Bouc-Wen Hysteresis Model Research Articles

Modeling SMA actuated systems based on Bouc-Wen hysteresis model and feed-forward neural network

Despite the fact that shape-memory alloy (SMA) has several mechanical advantages as it continues being used as an actuator in engineering applications, using it still remains as a challenge since it shows both non-linear and hysteretic behavior. To improve the efficiency of SMA application, it is required to do research not only on modeling it, but also on control hysteresis behavior of these materials which are the fundamentals of several research opportunities in this area. Having considered these requirements, we have introduced a mathematical model to describe the hysteresis behavior of a mechanical system attached to SMA wire actuators using Bouc-Wen hysteresis model and feed-forward neural network. Due to inability of linear mass-spring-damper equations of classic Bouc-wen model to explain the hysteresis behavior of SMA actuators, in this paper we have applied changes in the mentioned equations of classic Bouc-Wen model to describe hysteresis loops of model. We also have used flexibility of the neural network systems to describe Bouc-Wen output in the main equation. Parameters of the developed model have been trained for a real mechanical system using simulation data after selecting proper configuration for the selected neural network. Finally, we have checked the accuracy of our model by applying two different series of validation data. The result shows the acceptable accuracy of the developed model.

Dynamic performance and mechanical model analysis of a shear thickening fluid damper

This paper presents an experimental study of the dynamic performance of a self-developed shear thickening fluid (STF) damper and its mechanical model was proposed by nonlinear fitting. First, STF samples with different mass fraction and dispersion medium were fabricated by nano fumed silica and polyethylene glycol, and its rheological properties were investigated by a rheometer. Second, a smart STF damper was developed and manufactured. Its dynamic properties were experimentally investigated by establishing a vibration test bench, and results indicated that the STF damper can output variable damping force by controlling the loading frequency, loading amplitude and fluid gap. Third, the Bouc–Wen model was proposed to address the dynamic properties of STF damper, and mechanical model analysis was carried out by comparing several fitting functions. It verified that the Bouc–Wen hysteresis model can be better used to describe the nonlinear stiffness, nonlinear damping and rate-dependence characteristics of the STF damper. All these investigations can offer an effective guidance for further theoretical and application study of the smart STF damper in energy dissipation fields.

Parameter identification of piezoelectric hysteresis model based on improved artificial bee colony algorithm

The widely used Bouc–Wen hysteresis model can be utilized to accurately simulate the voltage–displacement curves of piezoelectric actuators. In order to identify the unknown parameters of the Bouc–Wen model, an improved artificial bee colony (IABC) algorithm is proposed in this paper. A guiding strategy for searching the current optimal position of the food source is proposed in the method, which can help balance the local search ability and global exploitation capability. And the formula for the scout bees to search for the food source is modified to increase the convergence speed. Some experiments were conducted to verify the effectiveness of the IABC algorithm. The results show that the identified hysteresis model agreed well with the actual actuator response. Moreover, the identification results were compared with the standard particle swarm optimization (PSO) method, and it can be seen that the search performance in convergence rate of the IABC algorithm is better than that of the standard PSO method.

Adaptive Neural Tracking Control of Switched Stochastic Pure-Feedback Nonlinear Systems With Unknown Bouc-Wen Hysteresis Input.

This paper aims to analyze the problem of adaptive neural network (NN) tracking control for a class of switched stochastic nonlinear pure-feedback systems with unknown direction hysteresis. In the light of recent studies on the hysteresis phenomenon in the field of nonlinear switched systems, this paper focuses on Bouc-Wen hysteresis model with unknown parameters and direction conditions. To simplify the control design, the following procedure is applied. Prior to tackling the unknown direction hysteresis problem based on the Nussbaum function and the backstepping techniques, the pure-feedback structure difficulty is governed by the mean value theorem. Furthermore, an optimized adaptation method is utilized to cope with computational burden. Universal approximation capability of radial basis function NNs and Lyapunov function method is synthesized to develop an adaptive NN tracking control scheme. It is demonstrated that under arbitrary deterministic switching, the presented controller can guarantee that all signals in the closed-loop system are semiglobally uniformly ultimately bounded in probability and the tracking error converges to a neighborhood of the origin. Finally, two simulation examples are given to illustrate the advantages of the proposed control design approach.

