Rate-dependent Prandtl-Ishlinskii Research Articles

Research on active-passive integrated vibration isolator based on metal rubber and piezoelectric actuator

Abstract The paper introduces a novel active-passive integrated vibration isolator based on metal rubber and piezoelectric actuator, along with an adaptive active vibration control strategy. The active control strategy employs the adaptive dynamic step filtered-x normalized least mean squares algorithm, allowing the step size to adaptively adjust with the error. The secondary control path of the algorithm is modeled using the enhanced rate-dependent Prandtl–Ishlinskii model and the auto-regressive with extra inputs model. The active-passive integrated vibration isolator achieves broadband vibration isolation from 10 to 200 Hz. Compared to passive isolation, the transmissibility decreases from 0.99 to 0.056 at 10 Hz, from 3.02 to 0.068 at the resonance frequency, and from 0.057 to 0.046 at 200 Hz. This study provides a theoretical and experimental foundation for the design of a novel, broadband, and efficient active-passive integrated vibration isolator structure and active control method.

Coupled hysteresis and resonance control of three-degree-of-freedom tip-tilt-piston piezoelectric stage

In order to solve the coupled hysteresis and resonance problems in three-degree-of-freedom tip-tilt-piston piezoelectric stage, a coupled hysteresis model and a coupled integral resonance compensation model are designed. The inverse coupled hysteresis feedforward control combined multi-axis coupled resonance control and high-gain integral tracking controller are used to improve the tracking speed and positioning accuracy of the stage. Firstly, a kinematic model of the stage is built to translate the three-degree-of-freedom motion of the end-effector into the outputs of three piezoelectric actuators. Then, a coupled hysteresis model based on the rate-dependent Prandtl–Ishlinskii model is established and parameterized to simultaneously compensate for the hysteresis of a single piezoelectric actuator and the coupled hysteresis between multiple piezoelectric actuators. The effectiveness of the model is verified by open-loop and closed-loop inverse model feedforward control experiments. Afterwards, a coupled integral resonance compensation model is also established and parameterized to suppresses the resonance and expand the system bandwidth. Finally, the proposed controller is used to conduct tracking experiments on a composite signal, and the results show that the accuracy and speed of trajectory tracking are further improved, and the mechanical coupling between axes are significantly reduced.

Memory reduction of rate-dependent Prandtl–Ishlinskii compensators in applications on high-precision motion systems

Inverse compensation of rate-dependent Prandtl–Ishlinskii operators with finitely many thresholds can be carried out explicitly under some structural conditions. However, if the number of thresholds is very high, the formulas become complicated. A simple and elegant framework for the investigation of such problems encompasses a recently proposed extension of the class of rate-dependent Prandtl–Ishlinskii operators to the case of a whole continuum of play operators with time-dependent thresholds. Indeed, such a theory allows for reducing the number of necessary thresholds in the compensation procedure and estimating the errors of the memory-discrete compensation in terms of the distance between the thresholds and weights of the individual plays. Following these results, our goal in this work is the validation of these theoretical models via numerical simulations and experimental results. In particular, we show that high accuracy of the hysteresis compensation algorithm can be achieved even with a relatively small number of thresholds.

Modeling and inverse compensation of dynamic hysteresis in voice coil motors using an extended rate-dependent Prandtl-Ishlinskii model

The objective of this study is to examine the influence of input current frequency on the hysteresis behaviour of voice coil motors (VCMs). The present study introduces the extended rate-dependent Prandtl-Ishlinskii (ERDPI) model, which integrates the Fermi-Dirac distribution into the envelope function. Additionally, the model combines rate-dependent thresholds and rate-dependent Prandtl-Ishlinskii compensation. The model parameters are identified using the improved grey wolf optimizer algorithm. The analysis of the model responses and observed data across various frequencies of current input signals demonstrates the ERDPI model's ability to accurately capture the rate-dependent nonlinear hysteresis features of the VCM. To compensate for dynamic hysteresis in VCMs, an ERDPI inverse model is established, showcasing unique convergence when the model parameters are assigned specific values. Simultaneously, an ERDPI inverse model-based feedforward compensator is presented, demonstrating a significant reduction in the hysteresis rate of VCMs by a factor of magnitude, ensuring its stabilization below 5%.

