Asymmetric Hysteresis Nonlinearities Research Articles

Adaptive Neural Control for Hysteretic Nonlinear Systems With Hysteresis Neural Direct Inverse Compensator and Its Application.

Aiming at high precision control for a class of hysteretic nonlinear systems, a new hysteresis direct inverse compensator-based adaptive output feedback control scheme is designed in this article. First, a novel long short-term memory neural network (LSTMNN)-based hysteresis inverse compensator is established to compensate the asymmetric hysteresis nonlinearity, where the LSTMNN is used as the prediction mechanism for model operator weights, rather than the overall mapping of hysteresis input and output. Second, by designing the modified high-gain K-Filter states observer and the error transformed function, the unmeasurable states are estimated with arbitrarily small estimation error and the prespecified tracking performance is achieved. Lastly, the biconical dielectric elastomer actuator (DEA) motion platform is constructed. Then, the effectiveness of the proposed LSTMNN-based hysteresis inverse compensator and control scheme are verified on the experimental platform. The experimental results illustrate the effectiveness and advantages of proposed control scheme.

Model-free compensation learning control of asymmetric hysteretic systems with initial state learning

In this article, a model-free compensation learning control scheme is presented for asymmetric hysteretic systems to achieve high-precision output tracking, where the effects of asymmetric input hysteresis nonlinearities are denoted by the asymmetric Prandtl–Ishlinskii model (APIM). In the presented control scheme, the feedforward iterative learning technique is generalized to the control design of asymmetric hysteretic systems. To improve the robustness and dynamic performance of the existing feedforward learning control for hysteretic systems, both the feedback action and the differential term are utilized to design a discrete-time PD-P open-closed-loop learning control law for simultaneously compensating the asymmetric input hysteresis nonlinearities and the linear dynamics effects without constructing compensators based on their models. The initial state error of such a system is also considered, a modified initial state learning strategy is proposed to ensure the initial state error tends to a prescribed level with the increasing of iterations. By fully analyzing the properties of the APIM, the convergence conditions with respect to the input error, the state error, and the tracking error along the iteration domain are given. The simulation and experimental results are provided to demonstrate strong robustness and excellent tracking accuracy with the proposed model-free compensation learning control scheme.

Precision positioning based on temperature dependence self-sensing magnetostrictive actuation mechanism

The self-sensing actuator that integrates both actuation and sensing functions is an effective way to simplify the structure of electromechanical systems. This paper proposes a temperature-dependent self-sensing actuation strategy based on a self-sensing giant magnetostrictive actuator (SSGMA) by sensing online stiffness. Utilizing the developed model considering temperature-dependent hysteresis nonlinearity, the self-sensing output characteristics of SSGMA are first evaluated. The self-sensing based control system is then designed in detail. The relationship between the self-sensing signal and the output displacement of SSGMA at different temperatures is constructed by General Regression Neural Network (GRNN) model for fast recognition by the controller. On this basis, a composite control scheme that takes into account rate-dependent asymmetric hysteresis nonlinearities and combines an adaptive feedforward controller with PID feedback controller is proposed for precision actuation of SSGMA. Finally, a temperature-controlled experimental platform is assembled for verification. Experimental results demonstrate that, based on the developed model, the SSGMA is capable of accurate self-sensing output at temperatures of 22 °C, 40 °C, and 70 °C, respectively. The SSGMA with the proposed control method enables the synchronous and precise self-sensing positioning of step and multiple-frequency sinusoidal expectations at different temperatures.

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.

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.

