o-Ying Gu

Modeling and Compensation of Asymmetric Hysteresis Nonlinearity for Piezoceramic Actuators With a Modified Prandtl–Ishlinskii Model

This paper presents a modified Prandtl-Ishlinskii (P-I) (MPI) model for the asymmetric hysteresis description and compensation of piezoelectric actuators. Considering the fact that the classical P-I (CPI) model is only efficient for the symmetric hysteresis description, the MPI model is proposed to describe the asymmetric hysteresis nonlinearity of piezoceramic actuators (PCAs). Different from the commonly used approach for the development of asymmetric P-I models by replacing the classical play operator with complex nonlinear operators, the proposed MPI model still utilizes the classical play operator as the elementary operator, while a generalized input function is introduced to replace the linear input function in the CPI model. By this way, the developed MPI model has a relative simple mathematic format with fewer parameters to characterize the asymmetric hysteresis behavior of PCAs. The benefit for the developed MPI model also lies in the fact that an analytic inverse model of the CPI model can be directly applied for the inverse compensation of the asymmetric hysteresis nonlinearity represented by the developed MPI model in real-time applications. To validate the developed MPI model and the inverse hysteresis compensator, simulation, and experimental results on a piezoceramic actuated platform are presented.

Motion Control of Piezoelectric Positioning Stages: Modeling, Controller Design, and Experimental Evaluation

In this paper, a general skeleton on modeling, controller design, and applications of the piezoelectric positioning stages is presented. Toward this framework, a general model is first proposed to characterize dynamic behaviors of the stage, including frequency response of the stage, voltage-charge hysteresis and nonlinear electric behavior. To illustrate the validity of the proposed general model, a dynamic backlash-like model is adopted as one of hysteresis models to describe the hysteresis effect, which is confirmed by experimental tests. Thus, the developed model provides a general frame for controller design. As an illustration to this aspect, a robust adaptive controller is developed based on a reduced dynamic model under both unknown hysteresis nonlinearities and parameter uncertainties. The proposed control law ensures the boundedness of the closed-loop signals and desired tracking precision. Finally, experimental tests with different motion trajectories are conducted to verify the proposed general model and the robust control law. Experimental results demonstrate the excellent tracking performance, which validates the feasibility and effectiveness of the proposed approach.

Modeling and Control of Piezo-Actuated Nanopositioning Stages: A Survey

Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.

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 and control of a decoupled two degree of freedom translational parallel micro-positioning stage

This paper presents a novel decoupled two degrees of freedom (2-DOF) translational parallel micro-positioning stage. The stage consists of a monolithic compliant mechanism driven by two piezoelectric actuators. The end-effector of the stage is connected to the base by four independent kinematic limbs. Two types of compound flexure module are serially connected to provide 2-DOF for each limb. The compound flexure modules and mirror symmetric distribution of the four limbs significantly reduce the input and output cross couplings and the parasitic motions. Based on the stiffness matrix method, static and dynamic models are constructed and optimal design is performed under certain constraints. The finite element analysis results are then given to validate the design model and a prototype of the XY stage is fabricated for performance tests. Open-loop tests show that maximum static and dynamic cross couplings between the two linear motions are below 0.5% and -45 dB, which are low enough to utilize the single-input-single-out control strategies. Finally, according to the identified dynamic model, an inversion-based feedforward controller in conjunction with a proportional-integral-derivative controller is applied to compensate for the nonlinearities and uncertainties. The experimental results show that good positioning and tracking performances are achieved, which verifies the effectiveness of the proposed mechanism and controller design. The resonant frequencies of the loaded stage at 2 kg and 5 kg are 105 Hz and 68 Hz, respectively. Therefore, the performance of the stage is reasonably good in term of a 200 N load capacity.

High-speed tracking control of piezoelectric actuators using an ellipse-based hysteresis model

In this paper, an ellipse-based mathematic model is developed to characterize the rate-dependent hysteresis in piezoelectric actuators. Based on the proposed model, an expanded input space is constructed to describe the multivalued hysteresis function H[u](t) by a multiple input single output (MISO) mapping Gamma:R(2)-->R. Subsequently, the inverse MISO mapping Gamma(-1)(H[u](t),H[u](t);u(t)) is proposed for real-time hysteresis compensation. In controller design, a hybrid control strategy combining a model-based feedforward controller and a proportional integral differential (PID) feedback loop is used for high-accuracy and high-speed tracking control of piezoelectric actuators. The real-time feedforward controller is developed to cancel the rate-dependent hysteresis based on the inverse hysteresis model, while the PID controller is used to compensate for the creep, modeling errors, and parameter uncertainties. Finally, experiments with and without hysteresis compensation are conducted and the experimental results are compared. The experimental results show that the hysteresis compensation in the feedforward path can reduce the hysteresis-caused error by up to 88% and the tracking performance of the hybrid controller is greatly improved in high-speed tracking control applications, e.g., the root-mean-square tracking error is reduced to only 0.34% of the displacement range under the input frequency of 100 Hz.

