Hysteresis Compensation Research Articles

Wet clutch pressure hysteresis compensation control under variable oil temperatures for electro-hydraulic actuators

The hysteresis characteristics and oil temperatures of wet clutch electro-hydraulic actuators have a significant impact on clutch pressure tracking performance, thereby influencing the launch, shift, and mode transition performance of both fuel and hybrid electric vehicles. In this study, we introduce a novel compensator for wet clutch pressure hysteresis that effectively adapts to variations in oil temperature. Experimental investigations were conducted to examine the hysteresis characteristic of the electro-hydraulic actuator and its susceptibility to changes in oil temperature. Subsequently, a temperature-dependent modified generalized Prandtl–Ishlinskii (TDMGPI) hysteresis model that accounts for the influence of oil temperature was established. To mitigate the effects of oil temperature fluctuations on the controller, we developed a fuzzy proportional-integral-derivative (FPID) controller, which dynamically adjusts controller gain. Furthermore, a feedforward-feedback controller for clutch pressure was established, incorporating the inverse solution of the TDMGPI model as the feedforward component and the FPID controller as the feedback element. The experiments were conducted at various oil temperatures, revealing that the proposed controller significantly enhances response speed and pressure tracking accuracy, maintaining good control performance across the tested range of oil temperatures.

A Physics-Based Hybrid Dynamical Model of Hysteresis in Polycrystalline Shape Memory Alloy Wire Transducers

Shape memory alloys (SMAs) are a class of smart materials that exhibit a macroscopic contraction of up to 5% when heated via an electric current. This effect can be exploited for the development of novel unconventional actuators. Despite having many features such as compactness, lightweight, and high energy density, commercial SMA wires are characterized by a highly nonlinear behavior, which manifests itself as a load-, temperature-, and rate-dependent hysteresis exhibiting a complex shape and minor loops. Accurate modeling and compensation of such hysteresis are fundamental for the development of high-performance SMA applications. In this work, we propose a new dynamical model to describe the complex hysteresis of polycrystalline SMA wires. The approach is based on a reformulation of the Müller–Achenbach–Seelecke model for uniaxial SMA wires within a hybrid dynamical framework. In this way, we can significantly reduce the numerical complexity and computation time without losing accuracy and physical interpretability. After describing the model, an extensive experimental validation campaign is carried out on a 75- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m diameter SMA wire specimen. The new hybrid model will pave the development of hybrid controllers and observers for SMA actuators.

Hysteresis modeling and compensation of a piezoelectric fast steering platform using multiple NARMA-L2 models

The piezoelectric fast steering platform (PFSP) enhances the scanning capabilities of lidar systems for autonomous vehicles. However, hysteresis nonlinearity degrades the scanning accuracy of the PFSP. To meet this challenge, this paper proposes a novel approach for hysteresis modeling and compensation using multiple nonlinear autoregressive moving average (NARMA)-L2 models. First, the hysteresis model is partitioned into a collection of submodels based on the K-means methodology, where the feature vector stems from the classical Bouc–Wen (CBW) model. Each submodel describes the dynamics of a specific hysteresis segment by a single NARMA-L2 model. The composite neural network (CNN), formed by combining two multilayer perceptron (MLP) networks, is trained to estimate the hysteresis output of the single NARMA-L2 model. Compared to the submodels obtained by evenly partitioning according to the input range, the submodels obtained by K-means partitioning offer higher hysteresis modeling accuracy. To compensate for the hysteresis nonlinearity, a novel adaptive Multi-NARMA-L2 (AMNL2) controller is then designed by online adjusting the parameters of the CNN. Furthermore, an adaptive filter is proposed to alleviate the oscillation caused by high-frequency disturbances during switching. Finally, experiments demonstrate that the AMNL2 controller outperforms the traditional MNL2 controller and the proportional–integral–derivative (PID) controller.

Equivalent-input-disturbance rejection-based adaptive motion control for pneumatic artificial muscle arms via hysteresis compensation models

With outstanding flexibility, pneumatic artificial muscles (PAMs) have shown unique advantages in human–robot interaction environments. However, asymmetric hysteresis nonlinearities, unknown transient or persistent time-varying disturbances, etc., seriously degrade control performance/robustness of PAM arms, and increase actuation failure risks. Meanwhile, existing disturbance rejection methods either rarely handle matched/unmatched disturbances, or require known disturbance dynamics. These defects limit the disturbance rejection ability in practical applications. To this end, a new adaptive output feedback control method is proposed in this article, which achieves efficient positioning and tracking control of PAM arms. Without requiring a priori knowledge of inverse plant models and disturbance upper bounds, the proposed method further enhances robustness against uncertainties and disturbances. Specifically, a generalized Bouc–Wen hysteresis loop is used to describe the asymmetric dynamic force of PAMs. Also, a new adaptive law is designed to compensate for the linearized parameters online. In particular, by applying a modified state observer to derive the equivalent-input-disturbance estimation solution, this article firstly realizes state observation, parameter estimation, and unknown transient/persistent external disturbance rejection simultaneously. The rigorous stability analysis demonstrates that the tracking errors converge to small neighborhoods of the origins. Finally, hardware experimental results with comparisons validate the effectiveness and robustness superiority of the proposed method.