Asymmetric Bouc-Wen hysteresis modeling for MFC actuator via hybrid APSO-TRR identification algorithm

Macro fiber composite (MFC) is widely used in active vibration and deformation control. The intrinsic asymmetric hysteresis nonlinearity of MFC affects the control accuracy. In this paper, a modified Bouc-Wen (MBW) model based on the sigmoid function is proposed to describe the asymmetric hysteresis characteristics of MFC, and its parameters are identified by a hybrid algorithm composed of the trust-region reflection method and asynchronous particle swarm optimization. The accuracy of the proposed MBW model is verified though hysteresis tests of MFC under different drive frequencies. The results show that the MBW model can accurately model the asymmetrical hysteresis of the MFC actuator, the modeling error is reduced by 72% compared with the classic Bouc-Wen model. The proposed hybrid parameter identification method saves 95% of the time compared with the particle swarm optimization and asynchronous particle swarm optimization algorithms. • A modified Bouc-Wen (MBW) model is proposed to describe the asymmetric hysteresis characteristics of MFC actuators. • A hybrid algorithm (APSO - TRR) with global and local search ability is proposed for parameter identification. • Performance of proposed APSO - TRR is compared with classical PSO、APSO and TRR algorithms. • Accuracy of proposed asymmetric Bou–Wen model is compared with classical Bou–Wen model.

A Fractional-Order Normalized Bouc–Wen Model for Piezoelectric Hysteresis Nonlinearity

This article presents a new fractional-order normalized Bouc–Wen (BW) (FONBW) model to describe the asymmetric and rate-dependent hysteresis nonlinearity of piezoelectric actuators (PEAs). In view of the fact that the classical BW (CBW) model is only efficient for the symmetric and rate-independent hysteresis description, the FONBW model is devoted to characterizing the asymmetric and rate-dependent behaviors of the hysteresis in PEAs by adopting an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> th-order polynomial input function and two fractional operators, respectively. Different from the traditional modified BW models, the proposed FONBW model also eliminates the redundancy of parameters in the CBW model via the normalization processing. By this way, the developed FONBW model has a relatively simple mathematic expression with fewer parameters to simultaneously characterize the asymmetric and rate-dependent hysteresis behaviors of PEAs. Model parameters are identified by the self-adaptive differential evolution algorithm. To validate the effectiveness of the proposed model, a series of model verification and inverse-multiplicative-structure-based feedforward control experiments are carried out on a PEA system. Results show that the proposed model is superior to the CBW model and traditional modified BW model in modeling accuracy and hysteresis compensation.

All state constrained decentralized adaptive implicit inversion control for a class of large scale nonlinear hysteretic systems with time-delays

This paper proposes an all state constrained decentralized adaptive implicit inversion control scheme for a class of large scale nonlinear systems with unknown time delays and asymmetric saturated hysteresis. First, to address the states constrained problem, the asymmetric barrier Lyapunov function is introduced to keep the error surface within an appropriate range from the view of engineering practice to ensure the performance and safety, such as for attitude tracking of rigid spacecraft, for spacecraft approach and intersection. Second, the transmission delays between different subsystems are considered and approximated through the incorporation of the neural-network approximators and the finite coverage lemma. Third, a new hysteresis implicit inverse algorithm is designed to effectively mitigate asymmetric and saturated hysteresis nonlinearities. It should be noted that the implicit inverse implies that the analytical inverse of the asymmetric and saturated hysteresis is not required. Instead, the decoupling algorithms are designed to extract the actual control signal from the temporarily hysteretic control signal , which reduces the preliminary work of the control algorithm. Finally, all of the signals in the closed-loop system are proved to be semi-globally ultimately uniformly bounded and the tracking errors converge to an arbitrarily small residual set. The experimental results on two-machine excitation power systems in the hardware-in-loop system are presented to illustrate the effectiveness of the proposed scheme.

Design and dynamic modeling of a continuum and compliant manipulator with large workspace

This paper focuses on the design and dynamic modeling of a novel multi-section continuum and compliant robotic manipulator with large workspace. In large scales, many of the design techniques and actuator types which have proved advantageous in creating continuum robots at smaller scales are not applicable. Fluidic muscles, a class of pneumatic muscle actuators (PMAs) with large scale movements, high actuation forces and compliant nature, are utilized in the design of the continuum manipulator. However, these actuators are capable of applying axial contracting forces and cannot produce bending movements. Moreover, their asymmetric hysteresis nonlinearity causes difficulties in the accurate control procedure. These drawbacks are addressed in the design and presented model of the manipulator. The presented model is based on constant curvature method and concentrated masses. The Bouc–Wen hysteretic function is modified to describe the asymmetric force/length hysteresis of the utilized PMAs in this model. Experimental results show that the proposed model has a proper performance to characterize the asymmetric hysteresis loop of the actuators. Finally, the design and dynamic model of the robot are validated experimentally on the implemented manipulator.