Direct torque control for cable conduit mechanisms for the robotic foot for footwear testing

As the shoe durability is affected directly by the dynamic force/pressure between the shoe and its working environments (i.e., the contact ground and the human foot), a footwear testing system should replicate correctly this interaction force profile during gait cycles. Thus, in developing a robotic foot for footwear testing, it is important to power multiple foot joints and to control their output torque to produce correct dynamic effects on footwear. The cable conduit mechanism (CCM) offers great advantages for designing this robotic foot. It not only eliminates the cumbersome actuators and significant inertial effects from the fast-moving robotic foot but also allows a large amount of energy/force to be transmitted/propagated to the compact robotic foot. However, CCMs cause nonlinearities and hysteresis effects to the system performance. Recent studies on CCMs and hysteresis systems mostly addressed the position control. This paper introduces a new approach for modelling the torque transmission and controlling the output torque of a pair of CCMs, which are used to actuate the robotic foot for footwear testing. The proximal torque is used as the input signal for the Bouc–Wen hysteresis model to portray the torque transmission profile while a new robust adaptive control scheme is developed to online estimate and compensate for the nonlinearities and hysteresis effects. Both theoretical proof of stability and experimental validation of the new torque controller have been carried out and reported in this paper. Control experiments of other closed-loop control algorithms have been also conducted to compare their performance with the new controller effectiveness. Qualitative and quantitative results show that the new control approach significantly enhances the torque tracking performance for the system preceded by CCMs.

Adaptive Sliding Mode Control of Hysteresis in Piezoelectric Actuator

Piezoelectric actuators are favorable choices for reaching ultrahigh precision in motion control and positioning, which are necessary in many applications. This is due to their fine resolution, response speed and output force. The nonlinear dynamics of piezoelectric actuators is an obstacle to this goal, and hysteresis is the major challenge that can deteriorate the actuator performance. In this study, sliding mode control with proportional-derivative (PD) sliding surface is adopted, using a Bouc-Wen model of hysteresis. Mismatch of this model with the actuator behavior is considered as an unstructured uncertainty. Asymptotic stability is proved using Lyapunov theorem. Structured uncertainty in model parameters is also unavoidable, so an online parameter estimator is proposed to compensate for those uncertainties. The parameters’ adaptation rule is derived so that asymptotic stability is guaranteed. Simulation results show the performance of the proposed algorithm.

Expected extreme value of pounding force between two adjacent buildings

Seismic pounding between adjacent buildings with inadequate separation and different dynamic characteristics can cause severe damage to the colliding buildings. Efficient estimation of the maximum pounding force is required to control the extent of damage in adjacent structures or develop an appropriate mitigation method. In this paper, an analytical approach on the basis of statistical relations is presented for approximate computation of extreme value of pounding force between two adjacent structures with equal or unequal heights subjected to stationary and non-stationary excitations. The nonlinearity of adjacent structures is considered using Bouc-Wen model of hysteresis and the pounding effect is simulated by applying the nonlinear viscoelastic model. It is shown that the proposed approach can significantly save computational costs by obviating the need for performing dynamic analysis. To assess the reliability and accuracy of the proposed approach, the results are compared with those obtained from nonlinear dynamic analysis.

A Hysteresis-Based Steering Feel Model for Steer-by-Wire Systems

A mathematical model of steering feel based on a hysteresis model is proposed for Steer-by-Wire systems. The normalized Bouc-Wen hysteresis model is used to describe the steering wheel torque feedback to the driver. By modifying the mathematical model of the hysteresis model for a steering system and adding custom parameters, the availability of adjusting the shape of steering feel model for various physical and dynamic conditions increases. Addition of a term about the tire dynamics to the steering feel model renders the steering wheel torque feedback more informative about the tire road interaction. Some simulation results are presented to establish the feasibility of the proposed model. The results of hardware-in-the-loop simulations show that the model provides a realistic and informative steering feel.