Design and control of an x-y-θz parallel piezoelectric nanopositioning stage with a large moving platform

This paper introduces the design and control of a new type of x- y-θ z parallel piezoelectric nanopositioning stage. Using the spatial cross-distributed double parallel four-bar linkage (DPFL), the mirror symmetrically distributed driving unit and auxiliary unit are designed. Then, a parallel piezoelectric nanopositioning stage with a large moving platform and good guidance and decoupling performance are designed. The workspace and frequency response characteristics of the stage are analyzed based on the stiffness and dynamic models. To improve the static and dynamic characteristics of the stage, the structural size is optimized, and the optimization results are verified by Finite Element Analysis (FEA). To reduce the response time, hysteresis nonlinearity, and external disturbance of the stage, a compound controller combining a rate-dependent Prandtl–Ishlinskii (PI) hysteresis compensator and a proportional-integral controller is designed. Finally, the prototype of the stage is made by Wire Electro-Discharge Machining (WEDM) technology. The open-loop performance of the stage is tested experimentally. The results show that the maximum relative coupling error between x and y directions is less than 0.5%. Also, the experimental control results show that the designed compound controller has a fast response speed, good positioning, and tracking performance.

Modelling of piezoelectric actuating systems subjected to variable loads and frequencies and applications to prescribed performance control

Piezoelectric actuators can offer micro/nano-level precision actuating ability and have been employed in different applications. For the piezoelectric actuating systems, the output actuating performance is affected not only by the internal non-smooth hysteresis but also by the operating load and the excitation frequency. To improve the actuating precision, predicting the nonlinear behaviour of the piezoelectric actuating system is essential for effective designs of control approaches. In this paper, a modified rate-dependent Prandtl–Ishlinskii model is presented to explore the coupling effects analytically between the internal hysteresis and the operating frequency with the external loads and predict the output behaviour of the piezoelectric actuating system accurately. The proposed modelling method is testified on a piezoelectric actuating platform under broad ranges of excitation frequencies (1–80 Hz) and external loads (0–0.5 kg), and the comparison results using the rate-dependent Prandtl–Ishlinskii (RDPI) model are also provided to prove the precision of the proposed method. Combining with the modified RDPI model, a guaranteeing preselected tracking controller is developed to ensure the output performance, and a set of tracking experiments under different frequencies with load is performed. The experimental results compared with PID control performance validate the effectiveness of the proposed prescribed performance control method and its high actuating performance against the adverse effects from the external hysteresis nonlinearities and external loads.

Intelligent feedforward hysteresis compensation and tracking control of dielectric electro-active polymer actuator

Dielectric electro-active polymer (DEAP) actuator has been considered potentially in recent decades for many applications, especially in intelligent bio-inspired robotics. However, the viscoelastic properties including rate-dependent and asymmetrical hysteresis, creep and the uncertainties under different operating conditions are still limiting its further development. In this paper, a feedforward-feedback tracking control approach is developed. Firstly, a long short term memory (LSTM) neural network combined with empirical mode decomposition (EMD), which has the information of reference as input and the control signal as output, is constructed using the data collected from the DEAP actuator. Thus, the well trained LSTM model can precisely capture the inverse hysteresis dynamics of the DEAP actuator, which can be used as a feedforward compensator to eliminate the hysteresis nonlinearities. Then, a conventional proportional-integral-derivative feedback controller is combined to compensate for the uncertainties and creep effect. To verify the effectiveness of the proposed feedforward compensator, comparative experiments on prediction of control signal and compensation of hysteresis among the traditional artificial back propagation neural network model, the inverse rate-dependent Prandtl-Ishlinskii model and the proposed LSTM-based compensator are conducted. The results validate that the LSTM-based compensator can precisely predict the control signal and eliminate the hysteresis with best performance indexes. Moreover, the tracking control experiments further validate the effectiveness of the proposed feedforward-feedback approach.

