Prandtl-Ishlinskii Hysteresis Model Research Articles

Modeling and adaptive NN control for SMA flexible actuating systems with modified GPI hysteresis model

In this study, a shape memory alloy (SMA) actuating system is constructed to achieve flexible actuation ability. To improve the actuating performance, an effective control scheme needs to be developed to address the negative effects caused by the nonlinear nature of the internal SMA material and accommodate complex operating conditions. A modified generalised Prandtl-Ishlinskii (MGPI) hysteresis model is proposed to accurately characterise the strong saturated asymmetric hysteresis nonlinearity in the SMA wires. The modification of the input shape function allows for greater flexibility in controller design. Using this hysteresis modelling approach, an adaptive neural network (NN) control with a command filter is designed to achieve superior control performance. Experimental results validate the effectiveness of the proposed controller strategy.

Development of a Prandtl-Ishlinskii hysteresis model for a large capacity magnetorheological fluid damper

Magnetorheological (MR) fluid (MRF) dampers, serving as fail-safe semi-active devices, exhibit nonlinear hysteresis characteristics, emphasizing the necessity for accurate modeling to formulate effective control strategies in smart systems. This paper introduces a novel stop operator-based Prandtl-Ishlinskii (PI) model, featuring a reduced parameter set (seven), designed to estimate the nonlinear hysteresis properties of a large-scale bypass MRF damper with variable stiffness capabilities under varying applied current. With only seven parameters, the model realizes current, displacement, and rate dependencies. The force-displacement and force-velocity responses of the designed MRF damper were experimentally characterized under broad ranges of applied current (0–2 A), excitation frequency (0.5–4 Hz), and displacement amplitude (1–2.5 mm). A training dataset was subsequently used to develop a novel field-dependent modified PI model, incorporating multiple hysteresis operators with and without a friction element. The proposed model accurately predicted the MRF damper behavior within the training dataset, and its validity was assessed against data from diverse experimental conditions. The PI model with friction element generally outperformed the model without friction when frequency exceeds 0.5 Hz, demonstrating its ability to characterize nonlinear hysteresis force-displacement and force-velocity properties of the MRF damper under the ranges of applied current and excitations considered with reasonable accuracy. Experimental data were also estimated by the Bouc–Wen model, and compared with those obtained via the formulated PI model, affirming the overall superiority of the proposed PI models considering the computational cost, and total number of parameters. Leveraging the simplicity, minimal parameter requirements, and analytic invertibility of PI models, the proposed PI model is considered a superior choice for modeling and subsequently controlling smart structures employing MRF dampers.

Robust Control of Dielectric Elastomer Smart Actuator for Tracking High-Frequency Trajectory

Dielectric elastomer smart actuator (DESA) has shown great potentials in soft robot applications. The control of the DESA is one of key issues for soft robots. However, the precise control of the DESA is a challenge work, especially when tracking high-frequency trajectories and guaranteeing a certain robustness. To this end, this paper presents a robust tracking control method for a DESA to track various high-frequency trajectories. Firstly, to characterize the complex nonlinear properties (including the quadratic input, asymmetric and rate-dependent hysteresis, as well as creep) of the DESA, its dynamic model is built by combining a square function module, a modified Prandtl-Ishlinskii (P-I) hysteresis model and a linear system. Subsequently, by combining the inverse of the modified P-I hysteresis model with a square root function module, the quadratic input and asymmetric hysteresis properties of the DESA are compensated to reduce tracking the control error. Since model uncertainties and external disturbances are unavoidable in practical applications, a robust controller is designed to achieve the tracking control of the DESA, the controller also guarantees the robustness of the control system. In the end, the effectiveness of the proposed control method is demonstrated through a series of tracking control experiments with different high-frequency trajectories, whose maximal frequency is 8 (Hz). The root- mean-square errors of all experimental results are lower than 1.5%, which proves that the presented method is remarkable from the respective of the practical application.