Comparative Studies of Base Isolation Systems Featured with Lead Rubber Bearings and Friction Pendulum Bearings

Due to the fact that safety is the major concern for civil structures in a seismic active zone, it has always been a challenge for structural engineers to protect structures from earthquake. During past several decades base isolation technique has become more and more popular in the field of seismic protection which can be adopted for new structures as well as the retrofit of existing structures. The objective of this study is to evaluate the behaviours of the building with different seismic isolation systems in terms of roof acceleration, elastic base shear and inter-storey drift under four benchmark earthquakes, namely, El Centro, Northridge, Hachinohe and Kobe earthquakes. Firstly, the design of base isolation systems, i.e. lead rubber bearing (LRB) and friction pendulum bearing (FPB) for five storey RC building was introduced in detail. The non-linear time history analysis was performed in order to determine the structural responses whereas Bouc-Wen Model of hysteresis was adopted for modelling the bilinear behaviour of the bearings. Both isolation systems increase the fundamental period of structures and reduces the spectral acceleration, and hence reduces the lateral force cause by earthquake in the structures, resulting in significant improvement in building performance; however the Lead Rubber Bearing provided the best reduction in elastic base shear and inter-storey drift (at first floor) for most of the benchmark earthquakes. For the adopted bearing characteristics, FPB provided the low isolator displacement.

Bifurcations and chaos of a vibration isolation system with magneto-rheological damper

Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.

Optimization of Parameters in the Hysteresis-based Steering Feel Model for Steer-by-Wire Systems**This research is principally funded by The European Union, Marie Curie Actions-Support for training and career development of researcher. [Project ID: PCIG09-GA-2011-294231 - SteeringFeelSBW

Abstract: In rubber-wheeled vehicles, mechanical connection between steering wheel and front wheels provides steering related feedback to the driver. The torque fed back to the driver through the steering linkages and steering wheel, which is called steering feel, helps the driver in controlling the vehicle. The torque feedback is reproduced via artificial methods in steer-by-wire systems due to the lack of mechanical connection. Different approaches have been reported to describe the steering feel for steer-by-wire systems. A recent study reports a steering feel design based on Bouc-Wen hysteresis model. This model describes the steering feel through five constant coefficients, longitudinal velocity and steering wheel angle. In this work, in order to minimize the physical workload and the lateral acceleration under the consideration of handling performance, optimization of those five parameters has been studied. A 2-DOF bicycle model based on Magic tyre formula has been used for simulations. The effect of each parameter on steering feel has been identified for the optimization study. A driver model with a controller has been designed to perform comparable and repeatable tests. Weave and double lane change tests have been performed in order to demonstrate and quantify the optimization of the hysteresis model.

On the Passivity of Hysteretic Systems with Double Hysteretic Loops.

The Bouc–Wen hysteresis model is widely employed to mathematically represent the dynamical behavior of several physical devices, materials and systems such as magnetorheological dampers, lanthanide zirconium or aluminum oxides, mechanical structures or biomedical systems. However, these mathematical models must account for different properties such as the bounded-input bounded-output stability, asymptotic motion, thermodynamic admissibility or passivity in order to be physically consistent with the systems they represent. The passivity of a system is related to energy dissipation. More precisely, a system is passive if it does not generate energy but only dissipates it. The objective of this paper is to prove that two different double-loop Bouc–Wen models are passive under a particular set of model parameters.

