Backlash-like Hysteresis Research Articles

Modeling Backlash-like Hysteresis and Feedforward Control of Tendon-Sheath Mechanism Pair with Arbitrary Shape: Excluding Distal Sensory Input

Abstract The tendon-sheath mechanism (TSM) has garnered attention for its versatile applications in soft robotics, robotic hands, and surgical robots due to its adeptness in transmitting force through tortuous and narrow channels. However, precise control of the TSM is challenging due to its shape-dependent deformation and force generation, highlighting the need to address shape variations in dynamic environments where direct measurement is impractical. This paper introduces a novel methodology leveraging the concept of the equivalent circle in TSM to model its shape under varying conditions. The equivalent circle substitutes an arbitrarily shaped TSM with a circle, whose radius is derived from TSM's deformation and forces measured at the proximal end during calibration. This approach provides a concise and effective framework for understanding and analyzing the distinct characteristics of TSM. Additionally, a control strategy is proposed, utilizing the estimated equivalent circle to adapt to dynamic environments. Experimental results demonstrate promising performance without distal end sensory feedback, with mean percentage errors (MPE) of 0.78% and 2.33% for predicting cumulated curve angle and equivalent circle radius, respectively. Moreover, by utilizing the equivalent circle to calculate and feedforward deadband, effective control is achieved. The root mean square error (RMSE) reduced from 1.31 mm to an average of 0.19 mm in two feedforward experiments, representing an average reduction of 85.5%. These findings shed light on effective control strategies for TSM, offering valuable insights for robotics and surgical applications where TSM shape configurations are uncertain and subject to dynamic change.

Predefined-time adaptive fuzzy control for nonlinear output constraint systems with unknown backlash-like hysteresis via command filtering

In this article, the predefined-time adaptive fuzzy control problem for strict-feedback nonlinear systems with asymmetric time-varying output constraint and unknown backlash-like input hysteresis is considered. An innovative predefined-time adaptive control method, in which utilises unified barrier function (UBF) to deal with the output constraint problem and adopts a differential equation to represent the unknown backlash-like hysteresis, is presented by combining a novel command filter with backstepping technology. Fuzzy logic systems (FLSs) are employed to estimate the unknown nonlinearities. Moreover, by designing appropriate parameters, the constructed control strategy ensures that all signals are predefined-time bound and the tracking error stays in a small neighbourhood adjacent zero. Ultimately, two simulation examples are given to prove the effectiveness of the presented control algorithm.

Self-Triggered Adaptive Bipartite Tracking Control for Nonlinear MASs With Unmatched Disturbances and Backlash-Like Hysteresis

Self-Triggered Adaptive Bipartite Tracking Control for Nonlinear MASs With Unmatched Disturbances and Backlash-Like Hysteresis

Adaptive prescribed performance tracking control for uncertain nonlinear systems with unknown backlash-like hysteresis

In this paper, an adaptive prescribed performance tracking control(PPTC) problem of uncertain nonlinear systems with unknown hysteresis input is investigated. For the purpose of implementing the PPTC, a performance function and an error conversion function are introduced. Moreover, a backlash-like hysteresis model is adopted to describe the hysteresis nonlinearity, which makes the controller design feasible. Additionally, by converting the backlash-like hysteresis model into a linear model with bounded error, the difficulties caused by hysteresis behavior on controller design are settled. Thus, integrating multi-dimensional Taylor network(MTN) approximation technique into adaptive backstepping method, an adaptive control scheme for uncertain nonlinear systems is proposed. Apart from ensuring that all signals of the closed-loop system keep bounded, the proposed control scheme not only makes the tracking error converge to an arbitrarily small neighborhood around the origin, but also guarantees the tracking error trajectory within the limits set by PPTC. Ultimately, two simulations are applied to verify the validity of the proposed control scheme.

