Bouc-Wen Hysteresis Research Articles

Adaptive asymptotic tracking control of constrained nonlinear MIMO systems subject to unknown hysteresis input: A novel network-based strategy

This paper presents a referential adaptive asymptotic tracking control scheme for nonlinear multi-input and multi-output (MIMO) systems with time-varying full-state constraints and unknown hysteresis input. In order to achieve good asymptotic tracking effect, a zero-limit positive continuous function is introduced into the adaptive backstepping design process while thoroughly considering the impact of disturbance-like terms on the tracking effect. Additionally, a new variable is also imported to replace the reciprocal of unknown coefficient of the Bouc–Wen hysteresis model. Then, a new adaptive law about the new variable is added by combining the positive function, which can not only lessen the impact of the unknown hysteresis input on the tracking effect, but also avoid the “singularity” problem. Aiming at the time-varying full-state constraints, a appropriate time-varying log-type barrier Lyapunov function (TLBLF) is constructed to ensure that all the states of the system are restricted within the constraint scope. Finally, a significant adaptive asymptotic tracking scheme is designed based on multi-dimensional Taylor network (MTN) approximation technology. Apart from achieving high-precision asymptotic tracking performance, the proposed scheme ensures the boundedness of all signals of the closed-loop system without violating the full-state constraints. And, three simulations are given to verify the effectiveness of the scheme.

Rotor dynamic response prediction using physics-informed multi-LSTM networks

The deep learning method provides an effective alternative to numerical simulations for establishing the nonlinear input-output relationship and calculating dynamic responses of rotor systems. To overcome the low generalization capability of pure data-driven long short-term memory (LSTM) networks when predicting dynamic responses to out-of-distribution inputs, a dynamic response prediction method using physics-informed multi-LSTM networks is proposed. This approach incorporates required physical constraints into the deep LSTM network, allowing the model training process to optimize the network parameters within the feasible solution space that adheres to physical laws. Consequently, this enhances the physical interpretability of the deep learning model. Specifically, two physics-informed multi-LSTM network architectures are introduced, and physical laws of equation of motion, state dependency and hysteretic constitutive relationship are considered to construct the physics loss. The feasibility of the proposed method is verified by a Bouc-Wen hysteresis model and a simulated gas generator rotor. The response prediction performance of the two networks is validated on a constructed fault rotor dataset with significant sample differences, along with cross-speed and cross-node prediction validation for the rotor system. The results demonstrate that the trained networks exhibit strong robustness and generalization capabilities, making them suitable as surrogate models for rotor systems.

Coupled wind-induced response of inter-story isolated eccentric tall buildings with friction-pendulum bearings

The isolation technology is widely used to protect structures against strong earthquake. For the inter-story isolated tall building located in strong wind-prone area, the soft isolation layer prolongs the structural period, which can make the wind effects significant. This study presents an analytical framework for assessing three-dimensional coupled wind-induced response of inter-story isolated eccentric tall buildings employing friction-pendulum bearings. The framework utilizes a biaxial Bouc-Wen hysteresis model and a velocity-dependent friction coefficient to describe the coupled frictional forces at each bearing. To enhance the computational efficiency, a simplified model with reduced degrees of freedom is proposed to represent the building. This study investigates eighty combinations of stiffness and mass eccentricities of lower and upper structures relative to isolation layer to analyze their impact on building acceleration. A spherical and two aspheric sliding surfaces of the bearing are examined to understand their effects on building response. The findings suggest that the stiffness eccentricity of either lower or upper building solely affects its own response without influencing other part of the structure. Conversely, the mass eccentricity of upper building induces significant mode coupling, resulting in noticeable impact on the accelerations of both upper and lower buildings. Moreover, the acceleration of the story conner farther from the mass eccentric position experiences significantly amplification. The proposed aspherical bearing demonstrates the capability to substantially reduce the bearing displacement, although with a limited increase in other building responses not exceeding 20 %.

Hysteretic models with damage and flexibility increase

The need to accurately describe nonlinear degrading phenomena in both modern and classical complex materials that exhibit hysteretic behavior is a relevant task for the analysis of their response. In the present study an enrichment to an existing formulation to describe strength and stiffness degradation is proposed. The description of damage, that reduces the hysteretic force, is then accompanied by the introduction of flexibility increase, which increments the elastic displacement experienced by the system. Both effects influence the energy dissipated by the system. The condition of thermodynamic admissibility in presence of damage and flexibility increase is derived, entailing constraints on system parameters. Additional constraints arise from consistency conditions on the transformation of the pure hysteretic system into the system with damage and flexibility increase. A numerical solution involving the forward Euler method is presented to evaluate the response quantities. The formulation is eventually applied to the elastic–plastic and Bouc Wen hysteresis models, and the influence of the degrading parameters is presented. The presented Bouc-Wen model with damage and flexibility increase is applied to study the cyclic response of a masonry panel experimentally tested to validate the numerical model and prove its capability of describing the structural response.