Bouc–Wen hysteresis model identification using Modified Firefly Algorithm

The parameters of Bouc–Wen hysteresis model are identified using a Modified Firefly Algorithm. The proposed algorithm uses dynamic process control parameters to improve its performance. The algorithm is used to find the model parameter values that results in the least amount of error between a set of given data points and points obtained from the Bouc–Wen model. The performance of the algorithm is compared with the performance of conventional Firefly Algorithm, Genetic Algorithm and Differential Evolution algorithm in terms of convergence rate and accuracy. Compared to the other three optimization algorithms, the proposed algorithm is found to have good convergence rate with high degree of accuracy in identifying Bouc–Wen model parameters. Finally, the proposed method is used to find the Bouc–Wen model parameters from experimental data. The obtained model is found to be in good agreement with measured data.

Parameters Identification for a Composite Piezoelectric Actuator Dynamics

This work presents an approach for identifying the model of a composite piezoelectric (PZT) bimorph actuator dynamics, with the objective of creating a robust model that can be used under various operating conditions. This actuator exhibits nonlinear behavior that can be described using backlash and hysteresis. A linear dynamic model with a damping matrix that incorporates the Bouc–Wen hysteresis model and the backlash operators is developed. This work proposes identifying the actuator’s model parameters using the hybrid master-slave genetic algorithm neural network (HGANN). In this algorithm, the neural network exploits the ability of the genetic algorithm to search globally to optimize its structure, weights, biases and transfer functions to perform time series analysis efficiently. A total of nine datasets (cases) representing three different voltage amplitudes excited at three different frequencies are used to train and validate the model. Four cases are considered for training the NN architecture, connection weights, bias weights and learning rules. The remaining five cases are used to validate the model, which produced results that closely match the experimental ones. The analysis shows that damping parameters are inversely proportional to the excitation frequency. This indicates that the suggested hysteresis model is too general for the PZT model in this work. It also suggests that backlash appears only when dynamic forces become dominant.

Time delay control of hysteretic composite plate

Due to boosting usage of flexible and damping materials, it is of great significance for both science and engineering to explore active control methods for vibration within time-delayed hysteretic structures. This paper conducts theoretical and experimental research on a time-delayed controller for a flexible plate with a single-layer rubber glued on its back. First of all, the dynamic equation for a composite plate is given on the base of the Kirchhoff–Love assumption, where damping-restoring force is described by the Bouc–Wen hysteresis model. Then, the influence of time delay is taken into account and the state equation of the plate with time delay is obtained. Next, a standard state equation, with implicit time delay, is derived using one specific form of integral transformation and vector augmentation. Finally, an instantaneous optimal control method is used to design an active controller. This controller does not only involve state feedback of the current step, but also a linear addition of former state feedbacks within several steps. In order to verify this method, experimental work is conducted. Problems encountered like differential computation and lifting of displacement signal are also handled. According to a comparison between simulations and experiments, the control method given in this paper is feasible and valid, and it is available for both small and large time delay.

Adaptive neural control for a class of nonlinear time-varying delay systems with unknown hysteresis.

This paper investigates the fusion of unknown direction hysteresis model with adaptive neural control techniques in face of time-delayed continuous time nonlinear systems without strict-feedback form. Compared with previous works on the hysteresis phenomenon, the direction of the modified Bouc-Wen hysteresis model investigated in the literature is unknown. To reduce the computation burden in adaptation mechanism, an optimized adaptation method is successfully applied to the control design. Based on the Lyapunov-Krasovskii method, two neural-network-based adaptive control algorithms are constructed to guarantee that all the system states and adaptive parameters remain bounded, and the tracking error converges to an adjustable neighborhood of the origin. In final, some numerical examples are provided to validate the effectiveness of the proposed control methods.