Precise dynamic modeling of pneumatic muscle actuators with modified Bouw–Wen hysteresis model

Pneumatic muscle actuators (PMAs) are frequently used in a wide variety of biorobotic applications, such as robotic orthoses and wearable exoskeletons, due to their high power/weight ratio and significant compliance. However, the asymmetric hysteresis nonlinearity reduces their fidelity and cause difficulties in the accurate control procedure. In this paper, Bouc–Wen hysteresis model is modified to describe the asymmetric force/length hysteresis of the PMA. The effect of muscle length on hysteretic restoring force is considered in this modified model and experimental results show that the proposed model has a better performance to characterize the asymmetric hysteresis loop of pneumatic muscles. The nonlinear pressure/force model of these actuators also is modeled precisely and its performance is experimentally verified for different muscle lengths.

Adaptive Pseudo Inverse Control for a Class of Nonlinear Asymmetric and Saturated Nonlinear Hysteretic Systems

This paper aims at eliminating the asymmetric and saturated hysteresis nonlinearities by designing hysteresis pseudo inverse compensator and robust adaptive dynamic surface control (DSC) scheme. The “pseudo inverse” means that an on-line calculation mechanism of approximate control signal is developed by applying a searching method to the designed temporary control signal where the true control signal is included. The main contributions are summarized as: 1) to our best knowledge, it is the first time to compensate the asymmetric and saturated hysteresis by using hysteresis pseudo inverse compensator because the construction of the true saturated-type hysteresis inverse model is very difficult; 2) by designing the saturated-type hysteresis pseudo inverse compensator, the construction of true explicit hysteresis inverse and the identifications of its corresponding unknown parameters are not required when dealing with the saturated-type hysteresis; 3) by combining DSC technique with the tracking error transformed function, the “explosion of complexity” problem in backstepping method is overcome and the prespecified tracking performance is achieved. Analysis of stability and experimental results on the hardware-in-loop platform illustrate the effectiveness of the proposed adaptive pseudo inverse control scheme.

Modeling and Compensation Algorithms of Asymmetric Nonlinearity for Piezoelectric Actuators Based on Madelung's Rules

This article presents a hysteresis modeling algorithm to describe the asymmetric nonlinearity in piezoelectric actuators (PEAs). The proposed algorithm primarily consists of two parts: 1) the wiping-out mechanism, and 2) the description method for the current hysteresis curve (CHC). The first part is associated with the realization of the wiping-out mechanism. It is used to determine the hysteresis curve where the hysteresis trajectory moves along, and this curve represents the CHC. In the second part, the information of the major ascending or descending curve is used to describe the CHC, and meanwhile, the trajectory is also described. The proposed algorithm works in real-time, which provides an intuitive mechanism to understand and investigate the asymmetric hysteresis nonlinearity in PEAs. Furthermore, the analytical inverse modeling algorithm is proposed to reduce the hysteresis effect. Experiments are conducted to validate the effectiveness of the proposed algorithms.

Adaptive Control for Pure-Feedback Nonlinear Systems Preceded by Asymmetric Hysteresis

An adaptive control scheme is proposed for a class of uncertain pure-feedback nonlinear systems preceded by asymmetric hysteresis nonlinearity. The asymmetric property is described by the modified Bouc-Wen model based on the proposed asymmetric factor. State variables in the controller design are directly replaced with nonaffine functions to address the control problem caused by nonaffine appearance. Moreover, the control method can handle systems with external disturbances and guarantee the global stability of all the signals in the closed-loop system. The feasibility of the control scheme is verified by a simulation example and experimental results.