Adaptive iterative learning control for a class of parameterized fractional-order systems subjected to backlash-like hysteresis

In this article, a fractional-order adaptive iterative learning control scheme is proposed for a class of parameterized fractional-order systems with unknown control gain and backlash-like hysteresis nonlinearity under disturbance. Based on the sufficient condition for the stability of linear fractional-order systems, a sliding mode surface of tracking errors is constructed to facilitate the controller design and stability analysis. A new boundary layer function is designed by using Mittag-Leffler function to relax the restriction of the identical initial condition of iterative learning control design. The fractional-order differential-type adaptive laws and difference-type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. To deal with the influence of backlash-like hysteresis nonlinearity reminder term and unknown bounded external disturbance, a robust control term is designed by employing the hyperbolic tangent function with a convergent series sequence which can guarantee the learning convergence along iteration axis. By constructing Lyapunov-like composite energy function, the stability analysis is presented to prove the convergence of the system output to a small neighborhood of the desired trajectory and the boundedness of all the closed-loop signals. Finally, a simulation example of second-order nonlinear fractional-order system is presented, which demonstrates the effectiveness of the proposed fractional-order adaptive iterative learning control scheme.

Neural networks-based adaptive command filter control for nonlinear systems with unknown backlash-like hysteresis and its application to single link robot manipulator

<abstract><p>In this paper, an adaptive neural network control problem for nonstrict-feedback nonlinear systems with an unknown backlash-like hysteresis and bounded disturbance was presented. Radial basis function neural networks (RBFNN) were used to approximate the unknown functions and the problem of the explosion of complexity problem was handled by utilizing the command filter method. Furthermore, the influence of an unknown backlash-like hysteresis input was addressed by approximating an intermediate variable. Based on the backstepping method and the command filter technique, an adaptive neural network controller was designed via the approximation abilities of RBFNN. With the help of the Lyapunov stability theory, the proposed controller ensures that all of the signals in closed-loop systems are bounded and that the tracking error fluctuates close to the origin within a bounded area. Finally, a real-world example based on the single-link manipulator was shown to demonstrate the viability of the presented approach.</p></abstract>

Adaptive neural output-feedback control for nonstrict-feedback stochastic nonlinear time-delay systems with hysteresis

This paper proposes an adaptive neural outputfeedback controller for a class of nonstrict-feedback stochastic nonlinear time-delay systems with unknown backlash-like hysteresis. First, a state observer is established for estimating the unmeasured states. Second, an appropriate Lyapunov-Krasovskii functional is used to compensate the unknown time-delay terms, and the neural network is employed to approximate the unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of the origin. Two examples are presented to further show the effectiveness of the proposed approach.

Adaptive Neural Network Control of an Uncertain 2-DOF Helicopter With Unknown Backlash-Like Hysteresis and Output Constraints.

An adaptive neural network (NN) control is proposed for an unknown two-degree of freedom (2-DOF) helicopter system with unknown backlash-like hysteresis and output constraint in this study. A radial basis function NN is adopted to estimate the unknown dynamics model of the helicopter, adaptive variables are employed to eliminate the effect of unknown backlash-like hysteresis present in the system, and a barrier Lyapunov function is designed to deal with the output constraint. Through the Lyapunov stability analysis, the closed-loop system is proven to be semiglobally and uniformly bounded, and the asymptotic attitude adjustment and tracking of the desired set point and trajectory are achieved. Finally, numerical simulation and experiments on a Quanser's experimental platform verify that the control method is appropriate and effective.

Event-based adaptive tracking control for robotic systems with deferred position constraints and unknown backlash-like hysteresis

This paper proposes an event-based adaptive tracking control scheme for the n-link robotic systems in the presence of unknown backlash-like hysteresis (BLH) and deferred position constraints. By combining a transformation error with an asymmetric Lyapunov function, the devised control tactic achieves that the position constraints of robotic systems are not violated after user pre-specified time. In contrast to the results of robotic systems with position constraints, this paper removes a common assumption condition generated by the conventional barrier Lyapunov function method. Then, the adverse effect of unknown BLH can be offset by the Nussbaum function. Meanwhile, an event-triggered mechanism is designed to economize on the network bandwidth resources. Finally, based on the Lyapunov theory, an event-based adaptive tracking control tactic is proposed to ensure that all the signals of robotic systems are bounded under unknown BLH and deferred position constraints. Some simulation results proof that the devised control scheme is valid.

Robust Adaptive Fault-Tolerant Control for a Riser-Vessel System With Input Hysteresis and Time-Varying Output Constraints.