Adaptive neural predefined-time hierarchical sliding mode control of switched under-actuated nonlinear systems subject to bouc-wen hysteresis

For switched under-actuated systems subject to bouc-wen hysteresis, an adaptive neural predefined-time control scheme is presented first time in this paper. To improve the robustness and response rate of the system under consideration, a hierarchical sliding mode control technique is introduced. Based on a predefined-time stability criterion, the stabilization time of the system can be directly preset under the designed controller. Besides, the convergence time depends only on the preset value and is independent of all other parameters. The projection algorithm is introduced to avoid the singularity problem in the controller design process. Meanwhile, it is proved that all signals of the closed-loop system are bounded after a preset time through the Lyapunov stability theory. Finally, a simulation example and a comparison example are given to further illustrate the effectiveness and superiority of developed control approach.

Modeling, identification, and high-speed compensation study of dynamic hysteresis nonlinearity for piezoelectric actuator

Hysteresis nonlinearity widely exists in the piezoelectric actuator (PEA), and the hysteresis nonlinearity has strong dynamic characteristics that lead to deterioration of tracking performance. To decrease the positioning error caused by hysteresis nonlinearity, a generalized Bouc-Wen (GBW) hysteresis model and its compensation method are proposed in this paper. First, based on the Bouc-Wen hysteresis model, two asymmetric terms and a second-order IIR filter are applied to describe the asymmetric hysteresis and high-frequency phase lag characteristics of PEA. Then, the model parameters with strong relevance to frequency variation are modified as frequency-dependent parameters. Meanwhile, based on the particle swarm optimization (PSO) algorithm, a novel parameter identification algorithm is designed for identifying the parameters of GBW hysteresis model. Then, an inverse feedforward controller is constructed based on the GBW hysteresis model, and a composite compensation control algorithm combining PID controller and repetitive controller is developed to reduce the unmodeled dynamics errors and unknown external disturbances. Finally, the comparison experiment results show that the accuracy and performance of the GBW model proposed in this paper are much better than the classical Bouc-Wen (CBW) model and the enhanced Bouc-Wen (EBW) model, and the developed compensation controller has excellent control performance and robustness.

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.

Disturbance Observer-Based Adaptive Neural Network Output Feedback Control for Uncertain Nonlinear Systems.

This article is devoted to the output feedback control of nonlinear system subject to unknown control directions, unknown Bouc-Wen hysteresis and unknown disturbances. During the control design process, the design obstacles caused by unknown control directions and Bouc-Wen hysteresis are eliminated by introducing linear state transformation and a new coordinate transformation, which avoids using the Nussbaum function with high-frequency oscillation to deal with the issue. Besides, to settle the issue caused by the unknown disturbances, a novel nonlinear disturbance observer is designed, which has the characteristics of simple structure, low coupling, and easy implementation. Especially, a compensation item is constructed to offset the redundant items generated in the backstepping design process. Simultaneously, using the neural network and backstepping technology, an output feedback controller is devised. The controller ensures that all closed-loop signals are bounded, and the system output, state observation error, and disturbance observation error converge to a small neighborhood of the origin. Finally, to illustrate the effectiveness of the proposed scheme, simulation verification is carried out based on a numerical example and a Nomoto ship model.

Dynamic Compression Simulation of Magnetorheological Elastomer Using Bouc-Wen Hysteretic Model

This paper explores the versatility of Bouc-Wen hysteresis model in simulating the dynamic behaviour of magnetorheological elastomer (MRE) material. Bouc-Wen model have been used in many field of science including modelling the hysteresis phenomenon happen in magnetic material, elastomer, base isolation of structures and many more. Introduced by the Robert Bouc, this nonlinear hysteretic model has been modified by many researchers to suit different applications. Compression testing of MRE material under high strain amplitude produces nonlinear hysteresis curve based on stress-strain data. Bouc-Wen hysteretic model has been found to be able to simulate the hysteresis curve of MRE material using parameter identification method within MATLAB Simulink.

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.