Output Feedback Adaptive Motion Control and Its Experimental Verification for Time-Delay Nonlinear Systems With Asymmetric Hysteresis

Focusing on the nonlinear time-delay systems actuated by smart-material-based actuators, an adaptive dynamic surface estimated inverse motion control scheme is proposed in this article. The asymmetric hysteresis nonlinearity is counteracted by constructing its evaluated inverse compensator. A state estimator is constructed to estimate the unmeasurable states and at the same time to cope with external disturbances. The assumptions on time-delay functions are removed, and the unknown time-delay function is online evaluated by combining the fuzzy logic system with a finite covering lemma. Also, the prespecified tracking performance is achieved by utilizing an error-transformed function. Experimental results of the proposed controller are performed on the piezoelectric positioning stage to verify the effectiveness of the control scheme.

Further results on open-loop compensation of rate-dependent hysteresis in a magnetostrictive actuator with the Prandtl-Ishlinskii model

Abstract Apart from the output-input hysteresis loops, the magnetostrictive actuators also exhibit asymmetry and saturation, particularly under moderate to large magnitude inputs and at relatively higher frequencies. Such nonlinear input-output characteristics could be effectively characterized by a rate-dependent Prandtl-Ishlinskii model in conjunction with a function of deadband operators. In this study, an inverse model is formulated to seek real-time compensation of rate-dependent and asymmetric hysteresis nonlinearities of a Terfenol-D magnetostrictive actuator. The inverse model is formulated with the inverse of the rate-dependent Prandtl-Ishlinskii model, satisfying the threshold dilation condition, with the inverse of the deadband function. The inverse model was subsequently applied to the hysteresis model as a feedforward compensator. The proposed compensator is applied as a feedforward compensator to the actuator hardware to study its potential for rate-dependent and asymmetric hysteresis loops. The experimental results are obtained under harmonic and complex harmonic inputs further revealed that the inverse compensator can substantially suppress the hysteresis and output asymmetry nonlinearities in the entire frequency range considered in the study.

Fuzzy Approximator Based Adaptive Dynamic Surface Control for Unknown Time Delay Nonlinear Systems With Input Asymmetric Hysteresis Nonlinearities

In this paper, a fuzzy approximator based adaptive dynamic surface control scheme is proposed for a class of unknown time delay nonlinear systems preceded by asymmetric hysteresis nonlinearities. The features of the proposed method are: 1) by combining the approximated property of the fuzzy logic systems (FLSs) with the finite covering lemma, the Krasovskii functionals are disposed of, achieving the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}_{{\infty }}$ </tex-math></inline-formula> norm of the tracking error by using the initializing technique; 2) the assumptions on the time-delay functions are removed due to the use of the finite covering lemma and the FLSs; and 3) the proposed adaptive fuzzy dynamic surface control scheme can also compensate the asymmetric shifted Prandtl-Ishlinskii (ASPI) hysteresis without constructing the inverse of the ASPI model with the density function of ASPI model being unknown and estimated online to compensate the hysteresis. It is proved that all the signals in the closed-loop system are ultimately uniformly bounded and can be made arbitrarily small. Simulation results show the validity of the proposed method.

Direct identification of generalized Prandtl–Ishlinskii model inversion for asymmetric hysteresis compensation

In this study, we present an identification-based direct construction of the inverse generalized Prandtl–Ishlinskii (P–I) model to facilitate inverse model-based feedforward compensation of asymmetric hysteresis nonlinearities. Compared with the derivation of the inverse model analytically from a generalized P–I model, this direct modeling approach has the following advantages. First, direct inverse model identification is formulated as a nonlinear optimization problem, which is not subject to the constraint condition on the generalized P–I model's threshold and density functions, where this is indispensable for the analytical model inversion procedure. Second, this approach may be a simple and attractive alternative when the identification precision of a generalized P–I model is limited by the constraint condition, which necessarily results in insufficient hysteresis compensation functionality for the analytically derived inverse model. Finally, direct inverse model identification can overcome the drawbacks of the analytical inversion method, including the accumulation of parameter estimation errors in an analytical inverse model because these parameters are computed from the generalized P–I model's parameters in a recursive manner. Our experimental results demonstrated that the implementation of open-loop control with the directly identified inverse generalized P–I model as a feedforward compensator achieved precise compensation for the asymmetric hysteresis nonlinearities of a piezoelectric stack actuator.