Recently, with the development of the marine economy, marine risers have garnered increasing attention as they present facile and reliable methods for oil and gas transportation. However, these risers are susceptible to vibrations, which can lead to system performance degradation and fatigue damage. Therefore, effective vibration control strategies are required to address this issue. In this study, a novel adaptive fault-tolerant control (FTC) strategy is adopted to suppress the vibrations of a 3-D riser-vessel system against the effects of actuator failures, backlash-like hysteresis, and external disturbances. A barrier-based Lyapunov function is merged to eliminate the time-varying output constraints of the system. Adaptive FTC laws with projection mapping operators are designed to compensate for parameter uncertainties and consider input nonlinearities to improve system robustness. Finally, a rigorous Lyapunov analysis and numerical simulations are performed to verify the validity of the proposed controller and guarantee uniformly bounded stability of the system.

Low-cost adaptive prescribed time tracking control for switched nonlinear systems

ABSTRACT This paper addresses a low-cost adaptive prescribed time tracking control strategy for switched nonlinear systems with input quantisation and unknown backlash-like hysteresis. Initially, a transformation function is introduced into the control design, which allows the tracking error of the controlled systems to a specified accuracy within a preassigned settling time. Unlike the existing prescribed time control scheme that only uses transformation function technique in the first step of the backstepping design, the transformation function is introduced to each step of the controlled systems, which makes only one adaptive parameter that needs to be updated online. Then, to synthesise a low-cost control scheme, a first-order sliding mode differentiator and a single-parameter estimation method are implemented based on the newly constructed coordinate transformations. Meanwhile, the Nussbaum technique successfully solves the effects caused by the unknown control direction, unknown backlash-like hysteresis and quantised input. All signals of the closed-loop systems are bounded under the proposed control scheme with arbitrary switching signal. Finally, the validity of the presented method is confirmed via two simulation examples.

Dynamic event-triggered adaptive fuzzy control for stochastic nontriangular nonlinear systems with unknown backlash-like hysteresis

A finite-time adaptive control is discussed in this paper for stochastic nontriangular nonlinear systems with unknown backlash-like hysteresis. The performance function is introduced to ensure that the tracking error of the system converges to the specified region in a finite time. Secondly, a controller is proposed using the fuzzy logic systems to approximate the unknown functions and backstepping technique. In addition, adding the dynamic event-triggered mechanism is able to reduce the network resources more effectively. At last, a few simulation examples are presented to demonstrate effective performance.

Development of a Butterfly Fractional-Order Backlash-Like Hysteresis Model for Dielectric Elastomer Actuators

Differential equation-based hysteresis model is an efficient approach to predict the hysteresis effect with less modeling parameters. Available differential equation-based hysteresis models mainly focus on describing the single-loop hysteresis effect and fail to describe the butterfly hysteresis effect. In this article, a butterfly fractional-order backlash-like hysteresis model is proposed to describe the butterfly hysteretic behavior. To this end, a twist mechanism is developed to transform the single-loop backlash-like hysteresis model into the one that is capable of representing the butterfly hysteresis. To further improve the modeling accuracy, a fractional-order expression is integrated into the butterfly backlash-like hysteresis model. In addition, considering the buckling threshold characteristic of the elastomer membrane in dielectric elastomer actuators, a buckling threshold selector is designed and incorporated into the model as well. Experiments are conducted to validate the effectiveness of the proposed model.

Antagonistic Interaction-Based Bipartite Consensus Control for Heterogeneous Networked Systems

This article investigates the bipartite consensus tracking control problem for nonlinear networked systems with antagonistic interactions and unknown backlash-like hysteresis. The generalized networked multiagent systems model is considered, in which every agent is an independent individual, and this model allows competitive and cooperative interactions to coexist. A Gaussian function is applied to simulate competition and cooperation among agents. Radial basis function (RBF) neural network (NN) is applied to estimate the unknown nonlinear function. By using backstepping technology, we propose an adaptive neural control protocol, which not only ensures that in the closed-loop system all the signals are bounded but also realizes bipartite consensus control. Finally, we present a simulation example to illustrate the effectiveness of the obtained result.

