Hysteresis Compensation Research Articles

Adaptive fast finite‐time control for nonlinear systems subject to output hysteresis by fuzzy approach

SummaryThis article investigates an adaptive fast finite‐time tracking control problem for a class of uncertain nonlinear systems with output hysteresis. The idea of output hysteresis compensation is skillfully extended to adaptive design by employing a hysteresis inverse transformation and barrier Lyapunov function. The backstepping technique is adopted to establish the fast finite‐time control strategy, which can realize finite‐time convergence of the closed‐loop system. A rigorous theoretical analysis is performed to illustrate that the signals in the closed‐loop systems are bounded in finite time, and the tracking error can converge into a compact set with sufficient accuracy. Finally, a numerical simulation is given to confirm the effectiveness of the presented strategy.

Proxy-Based Sliding Mode Force Control for Compliant Grinding via Diagonal Recurrent Neural Network and Prandtl-Ishlinskii Hysteresis Compensation Model

Traditional industrial robots often face challenges in achieving a perfectly polished surface on a workpiece because of their high mechanical rigidity. The active compliance force control device installed at the robotic arm’s end enables high-precision contact force control between the grinding tool and the workpiece. However, the complex hysteresis nonlinearity between cylinder air pressure and output force, as well as various random disturbances during the grinding process, can affect the accuracy of the contact force and potentially impact the grinding effect of the workpiece, even causing irreversible damage to the surface of the workpiece. Given the complex random variation of cylinder output force in the actual grinding process, a rate-dependent hysteresis model based on diagonal recurrent neural network and Pradtl–Ishlinskii models named dRNN-PI is designed to compensate for the complex nonlinear hysteresis of the cylinder and calculate the desired air pressure to maintain a steady contact force on the workpiece. The proxy-based sliding mode control (PSMC) is utilized to quickly track the desired air pressure without overshooting. This paper also proves the controller’s stability using the Lyapunov-based methods. Finally, the accuracy of the proposed hysteresis compensation model and the effectiveness and robustness of the PSMC are verified by experiment results.

On the hysteresis characteristics and compensation control strategy of a pneumatic hydrodynamic retarder

As the core component of the hydrodynamic retarder braking system, pneumatic proportional solenoid valve plays an important role in the process of braking torque control. However, the hysteresis characteristic caused by friction and air compressibility will lead to the deviation of braking torque. In order to solve this problem, the hysteresis characteristic of pneumatic proportional solenoid valve is experimentally studied, and the causes of hysteresis phenomenon are analyzed through mathematical modeling of the valve core. Then, a high-precision prediction model of braking torque is obtained by combining Computational Fluid Dynamics (CFD) and response surface method, which is used to construct the mapping relationship between control air pressure and braking torque. Furthermore, a feedforward controller based on Prandtl–Ishlinskii inverse model is designed to compensate the hysteresis characteristics. On this basis, a compound hysteresis characteristics compensation control strategy combined with Proportional Integral Derivative (PID) feedback control is proposed to realize the accurate control of braking torque. Finally, the test verification of braking torque control is carried out. The average error of compound control, feedforward control, and PID control under torque step working condition is 3.16%, 5.97%, and 6.23%, and the response time is 3.75, 8.75, and 3.2 s, respectively. The compound control strategy also has smaller torque error and shorter response time under both ramp torque tracking and constant torque conditions. To sum up, this compound control strategy can effectively compensate the hysteresis characteristics of the pneumatic hydrodynamic retarder and ensure the driving safety by improving the control accuracy and response speed of braking torque.

Active Neural Network Control for a Wearable Upper Limb Rehabilitation Exoskeleton Robot Driven by Pneumatic Artificial Muscles.

Pneumatic artificial muscle (PAM) has been widely used in rehabilitation and other fields as a flexible and safe actuator. In this paper, a PAM-actuated wearable exoskeleton robot is developed for upper limb rehabilitation. However, accurate modeling and control of the PAM are difficult due to complex hysteresis. To solve this problem, this paper proposes an active neural network method for hysteresis compensation, where a neural network (NN) is utilized as the hysteresis compensator and unscented Kalman filtering is used to estimate the weights and approximation error of the NN in real time. Compared with other inversion-based methods, the NN is directly used as the hysteresis compensator without needing inversion. Additionally, the proposed method does not require pre-training of the NN since the weights can be dynamically updated. To verify the effectiveness and robustness of the proposed method, a series of experiments have been conducted on the self-built exoskeleton robot. Compared with other popular control methods, the proposed method can track the desired trajectory faster, and tracking accuracy is gradually improved through iterative learning and updating.