Modeling, identification and compensation of hysteresis nonlinearity for a piezoelectric nano-manipulator

Hysteresis nonlinearity widely exists in piezoelectric actuated nano-positioning applications, which degrades their tracking accuracy and limits their precision positioning applications. This paper presents a novel hysteresis modeling and compensation approach to alleviate the adverse effect of the asymmetric and rate-dependent hysteresis nonlinearity for a piezoelectric transducer actuated servo stage. By integrating a generalized input function with the play operator of the classical Prandtl–Ishlinskii model, a novel polynomial-based rate-dependent Prandtl–Ishlinskii (PRPI) model is proposed to capture the hysteresis behavior of the piezoelectric positioning stage, where a polynomial function of input and a time rate function of input are introduced to formulate the generalized input function. Meanwhile, a new adaptive differential evolution optimization algorithm is developed to identify the parameters of the proposed PRPI hysteresis model. Based on the PRPI hysteresis model with the identified parameters, an inverse feedforward controller is constructed to achieve the accurate tracking motion. Furthermore, the hysteresis compensation error of the proposed PRPI model is theoretically analyzed. Finally, comparative experiments are conducted, and the experimental results provided in this paper demonstrate the effectiveness and superiority of the proposed inverse PRPI model compensation approach.

High precision tracking of a piezoelectric positioner using a discrete-time sliding mode control

This paper proposes a new comprehensive control strategy to precisely control a piezoelectric positioner by combining discrete-time sliding mode control (DSMC) with the Prandtl-Ishlinskii hysteresis model. In order to obtain precision tracking control, a direct inverse hysteresis compensation method is firstly adopted to compensate for the asymmetric hysteresis nonlinearity. Due to the existence of hysteresis modeling error, the dynamics behavior of the piezoelectric positioner with hysteresis compensation can be treated as a linear second order plant plus an unknown lumped disturbance term. Then a discrete-time sliding mode controller with a disturbance observer is designed to stabilize the position error and improve the position accuracy. The stability of DSMC and the convergence of the disturbance observer are both carried out. It is shown that the tracking performances are robust to the parametric uncertainties and unknown disturbances. Eventually, different trajectory-tracking experiments are performed, and the comparative experimental results are presented to confirm the significantly better performance of the proposed control strategy.

High-precision control of piezoelectric nanopositioning stages using hysteresis compensator and disturbance observer

This paper proposes a novel high-performance control scheme with hysteresis compensator and disturbance observer for high-precision motion control of a nanopositioning stage driven by a piezoelectric stack actuator (PSA). In the developed control scheme, a real-time inverse hysteresis compensator (IHC) with the modified Prandtl-Ishlinskii model is firstly designed to compensate for the asymmetric hysteresis nonlinearity of the PSA. Due to the imperfect compensation, the dynamics behaviors of the PSA-actuated stage with the IHC can be treated as a linear dynamic system plus a lumped disturbance term. Owing to the unknown nature of this lumped disturbance term, a disturbance observer (DOB) is used as a means for disturbance rejection. With the DOB, a tracking controller is finally designed and implemented to stabilize the position error. To verify the proposed control scheme, a real-time experimental platform with a PSA-actuated nanopositioning stage is built, and extensive experimental tests are performed. The comparative experimental results demonstrate the effectiveness and improved performance of the developed control approach in terms of the maximum-value errors, root-mean-square-value errors and hysteresis compensation.