Decoupled identification and compensation of nonlinear hysteresis cascading with linear dynamic in a moving magnet voice coil actuator.

The moving magnet voice coil actuator (MMVCA) is a promising choice for the long stroke nanopositioning stage with the advantage of low moving mass. However, the hysteresis observed in MMVCA limits further improvement on tracking performance. The hysteresis is cascading with the linear dynamic of the positioning stage, which makes common hysteresis identification inapplicable. In this paper, the cause and influence of hysteresis in MMVCA are analyzed, which reveal that the magnetic hysteresis leads to a hysteresis of force and causes motion accuracy to degrade. A modified rate-dependent Prandtl-Ishlinskii (P-I) model is proposed to describe the hysteresis in MMVCA. The decoupled method is implemented to identify the parameters of the linear dynamic model and nonlinear hysteresis model. The experimental results validate the feasibility of the proposed P-I model. Based on the hysteresis compensation, the peak-to-peak tracking errors are reduced by 30% and the root-mean-square (rms) tracking errors are decreased by 41% on average for the trajectories with amplitudes from 1 to 3mm and frequencies from 1 to 5Hz.

Model Reference Adaptive Control of Cross-Coupling Hysteresis in Piezoceramics With Dynamic Loads

During the ultraprecise cutting of micro-structure surface with fast tool servo (FTS), the hysteresis of piezoelectric actuators (PEAs) are affected by dynamic voltage excitations and real-time cutting force, which declines the servo accuracy and cutting performance. In this paper, for a multi-input-single-output (MISO) cutting system, a cross-coupling rate-dependent Prandtl-Ishlinskii (CRPI) model is proposed and identified for the dynamic hysteresis of PEAs under dynamic voltage excitation and external loads. A model reference adaptive control method is then presented to eliminate the positioning nonlinearity of PEAs. The hysteresis modeling accuracy is discussed and the adaptive controller is validated through experiments.

Precision motion control of a piezoelectric cantilever positioning system with rate-dependent hysteresis nonlinearities

The study proposed a feedforward– feedback combined architecture to control a piezoelectric motion system with rate-dependent hysteresis nonlinearities. First, the feedforward control that considered the inverse rate-dependent Prandtl–Ishlinskii (RDPI) model was presented. Based on the inverse RDPI model, a formula that characterizes the output of the inverse compensation considering modeling errors and uncertainties was obtained. More precisely, the output of the inverse compensation of RDPI model consists of an invertible linear term and a bounded nonlinear term. Afterward, the feedforward control is extended with a feedback control architecture. In order to satisfy performance criteria in the presence of the uncertainties, the design of the feedback controller was based on the performances inclusion theorem from interval techniques. Experiments were conducted on a piezoelectric actuator to confirm the effectiveness of the combined feedforward–feedback control.

Hysteresis Modeling of Robotic Catheters Based on Long Short-Term Memory Network for Improved Environment Reconstruction

Catheters are increasingly being used to tackle problems in the cardiovascular system. However, positioning precision of the catheter tip is negatively affected by hysteresis. To ensure tissue damage due to imprecise positioning is avoided, hysteresis is to be understood and compensated for. This work investigates the feasibility to model hysteresis with a Long Short-Term Memory (LSTM) network. A bench-top setup containing a catheter distal segment was developed for model evaluation. The LSTM was first tested using four groups of test datasets containing diverse patterns. To compare with the LSTM, a Deadband Rate-Dependent Prandtl-Ishlinskii (DRDPI) model and a Support Vector Regression (SVR) model were established. The results demonstrated that the LSTM is capable of predicting the tip bending angle with sub-degree precision. The LSTM outperformed the DRDPI model and the SVR model by 60.1% and 36.0%, respectively, in arbitrarily varying signals. Next, the LSTM was further validated in a 3D reconstruction experiment using Forward-Looking Optical Coherence Tomography (FL-OCT). The results revealed that the LSTM was able to accurately reconstruct the environment with a reconstruction error below 0.25 mm. Overall, the proposed LSTM enabled precise free-space control of a robotic catheter in the presence of severe hysteresis. The LSTM predicted the catheter tip response precisely based on proximal input pressure, minimizing the need to install sensors at the catheter tip for localization.