Trajectory Tracking Control of Dual-PAM Soft Actuator With Hysteresis Compensator

Trajectory Tracking Control of Dual-PAM Soft Actuator With Hysteresis Compensator

Motion Hysteresis Compensation Based on Motor Current Segmentation for Elongated Cable-Driven Surgical Instruments

Cable-driven surgical instrument is a reusable and disposable component of Robot-assisted Minimally Invasive Surgery, and it is time-consuming to identify the motion hysteresis compensation model of each instrument in large-scale identification. Besides, the identification results failure caused by the loss of cable tension or lubrication conditions during repeated usage interferes with the accuracy of motion hysteresis compensation. To simplify the identification process and lengthen the instrument life, this paper leverages the relationship between actuate motor current and hysteresis phases, developing a novel motion hysteresis compensation method to compensate the motor reference trajectory. Firstly, prior knowledges including motor current and hysteresis curves of several instruments are collected to train the Hysteresis Identification model and Curve Generation model. Once the two models are well-trained in practical use, the only sensor data in need is the motor current for the Hysteresis Identification model, and the compensation curve will be generated pertinently for the instrument under current use. Finally, Feedforward Compensation scheme is conducted to compensate the reference trajectory of the actuate motor. Experiments study the range of hysteresis compensation errors when the method is applied to numerous surgical instruments with different motion hysteresis, and the feasibility and accuracy are verified. The method can be potentially applied to a wide range of cable-driven mechanisms facing the problem of large-scale identification or the identification results failure after repeated use. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes a feasible motion hysteresis compensation method for cable-driven mechanism (CDM). For some CDMs like elongated cable-driven surgical instrument, their motion hysteresis characteristics will change during repeated use, and their distal angle and cable tension are not available in the environment of use. In these cases, the proposed method enables re-identification because the distal angle or cable tension are not needed during the practical use of our method. Besides, it is easy and low-cost for large-scale identification due to the simplicity of identification procedure. Once the Hysteresis Identification model and Curve Generation model are trained using the pre-collected prior knowledge including motor current and the angle of the end effector, the only sensor data in need to identify and compensate a certain CDM is the its motor current. Then, the pertinent compensation curve for the CDM device can be generated for the actuate motor to follow. The experimental results reveal that the competitive performance with other state-of-the-arts can be achieved. In the future research, we will integrate dynamic characteristics of CDM into the method to expand the scope of application.

A Method Toward Comprehensive Identification for Piezoelectric Dynamic System With Multimodal Hysteresis and Uncertainty Compensation

A Method Toward Comprehensive Identification for Piezoelectric Dynamic System With Multimodal Hysteresis and Uncertainty Compensation

A Modular Direct Description Method With Low Memory Usage and Execution Time for Hysteresis Modeling and Compensation of Piezoelectric Actuators

A Modular Direct Description Method With Low Memory Usage and Execution Time for Hysteresis Modeling and Compensation of Piezoelectric Actuators

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.

Disturbance observer-based robust optimal control of rate-dependent hysteretic systems: Application to a piezoelectric nano-manipulator

This article investigates the robust and optimal control problem of hysteretic systems with both parameter variations and unmodeled dynamics. By means of a hysteresis compensator based on a modified Prandtl–Ishlinskii model and a feedback controller, a novel robust optimal control architecture is proposed to address the asymmetric and rate-dependent hysteresis nonlinearities and various disturbances, where the compensation errors, parameter variations, and unmodeled dynamics are treated as a bounded disturbance. The proposed controller is composed of two components: a high order sliding mode observer and an extended linear quadratic controller. The high order sliding mode observer is introduced to guarantee that the disturbance observation error converges to the origin in a finite time such that the extended linear quadratic controller enables the predefined optimal performance to be achieved. Moreover, the exponential stability of the closed-loop system has been proven, and some sufficient conditions are given. Finally, the proposed control algorithm is applied to a piezoelectric nano-manipulator system, both the good hysteresis modeling accuracy and excellent tracking performance are demonstrated in the real-time experiments.

Hysteresis compensation by deep learning algorithms

We propose a Deep Learning (DL) algorithm, which connected to a Preisach-memory updating rule, allows to describe rate-independent memory phenomena. Memory rules could be realized through the employment of Play or Stop operators, which, as known, show counter- or clockwise loops. The former are suitable to represent the classical operators of Preisach type, while the latter, showing clockwise cycles, is well behaved to describe the inverse or compensator operator. The paper is aimed to propose a unified approach that, through a specific structure of the hysteresis model (splitting the memory rules from the rest) is able to optimize performances of a Deep Learning (DL) algorithm and describe both hysteresis process and its compensator with good accuracy and computational efficiency. The approach would pander the actual stream that locates the need to extract the basic features of the phenomenon in connection to a neural algorithm in order to improve the modeling performances of the whole model, specifically aimed to implement compensator operators for e.g. control tasks.