Hysteresis Modeling and Compensation for a Fast Piezo-Driven Scanner in the UAV Image Stabilization System

The fast piezo-driven scanner (FPDS) compensates for vibrations in the unmanned aerial vehicle (UAV) image stabilization system. However, the hysteresis nonlinearity reduces the positioning accuracy of the FPDS. To address this challenge, this paper presents a novel weighted polynomial modified Bouc–Wen (WPMBW) model cascaded with a linear dynamic model to describe counterclockwise, asymmetric, and rate-dependent hysteresis loops of an FPDS. The proposed approach utilizes the weighted polynomial function to describe the asymmetric characteristic and the linear dynamic model to capture the rate-dependent behavior. By modifying the last two terms in the classical Bouc–Wen (CBW) model, the modified BW model directly characterizes the counterclockwise hysteresis loops with fewer parameters, circumventing the algebraic-loop problem that arises in the inverse CBW model. The pseudorandom binary sequence (PRBS) input is employed to decouple the linear dynamic model from the WPMBW model. The sinusoidal input is then applied to stimulate the hysteresis phenomenon, and the parameters of the WPMBW model are estimated by the particle swarm optimization (PSO) toolbox. Experimental results on a commercial FPDS show that the proposed model is superior to the CBW and traditional asymmetric BW models in modeling accuracy and feedforward hysteresis compensation.

Robust composite repetitive control with disturbance observer for high-precision tracking of piezo-actuated nano-stages with measurement delays.

In this paper, a robust composite control strategy in the framework of unified infinite-dimensional H∞ optimal control is developed to support nano-scale periodic tracking with improved non-harmonic disturbance attenuation of piezo-actuated nano-stages with sensor-induced measurement delays. In particular, we analyze the electromechanical coupled dynamics and derive a multi-perturbation model, where an extended Youla-Kucera parameterization-based repetitive controller with a disturbance observer is constructed to optimize control performances on high-precision tracking and perturbation rejection. The controller parameters are solved by using a unified infinite-dimensional H∞ optimization method. Comprehensive experiments on a piezo-actuated stage are conducted, where comparative results with representative methods, such as the conventional repetitive control and proportional-integral-derivative control, demonstrate significant performance improvements in hysteresis compensation, trajectory tracking, and disturbance suppression of the proposed method.

Fixed-time observer-based tracking controller for a hysteretic piezoelectric deformable mirror of an adaptive optic system.

Piezoelectric deformable mirrors (DM) are benefited from the high accuracy and swift dynamics. The hysteresis phenomenon, which inherently exists in piezoelectric materials, degrades the capability and precision of the adaptive optics (AO) systems. Also, the dynamics of piezoelectric DMs make the controller design more complicated. This research aims to design a fixed-time observer-based tracking controller (FTOTC), which estimates the dynamics, compensates the hysteresis, and ensures tracking to the actuator displacement reference, in the fixed time. Unlike the existing inverse hysteresis operator-based methods, the proposed observer-based controller overcomes the computational burdens and estimates the hysteresis in real-time. The proposed controller tracks the reference displacements, while the tracking error converges in the fixed time. The stability proof is presented by two consecutive theorems. Numerical simulations demonstrate superior tracking and hysteresis compensation by the presented method, from a comparison viewpoint.

Separable Tendon-Driven Robotic Manipulator with a Long, Flexible, Passive Proximal Section.

This work tackles practical issues which arise when using a tendon-driven robotic manipulator (TDRM) with a long, flexible, passive proximal section in medical applications. Tendon-driven devices are preferred in medicine for their improved outcomes via minimally invasive procedures, but TDRMs come with unique challenges such as sterilization and reuse, simultaneous control of tendons, hysteresis in the tendon-sheath mechanism, and unmodeled effects of the proximal section shape. A separable TDRM which overcomes difficulties in actuation and sterilization is introduced, in which the body containing the electronics is reusable and the remainder is disposable. An open-loop redundant controller which resolves the redundancy in the kinematics is developed. Simple linear hysteresis compensation and re-tension compensation based on the physical properties of the device are proposed. The controller and compensation methods are evaluated on a testbed for a straight proximal section, a curved proximal section at various static angles, and a proximal section which dynamically changes angles; and overall, distal tip error was reduced.