Safety-Critical Control Systems [About this Issue

This issue of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IEEE Control Systems</i> includes one feature and one lecture note. In the feature, “Runtime Assurance for Safety-Critical Systems: An Introduction to Safety Filtering Approaches for Complex Control Systems” <xref ref-type="list-item" rid="list-itemA1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[A1]</xref> , authors Kerianne L. Hobbs, Mark L. Mote, Matthew C.L. Abate, Samuel D. Coogan, and Eric M. Feron provide an introductory tutorial of runtime assurance (RTA) concepts and their role in ensuring safety of complex control systems. Assuming an undergraduate-level understanding of control theory and state-space concepts, this article provides theory and examples for RTA architectures, four types of RTA approaches, and a number of systems engineering and practical considerations for employing RTA in safety-critical, cyberphysical systems. In the “Lecture Notes” column, “The Prandtl-Ishlinskii Hysteresis Model: Fundamentals of the Model and Its Inverse Compensator,” <xref ref-type="list-item" rid="list-itemA2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[A2]</xref> Mohammad Al Janaideh, Mohammad Al Saaideh, and Xiaobo Tan introduce the mathematical formulations of the Prandtl–Ishlinskii (PI) and Generalized PI (GPI) hysteresis models as well as their analytical inverses. These models can effectively characterize hysteresis nonlinearities in various systems, especially smart-material actuators, and their inverses can be used in feedforward compensation to mitigate the effect of hysteresis. Numerical examples of the PI and GPI models as well as their analytical inverses are also included in the article. The intended audience includes graduate students and researchers from academia and industry interested in hysteresis modeling and compensation.

A Modified Prandtl-Ishlinskii Hysteresis Model for Modeling and Compensating Asymmetric Hysteresis of Piezo-Actuated Flexure-Based Systems.

Piezo-actuated flexure-based systems are widely used in applications with high accuracy requirements, but the intrinsic hysteresis has a detrimental effect on the performance which should be compensated. Conventional models were presented to model this undesired effect using additional dead-zone operators. This paper presents a new approach using two sets of operators with a distributed compensator to model and compensate for the asymmetric system hysteresis based on inversion calculation with a simplified digitized representation. The experimental results validate the effectiveness of the proposed model in modeling and compensating the asymmetric system hysteresis.

Towards the Design and Development of a Robotic Transcatheter Delivery System for Mitral Valve Implant.

Minimally-invasive surgeries using transcatheter approaches and sophisticated imaging modalities are gaining popularity to treat mitral regurgitation (MR). This paper proposes the next generation of a robotic catheter to deliver an implant onto the mitral valve (MV) through a transseptal approach. The proposed robot has an outer diameter (OD) of 5.7 mm, a rigid distal end length of 20 mm, a prismatic tube that can be advanced by 50-60 mm, and a bending joint that can easily bend 120° to reach the valve opening. The implant can be rotated 75° bidirectionally by the distal torsion joint to orient it with the MV leaflet for precise implantation. The robotic joints are modeled individually, the forward and inverse kinematics are derived, and the robot motion validation is carried out through experimentation. A modified kinematics (MK) model, Prandtl-Ishlinskii (PI) hysteresis model, and hybrid of MK and PI model are used to compensate for the catheter nonlinearities. A preliminary study is conducted to evaluate if force sensing can be used to compensate for the effects of fluid flow. Also, the implantation procedure is demonstrated in a phantom heart.

Precision Compensation Control of a Piezo-Scanning Mechanism

In this study, a controller based on two compensators is developed to support a two-axis piezo-scanning mechanism for tracking control. The hysteresis compensator is designed based on a Prandtl–Ishlinskii hysteresis model in order to reduce the nonlinear hysteresis effect of a piezoelectric actuator. Furthermore, to compensate for uncertainties due to parametric variations, hysteresis-compensated error, and un-modeled dynamics, the uncertainties compensator based on the neural network disturbance observer is proposed. The developed controller is verified with regard to control performance by experiment. Those two observers are used to complete hysteresis compensation and disturbance compensation, which will not reduce the stability and bandwidth of the system and improve the control accuracy. Experimental results show that the proposed hybrid controller can overcome the mentioned nonlinearity and uncertainty efficiently and preserve good positioning accuracy with high-bandwidth varying frequencies (1–150 Hz).

