Bouc-Wen Model Research Articles

Design and feedforward control of a two-degree-of-freedom positioning stage with bidirectional piezoelectric drive

The positioning stage composed of piezoelectric stacks and flexible mechanisms is highly competitive in the field of micro/nanomanipulation. Driving stroke and positioning accuracy are the two most important factors to evaluate the positioning stage. However, the attenuation of the driving stroke caused by the stiffness load of the flexible mechanism is an important but neglected problem. On the other hand, the hysteresis of piezoelectric ceramics directly affects the positioning accuracy of the platform. In this study, a two-degrees-of-freedom positioning stage with low displacement attenuation and hysteresis is proposed. Static and dynamic models of the positioning stage were established to derive analytical models of the displacement amplification ratio, structural stiffness, and natural frequency. The displacement transfer coefficient was introduced to establish an equivalent physical model for structural stiffness and displacement attenuation. Genetic algorithms were used to optimize the structural parameters. Finite element analysis is performed to verify the accuracy of the analytical model. The hysteresis is suppressed by the combination of bidirectional piezoelectric driving and inverse Bouc-Wen model feedforward compensation. The measurement results indicated that the proposed positioning stage had a displacement transfer coefficient of 0.82, which was 95.89% lower than the hysteresis of the piezoelectric stack.

Design and dynamic performance research of MR hydro-pneumatic spring based on multi-physics coupling model

Aiming at the problem that the damping coefficient of the traditional hydro-pneumatic spring cannot be adjusted in real-time, the magnetorheological (MR) damping technology was introduced into the traditional hydro-pneumatic spring with single gas chamber. A new shear-valve mode MR hydro-pneumatic spring was proposed. And its dynamic performance was analyzed based on multi-physical coupling simulation and mechanical property test. Firstly, a structural scheme of MR hydro-pneumatic suspension was proposed to ensure the original height adjustment function based on the working principle of traditional hydro-pneumatic suspension with single gas chamber. Secondly, based on the design requirements, the parameter of MR hydro-pneumatic spring damping structure was designed by using MR damper design method. Thirdly, the multi-physical coupling dynamic performance of the MR hydro-pneumatic spring damping structure was analyzed based on the electromagnetic field analysis theory, flow field analysis theory and thermal field analysis theory. The analysis results showed that the designed MR hydro-pneumatic spring has reasonable magnetic circuit structure and excellent working performance. Then, the mechanical properties of MR hydro-pneumatic spring were tested. The results showed that the maximum damping force can reach 20 kN, and the dynamic adjustable multiple can reach 6.4 times. It has good controllability and meets the design requirements. Finally, a nonlinear model of MR hydro-pneumatic spring was established based on the elastic force calculation model of the gas and the Bouc–Wen model. The simulation results of the established model agree well with the experimental results, which can accurately describe the dynamic properties of the hydro-pneumatic spring. The proposed design and modeling method of the MR hydro-pneumatic spring can provide a theoretical basis for the related vibration damping devices.

Observer-based fixed-time fuzzy tracking control for stochastic nonstrict nonlinear systems with hysteresis nonlinearity

In this paper, a new adaptive fuzzy fixed-time control strategy is proposed for stochastic nonstrict nonlinear systems with Bouc–Wen type of hysteresis input and unmeasured state variables. The Bouc–Wen model is recognized as one of the most intractable mechanical hysteresis models. The established state observer is used to assess unmeasurable states, and the fuzzy logic systems are utilized to approximate the uncertain nonlinear functions in the system. Based on the state observer and backstepping method, a fixed-time controller is recursively designed to ensure that all closed-loop signals of the system are bounded and the tracking error converges to a small neighborhood of the origin within a fixed-time. Finally, the effectiveness of the control strategy is verified by two simulation examples.

A Simple Model of the Energy Harvester within a Linear and Hysteresis Approach.

In this article, a model of an energy harvester, the mechanical part of which is an inverted pendulum, is proposed. We investigated the stability of a linearized system. It was proven that the stabilizing control of the pendulum, based on the feedback principle, enables the stabilization of the system. We have identified the zones of stability and the amplitude-frequency characteristics. In the second part of this article, a generalization of the dynamic system for the case of the hysteresis friction in the mechanical joint is considered. The role of nonlinear effects within the design Preisach model and the phenomenological Bouc-Wen model is shown.

