Piezoelectric actuators are gradually playing an important role in precision positioning applications due to their extremely fine resolution, fast responses, and large actuating forces. However, the existence of hysteresis behaviors makes a big influence on their positioning accuracies. To get high positioning accuracies, hysteresis modeling and control of piezoelectric actuators are meaningful and necessary. This paper reviews different models and control approaches of piezoelectric actuators. Novel categories of both hysteresis models and control approaches are presented. Furthermore, comparisons of different hysteresis models reveal that rate-dependent differential-based modeling is the future research focus. Comparisons of control approaches of piezoelectric actuators are presented and feedforward-feedback control and feedback control are the emphasis in the future.

Hysteresis behaviors exist in piezoelectric ceramics actuators (PCAs), which degrade the positioning accuracy badly. The classical Bouc–Wen (CB–W) model is mainly used for describing rate-independent hysteresis behaviors. However, it cannot characterize the rate-dependent hysteresis precisely. In this paper, a generalized Bouc–Wen (GB–W) model with relaxation functions is developed for both rate-independent and rate-dependent hysteresis behaviors of piezoelectric actuators. Meanwhile, the nonlinear least squares method through MATLAB/Simulink is adopted to identify the parameters of hysteresis models. To demonstrate the validity of the developed model, a number of experiments based on a 1-DOF compliant mechanism were conducted to characterize hysteresis behaviors. Comparisons of experiments and simulations show that the developed model can describe rate-dependent and rate-independent hysteresis more accurately than the classical Bouc–Wen model. The results demonstrate that the developed model is effective and useful.

A classical Bouc-Wen model is widely applied in hysteresis modeling and compensation for piezoelectric ceramic actuators. However, the classical Bouc-Wen model cannot characterize rate-dependent hysteresis under excitations at high frequencies precisely. In this paper, an enhanced Bouc-Wen model is developed by introducing the frequency of input voltage based on the classical Bouc-Wen model. A number of experiments were conducted to characterize the rate-dependent hysteresis of piezoelectric ceramic actuators under sinusoidal excitations at a range of 1–150 Hz. The measured data were used to demonstrate the validity of the developed model. A method of parameter estimation based on the Matlab/Simulink parameter estimation tool is adopted to identify the parameters of models. The comparisons of experiments and simulations show that the developed model can describe rate-dependent hysteresis more accurately than the classical Bouc-Wen model. The modeling errors of the developed model were decreased by nearly 75% compared with that of the classical Bouc-Wen model. The root-mean-square error of the developed model is controlled in 0.1719 μm.

In this paper, a generalized hysteresis model is developed to describe both rate-independent and rate-dependent hysteresis in piezoelectric actuators. Based on the classical Prandtl-Ishlinskii (P-I) model, the developed model adds a quadratic polynomial and makes other small changes. When it is used to describe rate-independent hysteresis, the parameters of the model are constants, which can be identified by self-adaptive particle swarm optimization. The effectiveness of this rate-independent modified P-I model is demonstrated by comparing simulation results of the developed model and the classic Prandtl-Ishlinskii model. Simulation results suggest that the rate-independent modified P-I model can describe hysteresis more precisely. Compared with the classical P-I model, the rate-independent modified P-I model reduces modeling error by more than 50%. When it is used to describe rate-independent hysteresis, a one-side operator is adopted and the parameters are functions with input frequency. The results of the experiments and simulations have shown that the proposed models can accurately describe both rate-independent and rate-dependent hysteresis in piezoelectric actuators.

Hysteresis behaviors are inherent characteristics of piezoelectric ceramic actuators. The classical Duhem model (CDM) as a popular hysteresis model has been widely used, but cannot precisely describe rate-dependent hysteresis behaviors at high-frequency and high-amplitude excitations. To describe such behaviors more precisely, this paper presents a modified Duhem model (MDM) by introducing trigonometric functions based on the analysis of the existing experimental data. The MDM parameters are also identified by using the nonlinear least squares method. Six groups of experiments with different frequencies or amplitudes are conducted to evaluate the MDM performance. The research results demonstrate that the MDM can more precisely characterize the rate-dependent hysteresis behaviors comparing with the CDM at high-frequency and high-amplitude excitations.

We propose a high-quality imaging method based on correspondence imaging (CI) using a sorting and compressive sensing (CS) technique. Unlike the traditional CI, the positive and negative (PN) subsets are created by a sorting method, and the image of an object is then recovered from the PN subsets using a CS technique. We compare the performance of the proposed method with different ghost imaging (GI) algorithms using the data from a single-detector computational GI system. The results demonstrate that our method enjoys excellent imaging and anti-interference capabilities, and can further reduce the measurement numbers compared with the direct use of CS in GI.

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