Funnel-based adaptive fuzzy finite-time control for non-affine nonlinear systems preceded by unknown actuators

In this paper, an adaptive finite-time funnel control for non-affine strict-feedback nonlinear systems preceded by unknown non-smooth input nonlinearities is proposed. The input nonlinearities include backlash-like hysteresis and dead-zone. Unknown nonlinear functions are handled using fuzzy logic systems (FLS), based on the universal approximation theorem. An improved funnel error surface is utilized to guarantee the steady-state and transient predetermined performances while the differentiability problem in the controller design is averted. Using the Lyapunov approach, all the adaptive laws are extracted. In addition, an adaptive continuous robust term is added to the control input to relax the assumption of knowing the bounds of uncertainties. All the signals in the closed-loop system are shown to be semi-globally practically finite-time bounded with predetermined performance for output tracking error. Finally, comparative numerical and practical examples are provided to authenticate the efficacy and applicability of the proposed scheme.

Adaptive Asymptotic Tracking Control for Stochastic Nonlinear Systems with Unknown Backlash-Like Hysteresis

Adaptive Asymptotic Tracking Control for Stochastic Nonlinear Systems with Unknown Backlash-Like Hysteresis

Finite-time command filter-based adaptive fuzzy tracking control for stochastic nonlinear induction motors systems with unknown backlash-like hysteresis

In this article, an adaptive fuzzy control method is proposed for induction motors (IMs) drive systems with unknown backlash-like hysteresis. First, the stochastic nonlinear functions existed in the IMs drive systems are resolved by invoking fuzzy logic systems. Then, a finite-time command filter technique is exploited to overcome the obstacle of “explosion of complexity” emerged in the classical backstepping procedure during the controller design process. Meanwhile, the effect of the filter errors generated by command filters is decreased by utilizing corresponding error compensating mechanism. To cope with the influence of backlash-like hysteresis input, an auxiliary system is constructed, in which the output signal is applied to compensate the effect of the hysteresis. The finite-time control technology is adopted to accelerate the response speed of the system and reduce the tracking error, and the stochastic disturbance and backlash-like hysteresis are considered to improve control accuracy. It’s shown that the tracking error can converge to a small neighborhood around the origin in finite-time under the constructed controller. Finally, the availability of the presented approach is validated through simulation results.

Adaptive asymptotic tracking control for multi-input and multi-output nonlinear systems with unknown hysteresis inputs

With the advantages in resolution, response speed, and reliability, smart materials such as piezoelectric ceramics and shape memory alloys are widely used in modern industries, and the hysteresis phenomenon in such smart materials has also received extensive attention. The existing tracking control schemes for nonlinear systems with backlash-like hysteresis inputs may have singularity problems, and it is difficult to obtain a high-precision tracking effect. To resolve the above issues, a novel adaptive asymptotic tracking control strategy is proposed for multi-input and multi-output nonlinear systems with unknown backlash-like hysteresis inputs, where the dependence on the system model is removed through fuzzy logic systems and elaborately designed adaptive laws. In contrast, the proposed tracking control scheme is free of any singularity problem, and the constructed controllers and adaptive laws including positive and continuous functions with zero limit make the output tracking error asymptotically converge to zero rather than near the origin. Moreover, this asymptotic convergence is proven by rigorous theoretical analysis. Finally, the effectiveness and robustness of the proposed tracking control scheme are also verified by numerical and practical simulations.

Neural network state observer-based robust adaptive iterative learning output feedback control for the rigid-flexible coupled robotic systems with unknown delays and backlash-like hysteresis

Neural network state observer-based robust adaptive iterative learning output feedback control for the rigid-flexible coupled robotic systems with unknown delays and backlash-like hysteresis

Neural network-based adaptive finite-time tracking control of switched nonlinear systems with time-varying delay

This work investigates the adaptive finite-time tracking control problem for switched nonlinear systems, in which backlash-like hysteresis and time-varying delay are taken into account. The nonlinear estimation ability of radial basis function neural networks is employed to relax the restriction on unknown nonlinear functions. The dynamic surface technology and the finite-time control approach avoid the “curse of dimensionality” and “singularity” problems existing in the backstepping design procedure, separately. By Lyapunov–Razumikhin function scheme, the proposed finite-time signal guarantees superior tracking performance under the average dwell time switching. Finally, to testify the practicability of the presented strategy, two simulation examples are shown.