Modeling of the dynamic hysteresis in DEAP actuator using an empirical mode decomposition based long-short term memory network

As a smart material-based actuator, the dielectric electro-active polymer (DEAP) actuator is widely considered to be a potential driving mechanism for many applications, especially in intelligent bio-inspired robotics. However, the DEAP actuator demonstrates rate-dependent and asymmetrical hysteresis phenomenon which leads to great tracking inaccuracy and even oscillatory response, severely limiting its further development. Feedforward Neural Network (FNN) model has already become a widely used method to describe this kind of strong hysteresis nonlinearity in recent years. However, the FNN has no ability to remember the historical state of long period of time which is also a very important factor to restrict hysteresis phenomenon. In this paper, a novel hybrid model, Long-Short Term Memory (LSTM) network combined with Empirical Mode Decomposition (EMD), is proposed to model the dynamic hysteresis nonlinearity in DEAP actuator. At first, the original control signal sequence is preprocessed into a series of sub-sequence by the EMD method and is reshaped by one-sided dead-zone operator. Then the input space of LSTM is conducted using the original control signal, the sub-sequence, and reshaped signal. Finally, the input space and the displacement signal are applied to train the long-short term memory network. In order to verify the performance of the proposed model, the traditional artificial back propagation neural network (BPNN) model, rate-dependent Prandtl-Ishlinskii (RPI) model, and nonlinear electromechanical (NEM) model are compared from prediction accuracy. The results demonstrate that: (1) the proposed model has a higher prediction accuracy than the traditional artificial BPNN, RPI, and NEM model; and (2) the prediction accuracy of LSTM network is significantly improved by using EMD. Therefore, the long-short term memory network combined with empirical mode decomposition is a competitive method compared to the existing state-of-the-art approach.

Modeling and Inverse Compensation of Cross-Coupling Hysteresis in Piezoceramics under Multi-Input.

In the fast tool servo (FTS) system for microstructure surface cutting, the dynamic voltage hysteresis of piezoelectric actuators (PEAs) and the cutting force produced in the manufacturing affect the driving accuracy and the cutting performance. For a multi-input-single-output (MISO) cutting system, in this paper, a dynamic hysteresis model based on a rate-dependent Prandtl–Ishlinskii model is proposed. A backpropagation neural network (BPNN) is established to describe the cross-coupling effect between the applied voltage and external load. An inverse dynamic model is developed to compensate the nonlinearity of PEAs. The accuracy of the model and its inverse is discussed and the performance of the inverse feedforward compensator is validated through experiments.

Modeling and compensation of asymmetric rate-dependent hysteresis of a miniature pneumatic artificial muscle-based catheter

Hysteresis phenomenon limits the effective use of pneumatic artificial muscles in numerous driving applications. Experimental results show widening hysteresis loops and lowering displacement amplitudes by increasing excitation frequency. In this study, a feedforward controller is proposed to compensate for this hysteretic behavior. This proposed controller is based on a rate-dependent Prandtl–Ishlinskii model. In order to avoid analytical calculation of inverse model, a direct inverse model is proposed. To identify unknown parameters of a direct inverse rate-dependent model, an inverse model of the rate-independent Generalized Prandtl-Ishlinskii (GPI) is used. The inverse GPI model can provide a fairly accurate output to diminish the hysteresis effect at a single-frequency hysteresis. The genetic algorithm combined with an interior-point method as a gradient-based optimization, is proposed to estimate the parameters of the proposed controller quickly. Simulation and experimental results show that the proposed feedforward controller that is identified along this new approach is able to compensate for the hysteresis in the PAM-driven catheter successfully. The identification procedure to optimize the parameters takes less than five minutes and is thus very convenient in use. It should be noted that while demonstrated on a single PAM, the approach is believed to be general and hence also applicable to other actuators that possess the complex hysteresis behavior.