Hysteresis Modeling and Compensation for Tendon-Sheath Mechanisms in Robot-Assisted Endoscopic Surgery Based on the Modified Bouc-Wen Model With Decoupled Model Parameters

The tendon-sheath mechanism (TSM) has been widely applied in flexible endoscopy (FE) and natural orifice transluminal endoscopic surgery (NOTES) owing to its advantages of remote force and displacement transmission, size reduction, compactness, and convenient implementation. However, the positioning accuracy of TSMs is highly restrained by the motion hysteresis due to the complex friction condition between the tendon and sheath. The hysteresis phenomenon has posed significant challenges for modeling and controlling TSMs. This paper proposes a modified Bouc-Wen-based mathematical model to characterize the asymmetric hysteresis loop with distinct inflection points. The model parameters are decoupled, facilitating identification and reducing computational costs. Moreover, the model has retained the Bouc-Wen model structure, allowing for efficient derivation of the feedforward compensator based on the inverse multiplicative structure. The compensator was derived and cascaded with the TSM system to suppress the hysteresis phenomenon. Totally 120 trials of experiments were conducted to validate the proposed model and the feedforward control scheme on the two TSMs with different accumulated curvatures of 180∘ and 360∘. The results indicated that the proposed method achieved a 25.5% and 43.9% lower estimation and compensation error than the classical Bouc-Wen model. Further, it is worth noting that the model parameter identification time consumption has been significantly reduced to 5.8ms. The proposed model and the feedforward compensator can effectively linearize the TSM system and further facilitate delicate operations in robot-assisted surgical procedures.

Hysteresis Loops and Compensation Behavior of Ferrimagnetic Mixed Spin (3/2,5/2) Hexagonal Ising Nanowire with Core-Shell Structure: Monte Carlo Simulation

Hysteresis Loops and Compensation Behavior of Ferrimagnetic Mixed Spin (3/2,5/2) Hexagonal Ising Nanowire with Core-Shell Structure: Monte Carlo Simulation

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.

Development of a three-degree-of-freedom piezoelectric actuator.

Multi-degree of freedom piezoelectric actuators are strongly needed for industrial applications, especially when manipulating a large and heavy mirror or lens in an optical system. A novel three-degree-of-freedom piezoelectric actuator, which is driven by two pairs of piezo-stack actuator with spatial compliant mechanisms designed to guide the motion and preload the piezo-stack actuators, is herein proposed. The structure and working principle of the proposed actuator are illustrated and its kinematic characteristic is analyzed. The stiffness of the spatial compliant mechanisms is modeled, and the dynamic characteristics are analyzed, Finite Element method is utilized to validate the correctness of the stiffness modeling and the free vibration analysis of the proposed actuator. A prototype actuator is fabricated and its output performances have been tested. Working space of X ranging from -7.1 to 5.6μm, Y ranging from -6.2 to 8.2μm and Z ranging from -2.3 to 2.1μm, displacement resolutions of 15/16/21nm along X-/Y-/Z-axis and average velocities of 52.3, 82.8 and 29.5 µm/s along X-axis, Y-axis, and Z-axis with carrying load up to 2kg and driving frequency of 500Hz have been achieved by the prototype actuator. The method of waveform generating for the proposed actuator has been developed with the inverse hysteresis compensation, and test results indicate that the positioning accuracy of the prototype actuator in the open loop has been improved from 0.94 to 0.23μm for a circular trajectory tracking, from 0.48 to 0.29 μmm for an elliptical trajectory tracking, and from 0.61 to 0.32μm for a rectangular trajectory tracking with the compensated waveform of driving voltage.

Tracking control with external force self-sensing ability based on position/force estimators and non-linear hysteresis compensation for a backdrivable cable-pulley-driven surgical robotic manipulator

Cable-pulley-driven (CPD) manipulators are widely used in minimally-invasive surgical robots and systems. However, the cable-pulley systems also bring with significant nonlinear characteristics such as the hysteresis effect and elastic creep. Moreover, it is difficult to integrate the position and force detection elements at the end of the surgical instrument. This study proposes a method of high-performance tracking control involving a self-sensing ability of external force based on the position/force estimators and non-linear hysteresis compensation (NLHC) algorithm for a CPD surgical robotic manipulator. The experiment results demonstrate that the proposed method can significantly reduce the tracking error of the joint angle and improve the position control accuracy to approximately 99% under a varying load. Additionally, the estimation resolution of the self-sensing ability of external force was approximately 0.05 N. The method proposed in this study has potential applications in the motion control and force sensing of CPD manipulators, particularly for backdrivable CPD surgical robots.

