Mei-Ju Yang

Real-time inverse hysteresis compensation of piezoelectric actuators with a modified Prandtl-Ishlinskii model

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.

Design, analysis and testing of a parallel-kinematic high-bandwidth XY nanopositioning stage.

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.

High-Speed Tracking of a Nanopositioning Stage Using Modified Repetitive Control

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.

High-Bandwidth Control of Nanopositioning Stages via an Inner-Loop Delayed Position Feedback

This paper presents a novel high-bandwidth control approach for piezo-actuated nanopositioning stages. A delayed position feedback (DPF) controller is first developed in the inner loop to damp the resonant mode of piezo-actuated stages. A generalized Runge-Kutta method (GRKM) is proposed to determine the parameters of the DPF controller with pole placement. The benefit of the DPF for active damping is its simple structure and ease of implementation. Then, a high-gain proportional-integral (PI) controller is designed in the outer loop to deal with the hysteresis nonlinearity, disturbance and modeling errors. The stability of the control system is analyzed via a graphical method. Finally, experiments are conducted to demonstrate the effectiveness and superiority of the proposed approach in terms of tracking accuracy at high speed as compared to the PI controller.

A Modified Prandtl-Ishlinskii Model for Rate-dependent Hysteresis Nonlinearity Using mth-power Velocity Damping Mechanism

Hysteresis of piezoelectric actuators is rate-dependent at high frequencies, but most of the hysteresis models are rate-independent and cannot describe the rate-dependent hysteresis nonlinearity independently. In this paper, a modified Prandtl-Ishlinskii (P-I) model is proposed to characterize the rate-dependent hysteresis of piezoelectric actuators under sinusoidal excitation. This model is formulated by a mth-power velocity damping model in conjunction with the rate-independent P-I model. The parameter identification of this model is divided into two steps using different experimental data and algorithms. The particle swarm optimization is introduced first to identify the rate-independent parameters, and the nonlinear least square method is adopted afterwards to identify the rate-dependent parameters which are functions of the excitation frequency. Moreover, the proposed P-I model is developed to describe hysteresis nonlinearity under triangular excitation by introducing weighted functions, i.e., Λ i . Finally, the model results attained under the sinusoidal and triangular inputs at different frequencies are compared with the corresponding experimental data. The comparisons demonstrate that the proposed P-I model can well describe hysteresis nonlinearity under sinusoidal excitation up to 1,500 Hz and triangular excitation up to 250 Hz, respectively.

Improving scanning speed of the AFMs with inversion-based feedforward control

This paper presents the design and experimental implementation of an inversion-based feedforward controller to achieve accurate tracking and fast scanning for an atomic force microscopy (AFM). The proposed controller reduces the tracking error by inverting the vibration dynamics and the hysteresis of the piezoelectric tube scanner (PTS). The hysteresis is compensated by directly constructing an inverse Prandtl-Ishlinskii model, while the vibration dynamics is suppressed by a zero magnitude error tracking controller. A comparison of the experimental images using the proposed controller and a dc-gain open-loop controller is given. The experimental results demonstrate the effectiveness of the proposed controller.

Development of a Parallel-Kinematic High-Speed XY Nanopositioning Stage

This paper presents a parallel-kinematic high-speed XY nano-positioning stage driven by piezoelectric stack actuators. With the purpose to achieve high resonance frequencies and a relatively large travel range, four special flexure modules are used to provide large stiffness. A symmetric configuration is adopted for the designed stage to reduce the cross-coupling between two axes and restrict parasitic motions as well. Static and dynamic analysis of the stage is performed respectively, and the dimensional optimization is carried out on the basis of static and dynamic models to maximize the first resonance frequency of the stage. Finite-element analysis (FEA) is utilized to confirm the effectiveness of the design. The FEA results show that the stage has good static and dynamic performances, which are well validated by the experiments. According to the experimental results, the stage is capable of a workspace of 11.2μm ×11.6μm with positioning resolution of 3 nm. Besides, the resonance frequencies of the stage are over 13.6 kHz with the cross-coupling between two axes lower than -44 dB. It is clearly demonstrated that the stage has high resonance frequencies, relatively large travel range and nearly decoupled performance in two axes.

Identification of prandtl-ishlinskii hysteresis models using modified particle swarm optimization

A modified particle swarm optimization algorithm (MPSO) is proposed in this paper. The algorithm is implemented to identify the parameters of the hysteresis nonlinearity, which is described by a modified Prandtl-Ishlinskii model. This new algorithm redefines the global best position and personal best position in the traditional PSO algorithm by an effective informed strategy, in order to balance the exploitation and exploration of the algorithm. Furthermore, a mutation operator is employed to increase the diversity of the particles and prevent premature convergence. Experiments have been conducted to verify the effectiveness of the proposed method. The comparisons with other variants of the PSO demonstrate that the identification of hysteresis based on the MPSO is effective and feasible.

Positive Position Feedback Based High-Speed Tracking Control of Piezo-actuated Nanopositioning Stages

This paper presents a high-speed tracking control approach for third-order piezo-actuated nanopositioning stages, which extends the vibration control strategies tailored for damping the resonant modes of second-order systems (SOSs) to third-order systems (TOSs). The extension consists of three steps: i) decomposing the TOS into a SOS and a first-order system (FOS); ii) designing the vibration controller for the SOS; iii) extending the vibration controller to the TOS by cascading the controller with the inversion of the FOS. To illustrate the effectiveness of the proposed approach, the positive position feedback (PPF) controller cascaded with dc-gain inversion of FOS is designed. The extended PPF controller is adopted in the inner feedback loop to damp the resonant mode of the system. Then, in the outer loop, a high-gain proportional-integral (PI) controller is utilized to minimize the tracking errors due to disturbances and modeling uncertainties. Experimental results on a piezo-actuated nanopositioning stage demonstrate that the proposed control approach achieves high-speed tracking by improving the control bandwidth from 80 Hz (with PI controller) to 322 Hz.