System Identification of Micro Piezoelectric Actuators via Rate-Dependent Prandtl-Ishlinskii Hysteresis Model Based on a Modified PSO Algorithm

As one of the high-precision actuating mechanisms, the piezoelectric actuators show the advantage of micro/nano stage maneuverability in facilitating the actuating performance of the mechanical systems. To improve the actuating accuracy, it is important to predict the output behavior accurately under the wide operating range, particularly, the change of the driving frequency. The modeling method using the rate-dependent Prandtl-Ishlinskii (RDPI) model is subsequently adopted, which can show the strong nonlinearities relating to the coupling effects between the internal hysteresis and the actuating frequency. Considering the electromechanical characteristics of piezoelectric actuators, a modified particle swarm optimization (MPSO) algorithm is introduced for identifying the RDPI model using the experimental measurement data. The developed MPSO algorithm can overcome the local optimizing limitation of the classical particle swarm optimization (CPSO) algorithm and guarantee the accuracy of predicting the output. The utility and superiority of the MPSO are verified by fitting the identified model to the actual output of the piezoelectric actuators in the micro range at different actuating frequencies. The comparisons with available models using MPSO, CPSO and LS algorithms have examined the validity of the proposed identification method.

Hysteresis modeling of piezoelectric micro-positioning stage based on convolutional neural network

The inherent hysteresis nonlinearity of piezoelectric actuator degrades the positioning accuracy of the micro-positioning stage. Prandtl–Ishlinskii model is widely used for piezoelectric hysteresis modeling, yet it is a rate-independent model with weak generalization ability. To overcome this problem, we proposed a convolutional neural network model based on the Prandtl–Ishlinskii model, which consists of a rate-dependent Prandtl–Ishlinskii model layer and convolutional network layer. The rate-dependent Prandtl–Ishlinskii model layer extends the traditional Prandtl–Ishlinskii model to describe the rate-dependent hysteresis behavior. The convolutional network layer with deep learning ability extracts the deep features of the input signal to improve the generalization ability of the hysteresis model. The experiment results indicate that the standard error of the proposed hysteresis model to predict displacement at unmodeled frequencies has been reduced by 18.74%–36.75% in comparison with the Prandtl–Ishlinskii model, which verifies that the proposed hysteresis model has not only higher accuracy but also stronger generalization ability.

Tracking control of an SMA-driven actuator with rate-dependent behavior using an inverse model of hysteresis

Hysteresis is a nonlinear phenomenon which may cause inaccuracies and delay in control applications. Shape memory alloys (SMAs) have an asymmetric saturated hysteresis. In addition, the excitation frequency changes the hysteresis behavior of SMA-driven systems and makes them challenging to track reference inputs at different frequencies. In this study, a rate-dependent Prandtl–Ishlinskii model coupled with a deadband function is proposed to characterize the asymmetric and saturated hysteresis behavior as well as its rate-dependency. Unknown parameters of the model are identified using genetic optimization algorithm in MATLAB Toolbox based on measured data. The identified model is validated to consider the excitation frequency effect with a different measured data set. The inverse model is also proposed as a compensator to mitigate hysteresis nonlinearity effects especially the frequency effect in tracking control. Although the proposed compensator cannot fully compensate for hysteresis effects, it can reduce the input–output hysteresis. The proposed rate-dependent compensator as a feedforward controller combined with a proportional–integral–derivative (PID) controller as a feedback mitigates hysteresis effects. The PID controller is used to improve the accuracy of compensated system and remove the steady-state error. Experimental results illustrate that the proposed controller has a great accuracy in tracking control to consider the excitation frequency effect as well as the asymmetric saturated hysteresis.