Seismic Upgrading of Existing Steel Buildings Built on Soft Soil Using Passive Damping Systems

In regions prone to seismic activity, buildings constructed on soft soil pose a significant concern due to their inferior seismic performance. This situation often results in considerable structural damage, substantial economic loss, and increased risk to human life. To address this problem, this study focuses on the seismic retrofitting of steel moment-resisting frames using friction and metal-yielding dampers, taking into account the soil-structure interaction. The effectiveness of these retrofit methods was examined through a comprehensive non-linear time history analysis of three prototype structures subjected to a series of intense seismic events. The soil behavior was simulated using a non-linear Bouc-Wen hysteresis model. Various parameters, including lateral displacement, maximum drift ratio, the pattern of plastic hinge formation, base shear distribution, and dissipated hysteretic energy, were used to compare the performance of the two retrofit strategies. The findings from the non-linear analyses revealed that both retrofit methods markedly enhanced the safety and serviceability of the deficient buildings. The retrofitted structures exhibited notable reductions in residual displacements and inter-story drift compared to the original frame structures. In the original frame, primary structural elements absorbed a significant amount of the seismic input energy through deformation. However, in the retrofitted frames, dampers dissipated up to 90% of the total input energy. Additionally, integrating dampers into the original frames effectively transferred the non-linear response of the structural elements to the dampers.

Identification of Asymmetric Bouc–Wen Hysteresis Under Intense Noise by Only Measuring Acceleration

Abstract Parameter identification of hysteretic models is significant for predicting structural dynamic response in vibration isolation structures. However, quasi-static testing and displacement measurement methods are not convenient for assembly structures and sensor layouts. Moreover, the methods based on evolutionary optimization need to provide appropriate boundary conditions for convergence and efficiency. Therefore, a novel hybrid identification method that takes the advantage of physics-informed parameter constraints and only acceleration measurement is proposed to identify the asymmetric Bouc–Wen hysteresis model. The restoring force surface is constructed for hysteretic force extraction based on the measurement of base excitation and isolated mass acceleration. The polynomial fitting and limit cycle approach are utilized for physical information given of an improved Bouc–Wen model. Furthermore, the evolutionary algorithm based on parameter constraints is implemented for final parameter estimation. A numerical simulation of an asymmetric Bouc–Wen model shows that the proposed method can keep an normalized mean square error (NMSE) of 0.19% under the noise level of 30 dB. The reconstructed hysteresis loop keeps in good agreement with the theoretical one.

Tracking control of a piezo-actuated compliant mechanism based on an improved Bouc–Wen hysteresis model with variable parameters

To deal with the challenges that the classical Bouc–Wen model fails to precisely characterize amplitude-dependent hysteresis and asymmetric hysteresis, an improved Bouc–Wen model with variable parameters is presented. The proposed model introduces asymmetric terms and parameter functions related to sinusoidal excitation amplitudes into the classical Bouc–Wen model. It has a relatively simple mathematic form and can be easily identified and applied for inverse feedforward compensation in real-time applications. By comparison with the classical Bouc–Wen model and other existing hysteresis models, the superiority of the proposed model has been verified. Furthermore, inverse hysteresis control and hybrid control combining the developed inverse control and proportional-integral feedback control are proposed. Several comparative experiments are conducted on a piezo-actuated micro-scanner. Results demonstrate that inverse control and hybrid control using the improved Bouc–Wen model with variable parameters can achieve better tracking performance and are meaningful in actual trajectory-tracking applications.

Event-triggered adaptive decentralised control of interconnected nonlinear systems with Bouc-Wen hysteresis input

ABSTRACT This article presents an event-based adaptive decentralised output feedback control scheme for interconnected systems with Bouc-Wen hysteresis and unmeasured system states. To reduce some unnecessary data transmissions, a novel dynamic threshold adjustable event-triggering mechanism is proposed. In contrast with the traditional static threshold event-triggering mechanism, communication efficiency is greatly enhanced. Then, a neural networks-based observer is constructed to address the problem of unmeasured states, and the dynamic surface control method is used to address the ‘explosion of complexity’ that comes up when traditional backstepping design processes are used. Meanwhile, the Nussbaum function is introduced to eliminate the effect of unknown hysteresis. By resorting to the Lyapunov stability theory, it can be verified that all signals in the close-loop system are uniformly ultimately bounded. Finally, a simulation example is given to verify the effectiveness of the developed control scheme.

Seismic response prediction of structures based on Runge-Kutta recurrent neural network with prior knowledge

In the seismic analysis of structural systems, dynamic response prediction is an essential problem and is significant in every stage during the structural life cycle. Conventionally, response analysis is carried out by numerical analysis. However, when the structural parameter is unknown, the establishment of a numerical model will be difficult. Enlightened by the Runge-Kutta (RK) numerical algorithm, this paper proposes a novel recurrent neural network named Runge-Kutta recurrent neural network (RKRNN) to realize the seismic response prediction. A partition training strategy is formulated to train the proposed neural network and to improve the efficiency of training. The proposed model can be trained by using a limited number of samples. Three numerical examples are utilized to validate the feasibility of RKRNN model including a linear three degrees of freedom (DOFs) system, a nonlinear single DOF system with Bouc-Wen hysteresis, and a numerical reinforced concrete bridge model. Additionally, the site monitoring data from a real-world bridge is utilized to further validate the proposed network. The results show that the proposed RKRNN model can effectively and efficiently predict the structural response under seismic load and exhibits robustness to noise, with good potential for applications in engineering practice.

