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The inherent nonlinearities of piezoelectric actuator (PEA), especially hysteresis, greatly reduce the tracking performance of PEA. With a lot of computing resources consumed in the predicting process, the hysteresis modeling method of PEA based on the least-squares support vector machine (LSSVM) cannot be used for hysteresis compensation at high frequency. To solve this problem, a sequential selection approximate algorithm is proposed to obtain a fast sparse LSSVM (SLSSVM) hysteresis model. The SLSSVM model’s support vectors are only 6.8% of the original LSSVM model, by which the modeling speed and calculation speed are greatly improved. The experimental results show that the SLSSVM model improves the tracking accuracy when used in hybrid control system, especially for high frequency trajectories.

A temperature-dependent asymmetric Prandtl-Ishlinskii (TAPI) model is developed to describe changes in hysteresis curves with respect to temperature found in the displacement curves vs. input voltage of a piezoelectric actuator (PEA). The proposed modeling scheme considers nonlinearities in an idealized capacitor term in the electromechanical model of the PEA to introduce both asymmetry and temperature dependence in the model. The developed model has the advantage of incorporating asymmetric and thermal effects in a hysteresis-free region of the model which simplifies inversion of the model as well as parameter determination. A parameter identification scheme is described to simplify model identification, even for a large number of thresholds, based on the advantages of the classical Prandtl-Ishlinskii model. The TAPI model is verified experimentally and a compensator is designed to demonstrate that the PEA output is effectively linearized throughout the temperature range.

In this paper, a hybrid control algorithm is proposed to control the rotation of a flexible beam while suppressing the beam's vibration. The control law combines an enhanced PD feedback with a nonlinear differentiator to derive a high-quality velocity signal to control the gross motion of the beam, and a vibration control by PZT actuators bonded on the surface of the beam. There are three advantages of the proposed method: (i) the enhanced PD control is model free, and appears to be more robust against the noise; (ii) the linear velocity rather than the angular velocity is used in the PZT actuator control, a signal which is easily available; (iii) a unique solution is provided for examination of the actuator placement, based on the analysis of mode shape functions. Experimental results validate these theoretical analyses.

This paper presents a systematic control system design for nano-positioning of a piezoelectric actuator (PEA). PEAs exhibit hysteresis nonlinearity, which can dramatically limit the application and performance of linear feedback control theory. Thus the hysteresis is compensated for based on the Maxwell resistive capacitor (MRC) model first. Then a proportional plus integral (PI) controller and a proportional double integral plus lead compensation (PII&L) controller are designed for the hysteresis-compensated PEA to account for model uncertainty, disturbance, and noise. The robust stability of both controllers is proved. The effectiveness of the proposed control scheme is demonstrated experimentally. Both controllers achieve fast precise positioning. The 2% settling times for the PI controller and the PII&L controller are 1.5 ms and 4.7 ms, respectively. The positioning resolution is upto 1 nm for both controllers.

This paper proposes a robust output feedback controller for a piezoelectrically actuated system with only position sensor. This considered piezoelectric actuator (PEA) system is subjected to model imperfection, creep nonlinearity, hysteresis nonlinearity and other external effects. The designed controller employs a second-order auxiliary system and a discontinuous uncertainty and disturbance estimation term to generate filtered error signals and to compensate for the model uncertainties and system disturbance, respectively. The global stability of the proposed controller is proved through Lyapunov-based stability analysis. The feasibility and effectiveness of the proposed control approach are verified experimentally using a PEA stage. Results demonstrate that both set-point and tracking control without/with external loads are realized with good performance and the PEA system with high-accuracy can be achieved. Moreover, the robustness of the controller is verified and analyzed through the sinusoidal tracking with external disturbance.

This paper presents the control system design for a piezoelectric actuator (PEA) for a high-speed trajectory scanning application. First nonlinear hysteresis is compensated for by using the Maxwell resistive capacitor model. Then the linear dynamics of the hysteresis-compensated piezoelectric actuator are identified. A proportional plus integral (PI) controller is designed based on the linear system, enhanced by feedforward hysteresis compensation. It is found that the feedback controller does not always improve tracking accuracy. When the input frequency exceeds a certain value, feedforward control only may result in better control performance. Experiments are conducted, and the results demonstrate the effectiveness of the proposed control approach.

This paper focuses on the dynamics and control of piezoactuators (PEAs) for high-speed large-range scanning applications. Firstly, the nonlinear hysteresis is modeled by using a modified Maxwell resistive capacitor (MRC) model. Secondly, an inverse-based feedforward controller is proposed for this application with hysteresis compensation. Then, the scanning trajectories are preshaped by treating the hysteresis-compensated PEA as a linear system. Finally, experiments are conducted to verify the effectiveness of the proposed approaches.

A physics-based fractional-order Maxwell resistive capacitor (FOMRC) model is proposed to characterize nonlinear hysteresis and creep behaviors of a piezoelectric actuator (PEA). The Maxwell resistive capacitor (MRC) model is interpreted physically in the electric domain for PEAs. Based on this interpretation, the MRC model is modified to directly describe the relationship between the input voltage and the output displacement of a PEA. Then a procedure is developed to identify the parameters of the MRC model. This procedure is capable of being carried out using the measured input and output of a PEA only. A fractional-order dynamics is integrated into the MRC model to describe the effect of creep, as well as the detachment of hysteresis loops caused by creep. Moreover, the inverse FOMRC model is constructed to compensate for hysteresis and creep in an open-loop positioning application of PEAs. Simulation and experiments are carried out to validate the proposed model. The PEA compensated by the inverse FOMRC model shows an excellent linear behavior. (Some figures may appear in colour only in the online journal)

A genetic algorithm is implemented to identify the transfer function of an experimental system consisting of a flexible manipulator with a collocated piezoelectric sensor/actuator pair. A multi-mode positive position feedback controller is then designed based upon the identified transfer function. To this end, the same iteratively implemented genetic algorithm is used to optimize all controller parameters by minimization of the closed loop H?-norm. The designed controller is then applied for vibration suppression on the experimental system.