Microscopic vibration suppression for a high-speed macro-micro manipulator with parameter perturbation

This paper reports electromechanical dynamics modeling and microscopic vibration suppression for a high-speed macro–micro manipulator with structural flexibility and parameter perturbation. The macro–micro manipulator contains an air-floating macro-motion platform and a macro-fiber-composite (MFC) micromanipulator. The electromechanical dynamics model is derived by combining the assumed mode method and the asymmetric Prandtl-Ishlinskii hysteresis model. Then, a robust control strategy combining a perturbation H-infinity controller with a Kalman filter is proposed to compensate for the hysteresis nonlinearity and suppress the microscopic vibration during and after the macro motion. In particular, an additive perturbation is used to estimate the model uncertainties from the varying end mass and all other unknown dynamics. Also, the Kalman filter is designed to improve the signal-to-noise ratio of the displacement detection based on the process and measurement noises. Several experiments are conducted to validate the effectiveness and feasibility of the proposed dynamic model and robust controller. The elastic vibrations during and after macro motion are significantly suppressed even with the parameter perturbation. Thus, the proposed control strategy can improve the manipulation stability, robustness, and accuracy.

A Digitized Representation of the Modified Prandtl-Ishlinskii Hysteresis Model for Modeling and Compensating Piezoelectric Actuator Hysteresis.

Piezoelectric actuators are widely used in micromanipulation and miniature robots due to their rapid response and high repeatability. The piezoelectric actuators often have undesired hysteresis. The Prandtl–Ishlinskii (PI) hysteresis model is one of the most popular models for modeling and compensating the hysteresis behaviour. This paper presents an alternative digitized representation of the modified Prandtl–Ishlinskii with the dead-zone operators (MPI) hysteresis model to describe the asymmetric hysteresis behavior of piezoelectric actuators. Using a binary number with n digits to represent the classical Prandtl–Ishlinskii hysteresis model with n elementary operators, the inverse model can be easily constructed. A similar representation of the dead-zone operators is also described. With the proposed digitized representation, the model is more intuitive and the inversion calculation is avoided. An experiment with a piezoelectric stacked linear actuator is conducted to validate the proposed digitized MPI hysteresis model and it is shown that it has almost the same performance as compared to the classical representation.

Stress-dependent generalized Prandtl–Ishlinskii hysteresis model of a NiTi wire with superelastic behavior

The extremely useful superelastic behavior of NiTi has been poorly explored because of the limited number of models that can describe the complete hysteretic behavior of NiTi, including a superelastic condition that strongly depends on the applied stress. This paper presents the development of a stress-dependent phenomenological model of NiTi by modifying the existing generalized Prandtl–Ishlinskii (GPI) model. The parameters of the envelop function of the GPI model’s play operator are reformulated as quadratic functions of the applied stress. The stress-dependent GPI model can satisfactorily predict the output strain of a NiTi #6 wire under temperature and stress variation.

Control and dynamic releasing method of a piezoelectric actuated microgripper

This paper proposes the control and dynamic releasing method of a symmetric microgripper with integrated position sensing. The microgripper adopted in this micromanipulation system is constructed by two L-shaped leverage mechanisms and the fingers of the microgripper is machined much thinner than the gripper body. A combined feedforward/feedback position controller is established to improve the motion accuracy of the microgripper in high frequency. The feedforward controller is established based on rate-dependent inverse Prandtl-Ishlinskii (P–I) hysteresis model. The inertial force generated in dynamic based releasing process is analyzed through MATLAB simulation. Open-loop experimental tests have been performed, and the results indicate the first natural frequency of the microgripper is 730 Hz. Then experiments in high frequency based on the developed combined controller are carried out and the results show the tracking error of a superimposed sinusoidal trajectory with the frequency of 100 Hz, 120 Hz and 130 Hz is 6.4%. Finally, the tiny objects releasing experiments are conducted where the combined controller is used to control the motion amplitude and frequency to achieve inertial force controllable to improve operation accuracy. And the results show that the dynamic releasing strategy is effective.

Multislope PI Modeling and Feedforward Compensation for Piezoelectric Beam

The hysteresis nonlinearity greatly reduces the tracking precision of piezoceramic actuators for expected displacement in a high-accuracy positioning system. In order to effectively compensate the hysteresis for piezoelectric ceramics, a novel modeling method, namely, multislope PI (Prandtl–Ishlinskii) was proposed. In view of the minimum mean square error (MSE) criterion, the weights of an improved PI model were identified by the quadratic programming optimization algorithm. For verifying the accuracy of the proposed multislope PI hysteresis model, a feedforward compensation control for piezoceramic beam was achieved. The corresponding experimental system was established, and the displacement tracking experiments were carried out. The results indicated that the mean tracking error was 0.2828 μm and within 1% of full scale, as well as the MSE was 0.3100 μm. Compared with the conventional PI model, the proposed multislope PI model demonstrated a significant improvement in positioning performance for the piezoceramic beam.