Modeling and characterization of the shape memory alloy–based morphing wing behavior using proposed rate-dependent Prandtl-Ishlinskii models

Unique features of shape memory alloys make them a proper actuation choice in various control systems. However, their nonlinear hysteresis behavior negatively affects wide utilization of such materials in structure actuation. In this study, the frequency effect on the hysteresis behavior of a shape memory alloy–actuated structure is experimentally investigated, and also two proposed versions of rate-dependent Prandtl-Ishlinskii (modified rate-dependent Prandtl-Ishlinskii and revised modified rate-dependent Prandtl-Ishlinskii) are presented, which are capable of characterizing this phenomenon. Experimental results show that increasing excitation frequency leads to bigger hysteresis loops. It is also proven that rate-dependency cannot be predicted by generalized Prandtl-Ishlinskii model. In addition, a comparison between the dead zone function-based rate-dependent Prandtl-Ishlinskii model as an only benchmark model and the proposed models have been done that proves the proposed models’ superiority. In addition, genetic algorithm is exploited to identify unknown parameters of all models. Trained models performance is also experimentally evaluated at different input frequencies. Comparison between simulation and experimental results indicates that the proposed models can reliably predict saturated, asymmetric, rate-dependent hysteresis behavior, and minor loops in shape memory alloy–embedded actuators.

Design of a Feedforward-Feedback Controller for a Piezoelectric-Driven Mechanism to Achieve High-Frequency Nonperiodic Motion Tracking

Piezoelectric-driven mechanisms have several advantages like high stiffness, rapid response, and good resolution. Therefore, they are widely used for many micro/nano trajectory-tracking applications. However, the existence of the hysteretic nonlinearity behavior makes it challenging to use in practice. In addition, the hysteresis changes with frequency and is dependent on environmental parameters like temperature and load. Finding a method that can track both continuous periodic and nonperiodic motion under wide frequency range with high precision is nontrivial. In this study, a feedforward-feedback control strategy is proposed to bridge this gap, where a direct inverse rate-dependent Prandtl–Ishlinskii model based on radial basis function neural network to compensate rate-dependent hysteresis and a proportional-integral controller with an inner-loop disturbance observer to further attenuate tracking error (caused by the imperfect modeling, unknown lumped disturbance). The proposed method can perform a wide-bandwidth tracking control of periodic and nonperiodic motion of a piezoelectric-driven mechanism. Experiments are then conducted to demonstrate the capability of the proposed controller.

High precision tracking of a piezoelectric nano-manipulator with parameterized hysteresis compensation

High performance scanning of nano-manipulators is widely deployed in various precision engineering applications such as SPM (scanning probe microscope), where trajectory tracking of sophisticated reference signals is an challenging control problem. The situation is further complicated when rate dependent hysteresis of the piezoelectric actuators and the stress-stiffening induced nonlinear stiffness of the flexure mechanism are considered. In this paper, a novel control framework is proposed to achieve high precision tracking of a piezoelectric nano-manipulator subjected to hysteresis and stiffness nonlinearities. An adaptive parameterized rate-dependent Prandtl-Ishlinskii model is constructed and the corresponding adaptive inverse model based online compensation is derived. Meanwhile a robust adaptive control architecture is further introduced to improve the tracking accuracy and robustness of the compensated system, where the parametric uncertainties of the nonlinear dynamics can be well eliminated by on-line estimations. Comparative experimental studies of the proposed control algorithm are conducted on a PZT actuated nano-manipulating stage, where hysteresis modeling accuracy and excellent tracking performance are demonstrated in real-time implementations, with significant improvement over existing results.