Simulation Study of New Buckling Restraint Bracing Based on Bayesian Optimization Algorithm to Identify the Parameters of Modified Bouc–Wen Model

The introduction of new materials can significantly improve the performance of existing dampers, but the constitutive model of new materials is difficult to be obtained in a short time, which makes its numerical simulation difficult. Bouc–Wen–Baber–Noori (BWBN) model can well describe the stress-strain relationship of materials, and it is helpful to introduce new materials into numerical simulation. In this paper, a new high manganese steel material is used to fabricate buckling restrained brace, and based on the improved Transition Markov Chain Monte Carlo (iTMCMC) sampling method and Bayesian reasoning, a new parameter identification of BWBN model is completed; model parameters are introduced into OpenSees to complete the response analysis of the new steel damper in the structure. It provides a new method and approach for introducing new materials into structural seismic resistance and proves its reliability.

Bouc-Wen model with machine learning for SISO and MIMO nano-positioning system

Most of the application in present world have taken ‘Nano’ as a part of their near future implementation. In Nano-Positioning System (NPS) mechanical dynamics are handled at Nano scale. Designing a precision NPS is a greater challenge. Modified linearized Bouc-Wen(BW) model gives the better hysteresis, static and dynamic behavior. In this work SISO (Sıngle-input Sıngle-Output) and MIMO (Multiple-Input Multiple-Output) models of NPS are designed. Previously, system was basically designed to handle conventional macro level dynamics and the same has been extended to handle Nano scale in this work. Kalman Filtering is included to achieve very sustainable results in NPS. The NPS is designed in MATLAB/Simulink with 3 types of electrical signals. Each design is compared using various performance parameters. Machine learning process is included to suggest the appropriate input voltage level sui to obtain desired displacement.

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.

Finite-Time Stabilization of the Generalized Bouc–Wen Model for Piezoelectric Systems

When designing controllers for piezoelectric systems with hysteresis, usually simplified models are used. This can lead to inaccuracies in the closed-loop system response. In this letter, we pose the problem of tracking stabilization of piezoelectric systems using the generalized Bouc-Wen model, a highly non-linear system rarely used to design controllers. Besides, we consider only partially knowledge of one hysteresis system parameter and external disturbances in all the system states. We propose an interconnected control composed of three parts for the solution: an observer, a virtual hysteresis control, and actuator control. It is demonstrated that the closed-loop system converges in finite time. Simulation experiments were carried out, demonstrating the effectiveness of our approach despite exogenous and unknown disturbances.

Classical Bouc-Wen Hysteresis Modeling and Force Control of a Piezoelectric Robotic Hand Manipulating a Deformable Object

This letter focuses on the modeling and control of a piezoelectric actuator that is designed to manipulate objects. This research considers both the non-linearity caused by the hysteresis of the actuator and the deformation of the object being manipulated. To approximate the hysteresis, a classical Bouc-Wen model is used. To stabilize the force-tracking error, we propose a novel control approach combining three advanced methodologies: an output-feedback method based on a nonlinear observer, a Barrier-Lyapunov function design, and bounded control based on saturation functions. Combining these three powerful techniques produces a bounded and highly robust controller that can effectively reject aggressive disturbances while maintaining the tracking error inside a predefined set. Under such a scenario, it is demonstrated that the equilibrium point of the closed-loop system is asymptotically stable. The effectiveness of the proposed control method is validated through extensive numerical simulations.

Dynamic modeling and disturbance rejection compensation for hysteresis nonlinearity of high voltage piezoelectric stack actuators

High voltage piezoelectric stack actuators (HVPSA) are widely used in the field of active vibration control of engineering structures due to their strong load capacity, fast response rate, and high mechanical output efficiency. However, their inherent hysteresis will have a direct impact on the stability and control efficiency of the piezoelectric active control system. To compensate the hysteresis nonlinearity of HVPSA, a high-precision dynamic hybrid method based on linear active disturbance rejection control (LADRC) is proposed. Starting from the hysteresis analysis of piezoelectric actuators, an exponential function butterfly-shape hysteresis operator is constructed and combined with the asymmetric Bouc–Wen model to present a novel hybrid static hysteresis model. In order to implement rate-dependent hysteresis modeling, the Hammerstein rate-dependent hysteresis model of HVPSA is further established, and its inverse model is built for feedforward compensation. Subsequently, the LADRC is used to adjust the driving voltage in real time to form the hysteresis closed-loop compensator of HVPSA. The experimental results show that the Hammerstein rate-dependent hysteresis model established has satisfactory modeling accuracy in the working voltage range and frequency band under consideration. Furthermore, compared with the traditional inverse model feedforward compensation strategy, the proposed hybrid compensation method based on LADRC improves the compensation efficiency by more than 11% and reduces the hysteresis nonlinearity of HVPSA to less than 3%, with strong anti-disturbance ability.