Design of State-Constrained Controllers for Bouc–Wen Hysteresis Systems

Design of State-Constrained Controllers for Bouc–Wen Hysteresis Systems

Distributed-parameter Bouc-Wen modeling and output feedback control of a piezoactuator for a manipulation task

The Bouc-Wen hysteresis model and an Euler-Bernouilli beam bending theory are extended to distributed parameter model for a piezoelectric actuator (piezo actuator). Then we use the separation principle for its control and two types of observers: a neural network-based observer and a high-gain observer. Simulations with various conditions show that better performances are obtained when using the neural network-based observer.

Improved estimation of time-varying mean displacement and parametric study of biaxial effect on inelastic responses of high-rise buildings to wind

Three reduced-order building models with different biaxial hysteretic generalized restoring force and displacement relations were developed using static modal pushover analysis of a nonlinear finite element model of a 60-story steel building. It was illustrated that the reduced-order models can give accurate estimations of fluctuating responses but overestimate the time-varying mean alongwind displacement. The nonphysical displacement drift of the Bouc-Wen hysteresis model is responsible for this overestimation. An improved estimation of time-varying mean alongwind displacement was presented. A comprehensive parametric study concerning the influence of biaxial interaction on inelastic responses was also performed. The biaxial interaction leads to faster growth of time-varying mean displacement but does not affect its steady-state value. It results in increase in the low-frequency component but decrease in the resonant component of alongwind displacement. It leads to more reduction in alongwind acceleration. The crosswind response, which is greater than the alongwind response, is not affected, or only slightly reduced when both alongwind and crosswind responses are close to each other in magnitude. The peak ductility demand of a combined alongwind and crosswind response is less affected by the biaxial interaction. The new insights of this study can have wide applications to other buildings and wind directions.

Development and Experimental Validation of Novel Thevenin-Based Hysteretic Models for Li-Po Battery Packs Employed in Fixed-Wing UAVs

Lithium batteries employed in lightweight fixed-wing UAVs are required to operate with large temperature variations and, especially for the emerging applications in hybrid propulsion systems, with relevant transient loads. The detailed dynamic modelling of battery packs is thus of paramount importance to verify the feasibility of innovative hybrid systems, as well as to support the design of battery management systems for safety/reliability enhancement. This paper deals with the development of a generalised approach for the dynamic modelling of battery packs via Thevenin circuits with modular hysteretic elements (open circuit voltage, internal resistance, RC grids). The model takes into account the parameters’ dependency on the state of charge, temperature, and both the amplitude and sign of the current load. As a relevant case study, the modelling approach is here applied to the Li-Po battery pack (1850 mAh, 6 cells, 22.2 V) employed in the lightweight fixed-wing UAV Rapier X-25 developed by Sky Eye Systems (Cascina, Italy). The procedure for parameter identification with experimental measurements, obtained at different temperatures and current loads, is firstly presented, and then the battery model is verified by simulating an entire Hybrid Pulse Power Characterisation test campaign. Finally, the model is used to evaluate the battery performance within the altitude (i.e., temperature) envelope of the reference UAV. The experiments demonstrate the relevant hysteretic behaviour of the characteristic relaxation times, and this phenomenon is here modelled by inserting Bouc–Wen hysteresis models on RC grid capacitances. The maximum relative error in the terminal output voltage of the battery is smaller than 1% for any value of state of charge greater than 10%.

Global fast non-singular terminal sliding-mode control for high-speed nanopositioning

This paper presents a new Global Fast Non-singular Terminal Sliding Mode Controller (GFNTSMC) that delivers high-precision tracking of high-frequency trajectories when applied to a piezo-driven nanopositioner. The control scheme is realized by combing inverse hysteresis model and global fast non-singular terminal sliding mode compensation. The inverse Bouc–Wen hysteresis model is used to calculate the required hysteresis-compensating feedforward control voltage according to the reference signal. The key uniqueness of the proposed control strategy is it’s red global fast convergence, achieved with high accuracy and high bandwidth. The stability of the reported GFNTSMC controller is proved with the Lyapunov theory. Its performance is verified through experimentally recorded tracking results, and its superiority over three benchmark control approaches, namely the Proportional–Integral–Derivative (PID), the Positive Position Feedback with integral action (PPF+I) and the conventional linear high-order sliding mode controller (LHOSMC) is demonstrated through comparative tracking error analysis. Its wide-band stability as well as its significant robustness to parameter uncertainty is also showcased.