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.

Proxy-Based Sliding-Mode Tracking Control of Piezoelectric-Actuated Nanopositioning Stages

In this paper, a proxy-based sliding-mode control (PBSMC) approach is proposed for robust tracking control of a piezoelectric-actuated nanopositioning stage composed of piezoelectric stack actuators and compliant flexure mechanisms. The essential feature of the PBSMC approach is the introduction of a virtual coupling proxy, which is controlled by the sliding-mode controller (SMC) to track the desired position. Simultaneously, due to the virtual coupling, a proportional-integral-derivative (PID) controller on the other side of the proxy ensures the position of the end-effector of the stage to follow the position of the proxy. Therefore, the PBSMC guarantees the end-effector to track the desired trajectory. The advantages of the developed PBSMC lie in the facts that 1) the discontinuous signum function in the traditional SMC is omitted without any approximation. Hence, the output of the PBSMC is continuous, which does not suffer from the chattering phenomenon; and 2) the PBSMC laws are developed without having the necessity to include the nominal system model, hysteresis model or the state observer. Hence, the PBSMC provides a novel effective yet simple control method, which permits to avoid the lack of performances from PID and the chattering from SMC, and permits to combine the advantages from them. The stability of the closed-loop control system is proved through Lyapunov analysis. Finally, comparative studies are performed on a custom-built piezo-actuated stage. Experimental results show that the tracking errors of the PBCM are reduced by 74.22%, as compared to the traditional PID controller, with the desired sinusoidal trajectory under the 50-Hz input frequency, which clearly demonstrates the superior tracking performance of the PBSMC.

Modeling and Identification of Piezoelectric-Actuated Stages Cascading Hysteresis Nonlinearity With Linear Dynamics

In this paper, we propose a new modeling and identification approach for piezoelectric-actuated stages cascading hysteresis nonlinearity with linear dynamics, which is described as a Hammerstein-like structure. In the proposed approach, the hysteresis and linear dynamics together with the delay time and higher order dynamic behaviors are obtained with three data-driven identification steps under designed input signals. In the first step, the step input signal is applied to estimate the delay time of the piezoelectric-actuated stages. In the second step, the autoregression with exogenous signal identification algorithm is adopted to identify the linear dynamics using a small-amplitude band-limited white noise input signal. In the third step, with the identified linear dynamics model, the parameters of the rate-independent Prandtl-Ishlinskii hysteresis model are identified by the particle swarm optimization algorithm using a simple low-frequency triangle input signal with different amplitudes. Finally, the experimental results on a piezoelectric-actuated stage show that both the hysteresis and dynamic behaviors of the piezoelectric-actuated stage are well predicted by the proposed modeling method. In addition, we provide the analysis of quantitative prediction errors of the identified model with comparison to experimental data, which clearly demonstrate the effectiveness of the proposed approach.

Design of a Distributed Multiaxis Motion Control System Using the IEEE-1394 Bus

This paper presents a distributed multiaxis motion control system based on the IEEE-1394 bus. In the system design, the Unified Modeling Language is employed to illustrate interactions of the objects required in the system. The developed system consists of a set of smart distributed control nodes connected one by one through the IEEE-1394 bus. Each smart node contains four modules, i.e., an IEEE-1394 interface module, a digital signal processor module, a field-programmable gate array module, and a digital-to-analog converter module. It accomplishes its own control task and coordinates with the others through information exchanges, sampling sensor signals, and controlling actuators. A scheduled communication protocol is proposed according to the criteria in terms of bounded time delay and guaranteed transmission. Time delays arising from data processing and message transmission are analyzed. A platform is built, and experiments are conducted to demonstrate the capabilities of the developed distributed control system for real-time communication and synchronous tracking control, which are required for multiaxis applications. The results verify the feasible application of the IEEE-1394 bus to distributed motion control.