Performance of wire rope damper in vibration reduction of stay cable

This paper systematically investigates the novel application of wire ropes as a damper rather than as an isolator to reduce the wind-induced high-mode vibration of stay cables. Three-direction cyclic loading tests, including tension–compression direction, shear direction, and roll direction, are conducted to clarify the damping behavior of the proposed wire rope damper. The wire rope damper exhibits asymmetric hysteretic characteristics in the tension–compression direction, while the hysteresis loops in the shear and roll directions are symmetrical. A modified normalized Bouc-Wen model is presented to describe the multi-directional hysteretic characteristics of the wire rope damper. An analysis method considering the nonlinear damping behavior is developed in this study to overcome the limitations of the traditional analysis using an equivalent damping coefficient. The proposed analysis method is validated against the physical experiments. The proposed wire rope damper system was installed on the Su-Tong Yangtze River Bridge to reduce the high-mode vortex-induced vibration of the stay cable. The field monitoring data demonstrate that the proposed wire rope damper can significantly reduce the in-plane and out-of-plane vibrations. The effect of the wire rope damper on the cable vibration control is further examined using the proposed analysis method. The finite element results further demonstrate the effectiveness of the wire rope damper in high-mode vibration reduction of stay cables. The features of the wire rope damper, such as multi-directional damping, broadband applicability, and simple configuration, are beneficial to its application in cable vibration control.

Hybrid Adaptive Controller Design with Hysteresis Compensator for a Piezo-Actuated Stage

Piezo-actuated stage (P-AS) has become the topic of considerable interest in the realm of micro/nanopositioning technology in the recent years owing to its advantages, such as high positioning accuracy, high response speed, and large output force. However, rate-dependent (RD) hysteresis, which is an inherent nonlinear property of piezoelectric materials, considerably restricts the application of P-AS. In this research paper, we develop a Hammerstein model to depict the RD hysteresis of P-AS. An improved differential evolution algorithm and a least-squares algorithm are used to identify the static hysteresis sub-model and the dynamic linear sub-model for the Hammerstein model, respectively. Then, a hysteresis compensator based on the inverse Bouc–Wen model is designed to compensate for the static hysteresis of the P-AS. However, the inevitable modeling error presents a hurdle to the hysteresis compensation. In addition, external factors, such as environmental noise and measurement errors, affect the control accuracy. To overcome these complications, a hybrid adaptive control approach based on the hysteresis compensator is adopted to increase the control accuracy. The closed-loop system stability is analyzed with the help of the Lyapunov stability theory. Finally, experimental results indicate that the raised control approach is effective for the accurate positioning of P-AS.

Selection of MR damper model suitable for SMC applied to semi-active suspension system by using similarity measures

Abstract This article discusses the research to determine the suitable magnetorheological (MR) damper model to produce the damping force generated by the sliding mode control (SMC) strategy. The MR damper models studied are parametric, i.e., the Bingham model, the Bouc-Wen model, and the Bouc-Wen model with a hyperbolic tangent function. The damping force of SMC usually includes sudden changes in the force and chattering. The research was carried out by calculating the value of the similarity measure of the damping force of the controller and the damping force of each model. The results show that the two Bouc Wen models had a high similarity measure. The Bouc Wen model with the hyperbolic tangent function was selected because it provides a sudden change of force and reasonable force tracking needed to develop the inverse MR damper model.

Base Isolated connected buildings subjected to seismic and blast induced vibrations

In the present study, the passive control of closely spaced base isolated and fixed base buildings are investigated under the effects of earthquakes and blast induced vibrations. The study advocates the installation of viscous dampers (FVDs) to protect the closely spaced base isolated buildings adjacent to fixed base buildings against seismic and blast excitations. The performance of a five storied base isolated building is reviewed such that time period of isolated building (Tb) is 2.5 sec with isolation damping is assumed as 5% and connected to an adjacent fixed base building such that it has three storey and structural time period 0.5 sec. The effectiveness of damper connected base isolated and fixed buildings is also analyzed for isolation period 2 sec and 3 sec respectively. Nonlinear direct integration method has been adopted to evaluate the performance of fixed base and base isolated structures for connected and unconnected state. The equations of motions are formulated and solved using MATLAB code by Newmark’s average acceleration method. The lead rubber isolators are designed and idealized as Bouc Wen model. A parametric study is also conducted to determine the optimum damper properties for the fixed base buildings and base isolated connected buildings with viscous dampers. Results exhibit the efficiency of viscous dampers in reducing the structural responses of the base isolated buildings. It has been observed that in case of fixed base buildings, the peak responses show an effective reduction in responses. The effectiveness of the passive control technique using viscous dampers in mitigating the bearing displacements of base isolated structures subjected to seismic and blast induced vibrations is also reported.

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.

