This paper presents a novel real-time inverse hysteresis compensation method for piezoelectric actuators exhibiting asymmetric hysteresis effect. The proposed method directly utilizes a modified Prandtl-Ishlinskii hysteresis model to characterize the inverse hysteresis effect of piezoelectric actuators. The hysteresis model is then cascaded in the feedforward path for hysteresis cancellation. It avoids the complex and difficult mathematical procedure for constructing an inversion of the hysteresis model. For the purpose of validation, an experimental platform is established. To identify the model parameters, an adaptive particle swarm optimization algorithm is adopted. Based on the identified model parameters, a real-time feedforward controller is implemented for fast hysteresis compensation. Finally, tests are conducted with various kinds of trajectories. The experimental results show that the tracking errors caused by the hysteresis effect are reduced by about 90%, which clearly demonstrates the effectiveness of the proposed inverse compensation method with the modified Prandtl-Ishlinskii model.

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This paper presents the design, analysis, and testing of a parallel-kinematic high-bandwidth XY nanopositioning stage driven by piezoelectric stack actuators. The stage is designed with two kinematic chains. In each kinematic chain, the end-effector of the stage is connected to the base by two symmetrically distributed flexure modules, respectively. Each flexure module comprises a fixed-fixed beam and a parallelogram flexure serving as two orthogonal prismatic joints. With the purpose to achieve high resonance frequencies of the stage, a novel center-thickened beam which has large stiffness is proposed to act as the fixed-fixed beam. The center-thickened beam also contributes to reducing cross-coupling and restricting parasitic motion. To decouple the motion in two axes totally, a symmetric configuration is adopted for the parallelogram flexures. Based on the analytical models established in static and dynamic analysis, the dimensions of the stage are optimized in order to maximize the first resonance frequency. Then finite element analysis is utilized to validate the design and a prototype of the stage is fabricated for performance tests. According to the results of static and dynamic tests, the resonance frequencies of the developed stage are over 13.6 kHz and the workspace is 11.2 μm × 11.6 μm with the cross-coupling between two axes less than 0.52%. It is clearly demonstrated that the developed stage has high resonance frequencies, a relatively large travel range, and nearly decoupled performance between two axes. For high-speed tracking performance tests, an inversion-based feedforward controller is implemented for the stage to compensate for the positioning errors caused by mechanical vibration. The experimental results show that good tracking performance at high speed is achieved, which validates the effectiveness of the developed stage.

In this paper, a modified repetitive control (MRC) based approach is developed for high-speed tracking of nanopositioning stages. First, the hysteresis nonlinearity is decomposed as a periodic disturbance over a linear system. Then, the MRC technique is utilized to account for the periodic disturbances/errors caused by the hysteresis and dynamics behaviors. The developed approach provides a simple and effective hysteresis compensation strategy, avoiding the constructions of hysteresis model and its inversion. Besides, with improved loop-shaping properties, the MRC can alleviate the nonperiodic disturbance amplification problem of the conventional repetitive control. Finally, the effectiveness and performance of the developed MRC-based approach are verified by the experimental results on a custom-built piezo-actuated stage in terms of hysteresis compensation, disturbance rejection and tracking accuracy. Note to Practitioners-High-speed piezo-actuated nanopositioning stages are playing an increasingly important role in the fields of scanning probe microscopes (SPMs). However, the tracking speed and accuracy of the nanopositioning stages are hindered by the hysteresis and dynamics behaviors of the piezo-actuated systems. In this work, a MRC-based approach is developed, which is tailored for the lateral scanning process of SPMs. TheMRC can directly mitigate the hysteresis by decomposing it as a periodic disturbance, which releases the burden of hysteresis model construction. Besides, the MRC has a better nonperiodic disturbance rejection capability than the conventional repetitive control. Experimental results demonstrate the merits of the MRC-based approach in terms of hysteresis compensation, disturbance rejection, and tracking accuracy. Due to a simple structure and ease of implementation, the developed MRC-based approach can be applied to other piezo-actuated nanopositioning systems involving with the hysteresis.Index Terms-Hysteresis compensation, modified repetitive control, nanopositioning stage, piezoelectric actuator, tracking control. 1545-5955

This paper presents a modified rate-dependent Prandtl-Ishlinskii (MRPI) model for the description and compensation of the rate-dependent asymmetric hysteresis in piezoelectric actuators. Different from the commonly used approach with dynamic weights or dynamic thresholds, the MRPI model is formulated by employing dynamic envelope functions into the play operators, while the weights and thresholds of the play operators are still static. By this way, the developed MRPI model has a relatively simple mathematic format with fewer parameters and easier parameter identification process. The benefit for the developed MRPI model also lies in the fact that the existing control approaches can be directly adopted with the MRPI model for hysteresis compensation in real-time applications. To validate the proposed model, an open-loop tracking controller and a closed-loop tracking controller are developed based on a dynamic hysteresis compensator, which is directly constructed with the MRPI model. Comparative experiments are carried out on a piezo-actuated nanopositioning stage. The experimental results demonstrate the effectiveness and superiority of the controllers based on the developed MRPI model compared to the controllers based on the rate-independent P-I model and the ratedependent P-I model with dynamic weighting functions.