresis in high voltages and creep in long-time static applications. Also, in high-frequency applications, especially near the actuator natural frequencies, the actuator dynamic is greatly affected by the material nonlinearity. Therefore, the control approaches based on the linear dynamic modeling cannot be effective at high frequencies. Thus, the position control of the foregoing actuators become challenging, and it has been of researchers’ interests in the last decade. In this article, the robust position control of a bimorph piezoelectric bending actuators is investigated. In this regard, based on the nonlinear constitutive equations and the Euler–Bernoulli beam theory, a nonlinear dynamic model is presented. Then, to track a desired motion trajectory, an observer-based robust position control algorithm is proposed. The proposed control methodology is able to accommodate parametric uncertainties and other un-modeled dynamics. Also, it ensures the elimination of the position tracking error in the presence of the estimated states. Finally, the tracking ability of the controller is demonstrated in an experimental study. The experimental results show that the identification of the system is properly conducted with the average error of 5.5%. Also, the efficiency of the robust controller is proved with the error of 3.7% and 4.9% in the position tracking of the actuator inside and outside of the identified region, respectively.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

High-frequency robust position control of a nonlinear piezoelectric bending actuator

Shahabi

Journal of Vibration and Control

Taghvaeipour

2020

“…However, their performance suffers from the effect of hysteresis non-linearity. This non-linear characteristic makes the control process a challenging problem (Ghafarirad et al, 2014). Several open- and closed-loop control schemes have been proposed for piezoelectric micropositioning (Ang et al, 2007; Xu and Li, 2010).…”

Section: Introductionmentioning

confidence: 99%

Modified robust external force control with disturbance rejection with application to piezoelectric actuators

Transactions of the Institute of Measurement and Control

Rezaei

Sarhan

et al. 2014

In micromanipulation applications, controlling the force exerted on the object is of great importance. In such cases, any uncontrolled forces may damage the object or cause system failure. However, the presence of disturbances such as impedance uncertainties and hysteresis can strongly degrade force control performance and even lead to instability. Therefore, accurate force control when internal and external disturbances occur is a significant challenge. Conventional control methods usually have a number of restrictive conditions especially on the disturbance bounds. To rectify those issues, a modified robust disturbance rejection-based force control approach is proposed in this paper. For this purpose, an appropriate disturbance observer is utilized to estimate the disturbance effect regardless of amplitude. Then a robust control method is employed to achieve the disturbance-free desired dynamic. A modification is also performed to rectify the need for acceleration measurement in the control design. Finally, the force control for an unknown environment in the presence of disturbances is accomplished. The efficiency of the proposed approach is evaluated through simulation studies and compared with the well-known PI method. The experimental results validate the force control performance for the micropositioning piezoelectric actuator.

Nonlinear vibration analysis of piezoelectric bending actuators: Theoretical and experimental studies

Shahabi

Comptes Rendus. Mécanique

Taghvaeipour

2019

Piezoelectric bimorph actuators are used in a variety of applications, including micro positioning, vibration control, and micro robotics. The nature of the aforementioned applications calls for the dynamic characteristics identification of actuator at the embodiment design stage. For decades, many linear models have been presented to describe the dynamic behavior of this type of actuators; however, in many situations, such as resonant actuation, the piezoelectric actuators exhibit a softening nonlinear behavior; hence, an accurate dynamic model is demanded to properly predict the nonlinearity. In this study, first, the nonlinear stress-strain relationship of a piezoelectric material at high frequencies is modified. Then, based on the obtained constitutive equations and Euler-Bernoulli beam theory, a continuous nonlinear dynamic model for a piezoelectric bending actuator is presented. Next, the method of multiple scales is used to solve the discretized nonlinear differential equations. Finally, the results are compared with the ones obtained experimentally and nonlinear parameters are identified considering frequency response and phase response simultaneously. Also, in order to evaluate the accuracy of the proposed model, it is tested out of the identification range as well.