Operator-based nonlinear free vibration control of a flexible plate with sudden perturbations

In this paper, a new nonlinear vibration control scheme using piezoelectric actuator is proposed for a flexible plate with a free vibration and sudden perturbations. First, the effect of hysteresis nonlinearity from the piezoelectric actuator is considered by Prandtl-Ishlinskii (P-I) hysteresis model. Simultaneously, a dynamic model of the flexible plate with piezoelectric actuator is considered. Then, based on the dynamic model of the flexible plate, operator-based controllers are designed to guarantee the robust stability of the nonlinear control system. In addition, for ensuring the desired vibration control performance of the flexible plate with a free vibration and sudden perturbations, operator-based compensation method is given by the proposed design scheme. In the designed compensator, the desired compensation performances of tracking and of perturbations are obtained by increasing the number of designed n-times feedback loops. Finally, both of numerical simulation and experimental result are shown to verify the effectiveness of the proposed design scheme.

A Frequency-Dependent Prandtl–Ishlinskii Model of Hysteresis Loop Under Rotating Magnetic Fields

Recently, and during the measurements of core losses in electrical steel laminations, it has been observed that as the excitation frequency of the rotating field increases the measured hysteresis B-H loop rotates around the origin, thus, a lower frequency loop seems to slide out of the higher frequency loop. This phenomenon complicates the frequency-dependent modeling of hysteresis under rotating fields and causes inaccurate prediction of core losses when conventional hysteresis models are used. In this study, a frequency-dependent Prandtl-Ishlinskii (FDPI) hysteresis model is proposed to characterize the hysteresis loops under rotating magnetic fields at different frequencies. The proposed FDPI model shows a decent level of accuracy in the prediction task of hysteresis loops at different frequencies.

Modeling and control methodology for an XYZ micro manipulator

This paper presents the modeling and control methodology for a piezoactuated compliant XYZ manipulator toward precision positioning. The manipulator was fabricated using a wire electrical discharge machining technique, and the system identification was conducted to obtain the dynamic model based on the frequency response. To reduce the effects of hysteresis, creep, and external disturbances, a feedforward/feedback hybrid controller is proposed, which contains a dynamic dependent Prandtl-Ishlinskii (DDPI) hysteresis model and a novel sliding mode controller. The DDPI hysteresis model has excellent modeling accuracy at high operating frequencies with consideration of the dynamic characteristics of the micromanipulator. The novel sliding mode controller integrated with uncertainty and disturbance estimation (SMCUDE) technique is developed, which has the advantages of fast response, strong robustness, and resistance to chattering. The performance of the DDPI hysteresis model and the novel sliding mode controller is validated and compared using experimental tests. The experimental results indicate that the DDPI model provides better positioning accuracy than the traditional Prandtl-Ishlinskii (P-I) model and the rate-dependent P-I model, and furthermore, the SMCUDE controller can improve the response speed without loss of stability, which demonstrates that precision positioning operations can be implemented by the developed manipulator using the proposed control strategy.

A Modified Prandtl-Ishlinskii Hysteresis Modeling Method with Load-dependent Delay for Characterizing Magnetostrictive Actuated Systems

Abstract. The actuating precision of a micro-positioning system, driven by a magnetostrictive actuator, is adversely limited by its nonlinearities, particularly the output-input hysteresis, which are further affected by the operating load and input frequency. In this paper, the output-input properties of a magnetostrictive actuated system are experimentally characterized considering a wide range of operating frequencies and loads. The measured data revealed that the hysteresis behaviour is strongly affected with a change of operating load, and a modified Prandtl-Ishlinskii model with load-dependent delay is subsequently formulated to describe the nonlinear characteristics of the magnetostrictive actuated system in terms of major and minor loop hysteresis, and output magnitude and phase responses. The proposed model integrates a load-delay function related to the load mass with the Prandtl-Ishlinskii hysteresis model so as to fully describe the coupled nonlinear delay effects of the system output. The validity of the proposed model is demonstrated through comparisons with the experimental data for a range of operating loads and frequencies. It is shown that the proposed model can accurately describe the load-dependent hysteresis effects of the magnetostrictive actuated system up to certain input frequencies.