Bouc–Wen Hysteresis Model Identification by the Metric-Topological Evolutionary Optimization

From a computational point of view, the identification of Bouc-Wen (BW) hysteresis model is a hard task due to the large number of parameters to be found. This is one of the reasons for which it is rarely used for modeling magnetic hysteresis, where other hysteresis models are widely used (e.g., Preisach and Jiles-Atherton). However, the opportunities that the differential expression of BW model could offer for its use in more complex computation task (e.g., nonlinear inductors inserted into a circuit and so on) justify a deeper investigation on its adoption in ferromagnetism. In this paper, using a new hybrid heuristic called metric-topological-evolutionary optimization (MeTEO), the BW identification is presented. MeTEO is a powerful algorithm based on a synergic and strategic use of three evolutionary heuristics: 1) the flock-of-starlings optimization, which shows not only high exploration capability, but also a lack of convergence; 2) the particle swarm optimization, which has a good convergence capability; and 3) the bacterial chemotaxis algorithm, which has no collective behavior or exploration skill, but has high convergence capability. MeTEO is designed to use parallel architectures and exploits the fitness modification technique. Numerical validations are presented in comparison with the performances obtained using other approaches available in the literature.

An Asymmetric Hysteresis Model and Parameter Identification Method for Piezoelectric Actuator

Hysteresis behaviour degrades the positioning accuracy of PZT actuator for ultrahigh-precision positioning applications. In this paper, a corrected hysteresis model based on Bouc-Wen model for modelling the asymmetric hysteresis behaviour of PZT actuator is established by introducing an input biasφand an asymmetric factorΔΦinto the standard Bouc-Wen hysteresis model. A modified particle swarm optimization (MPSO) algorithm is established and realized to identify and optimize the model parameters. Feasibility and effectiveness of MPSO are proved by experiment and numerical simulation. The research results show that the corrected hysteresis model can represent the asymmetric hysteresis behaviour of the PZT actuator more accurately than the noncorrected hysteresis model based on the Bouc-Wen model. The MPSO parameter identification method can effectively identify the parameters of the corrected and noncorrected hysteresis models. Some cases demonstrate the corrected hysteresis model and the MPSO parameter identification method can be used to model smart materials and structure systems with the asymmetric hysteresis behaviour.

Optimal Control of Magnetorheological Fluid Dampers for Seismic Isolation of Structures

This paper presents the modeling and control of a magnetorheological (MR) damper, installed in Chevron configuration, at the base of a 20-story benchmark building. The building structural model is created using the commercial software package ETABS. The MR damper model is derived from Bouc-Wen hysteresis model which provides the critical nonlinear dynamics that best represents the MR damper under a wide range of operating conditions. System identification is used to derive a low-order nonlinear model that best mimics the nonlinear dynamics of the actual MR damper. Dynamic behavior of this low-order model is tested and validated over a range of inputs. The damper model has proven its validity to a high degree of accuracy against the nonlinear model. A Kalman filter is designed to best estimate the state of the structure-damper system for feedback implementation purposes. Using the estimated states, an LQG-based compensator is designed to control the MR damper under earthquake loads. To demonstrate the effectiveness of this control strategy, four historical earthquakes are applied to the structure. Controlled and uncontrolled floor accelerations and displacements at key locations are compared. Results of the optimally controlled model demonstrate superior performance in comparison to the uncontrolled model.

Semi-active predictive control strategy for seismically excited structures using MRF-04K dampers

The theoretical study of a semi-active predictive control (SAPC) system with magnetorheological (MR) dampers to reduce the responses of seismically excited structures was presented. The SAPC scheme is based on a prediction model of the system response to obtain the control actions by minimizing an object function, which has a function of self-compensation for time delay occurring in real application. A double-ended shear mode combined with a valve mode MR damper, named MRF-04K damper, with the maximum force of 20 kN was designed and manufactured, and parameters of the Bouc-Wen hysteresis model were determined to portray the behavior of this damper. As an example, a 5-story building frame equipped with 2 MRF-04K dampers was presented to demonstrate the performance of the proposed SAPC scheme for addressing time delay and reducing the structural responses under different earthquakes. Comparison with the uncontrolled structure, the passive-off and passive-on cases indicates that both the peak and the norm values of structural responses are all clearly reduced, and the SAPC scheme has a better performance than the two passive cases.