Creep and Hysteresis Compensation in Pressure-Sensitive Mats for Improving Center-of-Pressure Measurements

Creep and Hysteresis Compensation in Pressure-Sensitive Mats for Improving Center-of-Pressure Measurements

Infinite Dimensional Design Approach of Robust Disturbance Observer for a Piezo-Actuated Nano-Positioner With Measurement Delays

In this article, we consider the disturbance observer (DOB) design supporting high performance nano-positioning with sensor-induced time delays, where the standard robust disturbance observer design methodology is extended to time-delay systems by employing an infinite dimensional approach. In particular, the dynamic model including the piezo-induced hysteresis and the measurement delays are investigated and the infinite dimensional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}^\infty$</tex-math></inline-formula> optimization problem is formulated to achieve an optimal Q-filter design in the DOB control framework. The fragility resulting from unstable pole-zero cancellations in the infinite dimensional Q-filter is further discussed and the direct-moment-matching-based rational approximation is developed for stable digital implementations of the proposed method. Comprehensive experimental studies are conducted on a piezo-actuated stage, where the proposed method successfully demonstrates excellent performances on hysteresis compensation, disturbance suppression, and trajectory tracking, significantly outperforming existing approaches.

Dynamic modelling and inverse compensation for coupled hysteresis in pneumatic artificial muscle-actuated soft manipulator with variable stiffness

The soft manipulator actuated parallel with contractile and extensor pneumatic artificial muscles (PAMs) can perform continuous operations and vary stiffness. Due to the hysteresis nonlinearity of PAMs and parallel driving, the manipulator shows coupled hysteresis with stiffness-dependent and rate-dependent characteristics, causing inaccurate positioning performance. This paper firstly proposes a comprehensive dynamic model consisting of two parts in series to predict the manipulator dynamical behaviors with coupled hysteresis. Furthermore, a decoupled inverse compensation and decoupling control on the basis of the proposed model is conducted on the soft manipulator. Experimental results and comparisons illustrate the high precision and strong generalization ability of the proposed model and the validity of the compensator in mitigating the coupled dynamic hysteresis of the system.

Design and Experiment of a Breakpoint Continuous Spraying System for Automatic-Guidance Boom Sprayers

Repeated and missed spraying are common problems during the working of boom sprayers, especially in the breakpoint continuous process. Therefore, the present study investigated a breakpoint continuous spraying system for automatic-guidance boom sprayers based on a hysteresis compensation algorithm for spraying. An operational breakpoint identification algorithm, which combines a real-time kinematic global navigation satellite system (RTK-GNSS) and wheel odometer, was proposed; a pre-adjusted proportional-integral-derivative (PID) control algorithm for the opening degree of the proportional control valve was designed in thus study. Tests were conducted to establish equations correlating the opening degree of the proportional control valve, pump output flow rate, and main pipeline flow rate, with an R2 ≥ 0.9525. The time to adjust to the target flow rate was experimentally tested. The breakpoint identification accuracy of the RTK-GNSS and RTK-GNSS + wheel odometer was experimentally assessed. A field spraying deposition variation experiment was conducted. According to the results, the system effectively eliminated missed spraying, with a maximum repeated spraying distance of ≤3.3 m, and it achieved a flow control error within 3%. This system also reduced the repeated spraying area and enhanced the pesticide spraying quality of breakpoint continuous spraying for automatic-guidance boom sprayers.

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%.

High-Bandwidth Repetitive Trajectory Tracking Control of Piezoelectric Actuators via Phase-Hysteresis Hybrid Compensation and Feedforward-Feedback Combined Control.