Operator‐based robust non‐linear vibration control for an L‐shaped arm with unknown load by using on‐line wavelet transform

An L-shaped arm with unknown load driven by a linear pulse motor is studied in this work. To control the motor motion and the arm vibration, an operator-based non-linear control is designed using an on-line discrete wavelet transform (DWT). First, the dynamics of the L-shaped arm vibration is modelled by considering the arm as a two-dimensional Euler–Bernoulli beam. The relationship between the load and the arm vibration is given. Second, by using the on-line DWT in the operator-based non-linear control, the proposed control for the system is designed. The wavelet transform is used to estimate the load and remove the influence of some undesired uncertainties. The operator-based right coprime factorisation method is used to guarantee the robust stability of the motor-arm system. The piezoelectric actuator is utilised to further reduce the arm vibration. The hysteresis of the piezoelectric actuator is compensated by using a Prandtl–Ishlinskii hysteresis model. Finally, simulation results are demonstrated to validate the proposed control.

Robust Control of Nonlinear System with Input and Output Nonlinear Constraints

With the development of modern technology, actuators and sensors composed of smart materials, such as piezoceramic and magnetostrictive materials, have been widely used in practice owing to their various advantages. However, in the working process of a smart material based actuator and sensor, non-smooth nonlinear constraints in their output responses may induce inaccuracies and oscillations, which severely degrade system performance. Therefore, input and output nonlinear constraints brought about by actuators and sensors should be considered. Generally, the output nonlinear constraint, namely, non-smooth effects from sensors, has been ignored. Therefore, in this paper, a robust control for a system with an output constraint as well as with both input and output constraints will be considered. Firstly, the generalized Prandtl-Ishlinskii (PI) hysteresis model is used for describing the input and output nonlinearities owing to its excellent characteristics, the model has proved suitable in theoretical operator based settings. Further, a robust control for a nonlinear system with an output nonlinear constraint is considered by using operator based robust right coprime factorization approach. Here, operator based robust stability is considered, and the control system structure including feedforward and feedback controllers is presented with a derivation of sufficient conditions for stable controller operation. Based on the proposed conditions, the influence from an output nonlinear constraint is rejected, the systems are robustly stable, and output tracking performance can be realized. Moreover, robust stability and output tracking performance for a nonlinear system with both input and output nonlinear constraints are also analyzed.

Grasping force hysteresis compensation of a piezoelectric-actuated wire clamp with a modified inverse Prandtl-Ishlinskii model.

This paper presents the grasping force hysteresis compensation of a piezoelectric-actuated wire clamp with a modified hysteresis model. Considering dynamic characteristics of the wire clamp, a modified inverse Prandtl-Ishlinskii (MIPI) hysteresis model is developed to improve the hysteresis modeling accuracy. The proposed MIPI model is composed of a P-I model and a dynamic model which are connected in parallel. The proposed hysteresis model has the advantage of high modeling accuracy with a concise identification process, which means the step by step identification is not needed here. Experiments on grasping force hysteresis compensation with a feedforward controller are carried out based on the developed MIPI model. The grasping force error in steady state lies in ±8.17 mN, while the maximum percentage and root mean square percentage of the grasping force error are 2.93% and 0.92%, respectively. The results show that the proposed hysteresis model is efficient and the wire clamp exhibits good performance with the feedforward controller. Therefore high frequency grasping operations can be realized based on the proposed MIPI hysteresis model.

Experimental Study on Robust Nonlinear Forced Vibration Control for an L-Shaped Arm with Reduced Control Inputs

This paper presents an operator-based robust nonlinear control approach for an L-shaped arm vibration experimental system. The arm is driven by a linear pulse motor to move along a frame and controlled by a piezoelectric actuator in parallel. The aim of this paper is to allow the motor to move fast and reduce the arm vibration by controlling the motion of the motor and the piezoelectric actuator simultaneously. In detail, first, the vibration dynamics of the L-shaped arm is modeled based on the Euler–Bernoulli beam theory. The hysteresis of the piezoelectric actuator is modeled using a Prandtl–Ishlinskii hysteresis model. Second, by using operator-based robust right coprime factorization approach, the proposed control for the system is designed where the linear motor is optimally controlled to reduce the time consumption and the vibration at the vertical part of the arm. Meanwhile, with the hysteresis compensation, the piezoelectric actuator is used to further reduce the vibration at the horizontal part of the arm. Finally, the results of the experiment are demonstrated to verify the effectiveness of the proposed control scheme.