Modeling and Control of Electromagnetic Coil System Using Model Order Reduction-Based LSSVM Method*

Magnetic micro/nanorobot (MM) is promising for in-body therapy due to its advantage of untethered controllability. Since the motion of MMs can be directly manipulated by the magnetic field (MF) created by electromagnetic coil systems, it is essential to study the MF generation control methods. In this study, iron core-based solenoids are employed in an electromagnetic coil system that can produce a stronger MF than regular coil systems. However, the coil system presents hysteretic nonlinearity due to the iron core's coercivity, which degrades closed-loop control performances. To tackle this challenge, an effective hysteresis compensation method is developed to linearize the solenoid system. Specifically, the least squares support vector machine (LSSVM) is adopted to model the hysteretic behavior of the solenoid system, and the discrete empirical interpolation method (DEIM) is applied to reduce the complexity of the model for improving the calculation efficiency. Based on the LSSVM and DEIM approaches, a highly efficient LSSVM-DEIM hysteresis compensator is developed. In order to generate precise dynamic MF effectively, the LSSVM-DEIM hysteresis compensator is combined with prevalent feedback controllers to form composite control schemes. Experiments show that the control system with the LSSVM-DEIM hysteresis compensator can produce a more accurate MF compared with that of the benchmark control methods.

Development of an Intuitive Interface with Haptic Enhancement for Robot-Assisted Endovascular Intervention.

Robot-assisted endovascular intervention has the potential to reduce radiation exposure to surgeons and enhance outcomes of interventions. However, the success and safety of endovascular interventions depend on surgeons' ability to accurately manipulate endovascular tools such as guidewire and catheter and perceive their safety when cannulating patient's vessels. Currently, the existing interventional robots lack a haptic system for accurate force feedback that surgeons can rely on. In this paper, a haptic-enabled endovascular interventional robot was developed. We proposed a dynamic hysteresis compensation model to address the challenges of hysteresis and nonlinearity in magnetic powder brake-based haptic interface, which were used for providing high-precision and higher dynamic range haptic perception. Also, for the first time, a human perceptual-based haptic enhancement model and safety strategy were integrated with the custom-built haptic interface for enhancing sensation discrimination ability during robot-assisted endovascular interventions. This can effectively amplify even subtle changes in low-intensity operational forces such that surgeons can better discern any vessel-tools interaction force. Several experimental studies were performed to show that the haptic interface and the kinesthetic perception enhancement model can enhance the transparency of robot-assisted endovascular interventions, as well as promote the safety awareness of surgeon.

Hybrid Adaptive Controller Design with Hysteresis Compensator for a Piezo-Actuated Stage

Piezo-actuated stage (P-AS) has become the topic of considerable interest in the realm of micro/nanopositioning technology in the recent years owing to its advantages, such as high positioning accuracy, high response speed, and large output force. However, rate-dependent (RD) hysteresis, which is an inherent nonlinear property of piezoelectric materials, considerably restricts the application of P-AS. In this research paper, we develop a Hammerstein model to depict the RD hysteresis of P-AS. An improved differential evolution algorithm and a least-squares algorithm are used to identify the static hysteresis sub-model and the dynamic linear sub-model for the Hammerstein model, respectively. Then, a hysteresis compensator based on the inverse Bouc–Wen model is designed to compensate for the static hysteresis of the P-AS. However, the inevitable modeling error presents a hurdle to the hysteresis compensation. In addition, external factors, such as environmental noise and measurement errors, affect the control accuracy. To overcome these complications, a hybrid adaptive control approach based on the hysteresis compensator is adopted to increase the control accuracy. The closed-loop system stability is analyzed with the help of the Lyapunov stability theory. Finally, experimental results indicate that the raised control approach is effective for the accurate positioning of P-AS.

An Extreme Learning Machine for the Simulation of Different Hysteretic Behaviors

Hysteresis is a non−unique phenomenon known as a multi−valued mapping in different fields of science and engineering. Accurate identification of the hysteretic systems is a crucial step in hysteresis compensation and control. This study proposes a novel approach for simulating hysteresis with various features that combines the extreme learning machine (ELM) and least−squares support vector machine (LS−SVM). First, the hysteresis is converted into a single−valued mapping by deteriorating stop operators, a combination of stop and play hysteresis operators. Then, the converted mapping is learned by a LS−SVM model. This approach facilitates the training steps and provides more accurate results in contrast to the previous experimental studies. The proposed model is evaluated for several hystereses with various properties. These properties include rate−independent or rate−dependent, congruent or non-congruent, and symmetric or asymmetric problems. The results indicate the efficiency of the newly developed technique in terms of accuracy, computational cost, and convergence rate.