Piezoelectric actuators (PEAs) are widely used in many nano-resolution manipulations. A PEA's hysteresis becomes the main factor limiting its motion accuracy. The distinctive feature of a PEA's hysteresis is the interdependence between the width of the hysteresis loop and the frequency or rate of the control voltage. Generally, the control voltage is first amplified using a voltage amplifier (VA) and then exerted on the PEA. In this VA-PEA module, the linear dynamics of the VA and the nonlinearities of the PEA are coupled. In this paper, it is found that the phase lag of the VA also contributes to the rate dependence of the VA-PEA module. If only the PEA's hysteresis is considered, it will be difficult to achieve high-frequency modeling and control. Consequently, great difficulties arise in high-frequency hysteresis compensation and trajectory tracking, e.g., in the fast scanning of atomic force microscopes. In this paper, the VA-PEA module is modeled to be the series connection of a linear subsystem and a nonlinear subsystem. Subsequently, a feedforward phase-dynamics compensator is proposed to compensate for both the PEA's hysteresis and the phase lag of the VA. Further, an unscented Kalman-filter-based proportional-integral-derivative controller is adopted as the feedback controller. Under this feedforward-feedback combined control scheme, high-bandwidth hysteresis compensation and trajectory tracking are achieved. The trajectory tracking results show that the closed-loop trajectory tracking bandwidth has been increased to the range of 0-1500 Hz, exhibiting excellent performance for fast scanning applications.

Compound Control of Trajectory Errors in a Non-Resonant Piezo-Actuated Elliptical Vibration Cutting Device.

To improve the machining quality of the non-resonant elliptical vibration cutting (EVC) device, a compound control method for trajectory error compensation is proposed in this paper. Firstly, by analyzing the working principle of non-resonant EVC device and considering the elliptical trajectory error caused by piezoelectric hysteresis, a dynamic PI (Prandtl-Ishlinskii) model relating to voltage change rate and acceleration was established to describe the piezoelectric hysteresis characteristics of EVC devices. Then, the parameters of the dynamic PI model were identified by using the particle swarm optimization (PSO) algorithm. Secondly, based on the dynamic PI model, a compound control method has been proposed in which the inverse dynamic PI model is used as the feedforward controller for the dynamic hysteresis compensation, while PID (proportion integration differentiation) feedback is used to improve the control accuracy. Finally, trajectory-tracking experiments have been conducted to verify the feasibility of the proposed compound control method.

Data-Based Shape Self-Sensing of a Cable-Driven Notched Continuum Mechanism Using Multidimensional Intrinsic Force Information for Surgical Robot

Abstract The accurate shape-sensing capability of the continuum mechanism is fundamental to improve and guarantee the motion control accuracy and safety of continuum surgical robots. This paper presents a data-based shape self-sensing method for a cable-driven notched continuum mechanism using its multidimensional intrinsic force information, which mainly includes the multidimensional forces/torques and driving cable tensions. The nonlinear hysteresis compensation and the shape estimation of the notched continuum mechanism play significant roles in its motion control. Calibration compensation of the notched continuum mechanism is performed based on kinematic modeling to improve the accuracy of its preliminary motion control. The hysteresis characteristics of the continuum mechanism are analyzed, modeled, and compensated through considering the abundant dynamic motion experiments, such that a feedforward hysteresis compensation controller is designed to improve the tracking control performance of the continuum mechanism. Based on the kinematic calibration and hysteresis compensation, combined with the motor displacement, driving cable tensions, and six-dimensional forces/torques information of the continuum mechanism, a data-based shape self-sensing method based on particle swarm optimization back propagation neural network (PSO-BPNN) is proposed in this study. Experimental results show that this method can effectively estimate the loaded and unloaded shape of the notched continuum mechanism, which provides a new approach for the shape reconstruction of cable-driven notched continuum surgical robots.

Compensation control strategy of hybrid driven three-dimensional elliptical vibration assisted cutting system based on piezoelectric hysteresis model

Three-dimensional elliptical vibration assisted cutting (3D-EVC) technology has been widely used in many high-precision technical fields due to its high-efficiency processing characteristics. However, the hysteresis and nonlinearity caused by the piezoelectric drive in the 3D-EVC system will impact the system control accuracy. This paper mainly studies the hysteresis and nonlinearity of the system, the feedforward-gray predicted fuzzy PID compound controller based on the generalized Bouc-Wen hysteresis nonlinear model and it is designed to realize the hysteresis compensation of the system. In this paper, input voltage and output displacement are represented by a mathematical relationship, and this relationship of the 3D-EVC system will be described by the generalized Bouc-Wen model. The improved flower pollination algorithm (IFPASO) is adopted in the identification process of parameters. A compound control strategy is formed based on traditional feed-forward control combined with fuzzy PID feedback control to compensate for hysteresis and nonlinearity, and an improved gray prediction model is introduced into the feedback loop. The 3D-EVC system tracking experiment verifies the effectiveness of the designed compound controller. Experiments have proved that the hysteresis component of the system is significantly reduced after the use of the compound controller for hysteresis compensation, and the system has a higher degree of stability.