Modeling and Compensation for Asymmetrical and Dynamic Hysteresis of Piezoelectric Actuators Using a Dynamic Delay Prandtl–Ishlinskii Model

Piezoelectric actuators are widely used in micro- and nano-manufacturing and precision machining due to their superior performance. However, there are complex hysteresis nonlinear phenomena in piezoelectric actuators. In particular, the inherent hysteresis can be affected by the input frequency, and it sometimes exhibits asymmetrical characteristic. The existing dynamic hysteresis model is inaccurate in describing hysteresis of piezoelectric actuators at high frequency. In this paper, a Dynamic Delay Prandtl–Ishlinskii (DDPI) model is proposed to describe the asymmetrical and dynamic characteristics of piezoelectric actuators. First, the shape of the Delay Play operator is discussed under two delay coefficients. Then, the accuracy of the DDPI model is verified by experiments. Next, to compensate the asymmetrical and dynamic hysteresis, the compensator is designed based on the Inverse Dynamic Delay Prandtl–Ishlinskii (IDDPI) model. The effectiveness of the inverse compensator was verified by experiments. The results show that the DDPI model can accurately describe the asymmetrical and dynamic hysteresis, and the compensator can effectively suppress the hysteresis of the piezoelectric actuator. This research will be beneficial to extend the application of piezoelectric actuators.

Stress-dependent generalized Prandtl–Ishlinskii hysteresis model of a NiTi wire with superelastic behavior

The extremely useful superelastic behavior of NiTi has been poorly explored because of the limited number of models that can describe the complete hysteretic behavior of NiTi, including a superelastic condition that strongly depends on the applied stress. This paper presents the development of a stress-dependent phenomenological model of NiTi by modifying the existing generalized Prandtl–Ishlinskii (GPI) model. The parameters of the envelop function of the GPI model’s play operator are reformulated as quadratic functions of the applied stress. The stress-dependent GPI model can satisfactorily predict the output strain of a NiTi #6 wire under temperature and stress variation.

On forward and inverse uncertainty quantification for models involving hysteresis operators

Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters.

Multidimensional play operators with arbitrary BV inputs

In this paper we provide an integral variational formulation for a vector play operator where the inputs are allowed to be arbitrary functions with (pointwise) bounded variation, not necessarily left or right continuous. We prove that this problem admits a unique solution, and we show that in the left continuous and right continuous cases it reduces to the well known existing formulations.

Hysteresis and controllability of affine driftless systems: some case studies

We investigate the controllability of some kinds of driftless affine systems where hysteresis effects are taken into account, both in the realization of the control and in the state evolution. In particular we consider two cases: the one when hysteresis is represented by the so-called play operator, and the one when it is represented by a so-called delayed relay. In the first case we prove that, under some hypotheses, whenever the corresponding non-hysteretic system is controllable, then we can also, at least approximately, control the hysteretic one. This is obtained by some suitably constructed approximations for the inputs in the hysteresis operator. In the second case we prove controllability for a generic hysteretic delayed switching system. Finally, we investigate some possible connections between the two cases.

Asymmetrically Dynamic Coupling Hysteresis in Piezoelectric Actuators: Modeling Identification and Experimental Assessments

An asymmetrically dynamic coupling hysteresis (ADCH) model is proposed as an extension of the Prandtl–Ishlinskii (PI) model to characterize the hysteretic nonlinearities in piezoelectric actuators (PEAs). When subject to two-input: dynamic excitation and external loads. In this model, the developed asymmetrically one-side play operator helps to represent the saturation, nonlinearity, and centrally asymmetric properties of PEAs employed inverse hyperbolic envelope functions. The dynamic threshold functions are put in place to characterize the width of rate-dependent hysteresis property. Introductions of continuously coupled density functions are beneficial to the cross-coupled hysteresis behaviors of external load/excitation voltage-to-expansion. Besides, the proposed ADCH model is verified to satisfy indeed the wiping-out property and equal vertical chords property, which means that it can be regarded as well-suited in modeling the complicated hysteresis nonlinearity of PEAs. Furthermore, this paper also tackles the identification issue of the proposed ADCH model by using a global research method, which possesses satisfactory accuracy without strict requirements for the initially iterative value.

Modeling, identification and compensation of hysteresis nonlinearity for a piezoelectric nano-manipulator

Hysteresis nonlinearity widely exists in piezoelectric actuated nano-positioning applications, which degrades their tracking accuracy and limits their precision positioning applications. This paper presents a novel hysteresis modeling and compensation approach to alleviate the adverse effect of the asymmetric and rate-dependent hysteresis nonlinearity for a piezoelectric transducer actuated servo stage. By integrating a generalized input function with the play operator of the classical Prandtl–Ishlinskii model, a novel polynomial-based rate-dependent Prandtl–Ishlinskii (PRPI) model is proposed to capture the hysteresis behavior of the piezoelectric positioning stage, where a polynomial function of input and a time rate function of input are introduced to formulate the generalized input function. Meanwhile, a new adaptive differential evolution optimization algorithm is developed to identify the parameters of the proposed PRPI hysteresis model. Based on the PRPI hysteresis model with the identified parameters, an inverse feedforward controller is constructed to achieve the accurate tracking motion. Furthermore, the hysteresis compensation error of the proposed PRPI model is theoretically analyzed. Finally, comparative experiments are conducted, and the experimental results provided in this paper demonstrate the effectiveness and superiority of the proposed inverse PRPI model compensation approach.