Data-driven fractional order phase-lead and proportional–integral feedback control strategy with application to a reluctance-actuated compliant micropositioning system

This paper aims to overcome complex dynamic problems such as low damping resonant frequency, resonant point drift, and uncertainty of dynamic model of the large stroke micropositioning stage, based on Maxwell reluctance actuator. A composite control method of data-driven fractional phase-lead proportional-integral feedback controller with series hysteresis compensator is proposed. Firstly, the working principle of the Maxwell reluctance actuator is briefly explained, a large stroke flexure micropositioning system is built, and its motor constant and stiffness characteristics are experimentally measured. Secondly, aiming at the rapid phase drop caused by low damping resonance, a data-driven fractional order phase-lead and proportional-integral feedback controller is designed, and the parameters of the fractional order feedback controller are experimentally adjusted based on the iterative feedback tuning algorithm. And the intrinsic hysteresis nonlinearity of the reluctance actuator is firstly compensated by a Prandtl–Ishlinskii model hysteresis compensator which is always placed in the feedback loop of the control system. Then, the proposed controller is compared with other controllers. The experimental results show that this method has a significant suppression effect on high-frequency noise, and the tracking error is significantly reduced, which proves the effectiveness of this stage and control method. • Based on the Maxwell reluctance actuator, a large stroke flexure micropositioning system is built. • A fractional order phase-lead proportional integral controller is proposed, and the integer order approximation of the controller is completed by using oustaloup approximation method • The data-driven method of iterative feedback tuning is used to obtain the parameters of the fractional order controller. • Through the analysis and comparison of linearity, sensitivity function and open-loop frequency response, the advantages of the proposed controller are fully proved.

Novel Calibration Methodologies for Compliant, Multiaxis, Fiber-Optic-Based Force/Torque Sensors

In this article, we present a number of novel calibration methodologies for compliant, multiaxis, fiber-optic-based force/torque sensors and evaluate the performance of these methods in real-time experiments with our custom-designed sensors. These methods address the challenges arising from the complex dynamic behavior of a compliant sensor and the nonlinearities in the force–deflection relationship. This article also investigates compliant sensor performance against its response characteristics, such as the impact of compliance on the sensor’s bandwidth using dynamic modeling and identification process. A powerful hysteresis compensation solution using a dynamic estimation model is also presented. Furthermore, we propose and apply a new calibration strategy building on the combination of a linear dynamic model combined with a static nonlinear model. This includes a state space (SS) model with Gaussian Process Regression (GPR) model named SSGPR. The results achieved from the proposed calibration method have revealed an improvement from an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R}$ </tex-math></inline-formula> -squared value of 93.86%–100% when compared to data obtained using a linear dynamic model.

Simultaneous micropositioning and microvibration control of a magnetostrictive Stewart platform with synthesized strategy

In this paper, we present a hybrid adaptive feedforward and feedback controller with hysteresis compensator on a magnetostrictive-actuated multi degree of freedom (DOF) positioning and vibration isolation integrated system (PVIIS). The PVIIS is custom-developed and based on “cubic” Stewart configuration. It is challenging to develop an effective controller to systematically address the issues of cross-coupling, strut hysteresis and dynamics for the PVIIS. Magnetostrictive asymmetric hysteresis leads to the loss of closed-loop output performance with conventional linear controller. To this end, a novel comprehensive controller is proposed in this paper. With the inverse kinematics analysis, the spatial motion of the mobile plate of the PVIIS is decoupled into the independent motions of six actuator struts. As for controlling the single strut of the PVIIS, the hybrid adaptive feedforward (AFF) and proportional–integral–derivative (PID) feedback controller with asymmetric hysteresis compensator (HC) is constructed. Among them, the AFF sub-controller is characterized by an adaptive finite impulse response (FIR) filter whose coefficients are updated by normalized least-mean squares (NLMS) algorithm. The PID feedback sub-controller is introduced to enhance the ability of positioning and vibration isolation. The arctangent-polynomial modified Prandtl–Ishlinskii (APMPI) model is used to build the inversion-based asymmetric hysteresis compensator. The experimental set-up is built. The positioning and vibration isolation experiments are conducted. Experimental studies show that the output performances are best with the proposed controller compared against sole AFF, hybrid AFF and PID controllers. With the proposed controller, the relative positioning error can maintain around 2.83% when the PVIIS performs 2-DOF rotation in the presence of 0.5 Hz disturbance.