Velocity Tracking Control Algorithm for Semiactive Control of Building Frames

A new control algorithm called velocity tracking control (VTC) is presented for the semi-active control of partially observed building frames using magneto-rheological (MR) dampers. The novelty of the control algorithm relies on the use of special features of the semi active control using MR dampers in which the time history of voltage to be applied to the MR damper can be generated with the help of feedback information from the observed states only; it does not require the estimation of the full state from the measured ones which introduces some errors in the estimated control force generated in the MR damper. The algorithm is developed based on a physical reasoning, which is validated by the Lyapunov stability condition of the first order filter used in the modified Bouc-wen model that models the MR damper. The efficiency of the control algorithm is compared with the passive on control for a number of earthquakes. The response quantities of interest, for which percentage reductions in responses are compared, include the peak top floor displacement, peak inter-story drift and maximum base shear. The results of the study show that the proposed control algorithm provides the maximum percentage reduction in peak inter-story drift in comparison to passive on control. Further, the efficiency of the proposed control algorithm, defined by the percentage reduction of responses per unit control force, is found to be more as compared to the passive on control.

Seismic Response Analysis of Vertically Irregular RC Building with MR Dampers

Seismic hazard mitigation has become one of the emerging problems in structural engineering therefore; many researchers have been studied on seismic performance of reinforced concrete structures having vertically regular and irregular. It is noted that vertically irregular structures are more prone to hazards due to earthquake. The recent emerging trend is to use active, passive, semi-active controls that aid in keeping the responses of structures in permissible. The most dynamically varied semi-active damper is a Magneto-Rheological (MR) damper which is used in this study to control the seismic responses. In the present study, four different models with and without MR dampers of which three models are vertically irregular in height are subjected to four realistic ground motions. The governing equation of motion for various building models is solved numerically by Newmark’s step-by-step integration method. The dynamic behaviour of semiactive MR damper has been predicted by modified Bouc-Wen model. This study employed the Lyapunov direct approach as a control algorithm for stability analysis and design of MR controller. The responses of various building models are simulated through MATLABâcomputing software. The study observed that considerable reduction in seismic responses of models with MR dampers is obtained as compared to respective building models without control. It is also observed that responses of building models are influenced by the vertical irregularities in mass and stiffness of building models.

Seismic Fragility Assessment of RC Building Using HAZUS Methodology and Incremental Dynamic Analysis

The technique of coupled building strategy is more viable to protect the adjacent buildings of dissimilar in characteristics against seismic hazards. The philosophy of coupled building control in which adjacent buildings are allowed to exerts counter-acting forces one upon another. This study includes the seismic performance of various Coupled Buildings with respect to Uncoupled Buildings for which two models of Coupled Building are considered that is, first one is the two-shear type adjacent buildings connected in-line with MR dampers and second one is same as first with taller building is isolated by Resilient-Friction Base Isolator at its foundation. The seismic response analysis of RC coupled buildings are studied in terms of peak responses subjected to unidirectional excitation due to Kobe 1995 earthquake. The governing equation of motion of various coupled buildings is solved numerically by Newmark’s step-by-step method. The dynamic behaviour of semiactive MR damper and R-FBI base isolation system has been predicted by modified Bouc-Wen model and Wen’s model respectively. This study employed the Lyapunov direct approach as a control algorithm for the stability analysis and design of semiactive MR controller. The responses of various coupled buildings and uncoupled buildings are simulated through MATLABâ computing software. This study outlined that model of Coupled Building-2 performs more effective in controlling the seismic responses whereas model of Coupled Building-1 performs well not only in reducing the responses but also avoid pounding from the adjacent buildings. Further, there is significant reduction in responses of taller building isolated by base isolation system whereas marginal reduction takes place in shorter building which is not isolated.

Predicting hydrodynamic forces on heave plates using a data-driven modelling architecture

Prior work has modelled heave forces on surface piercing bodies in real time for 2D, convex and static geometries using a Hammerstein framework. In this work, the modifications needed to make that framework suitable for a representative heave plate geometry in irregular waves are investigated in order to facilitate force prediction for heaving wave energy converters. Two candidate models are compared. The first introduces a Bouc–Wen model to the conventional internal force calculation in the Hammerstein framework. The second further modifies the dynamic block by replacing the linear ARX dynamic calculation with a nonlinear Kolmogorov–Gabor polynomial (KGP) structure. The addition of the Bouc–Wen model introduces velocity and acceleration dependence and a new hysteresis contribution to the internal force predictions to capture the form drag and inertial loads known to occur around heave plates from the entrained fluid. This addition reduces the average error in the internal force calculation by up to 70% for kinematically controlled bodies in irregular waves. Using the revised internal force in the system dynamic block identification process, it was found that the resulting models provided significant improvements (up to 38%) in prediction of the hydrodynamic heave force when using both the linear and nonlinear ARX formulations.

Modeling and identification of nonlinear hysteresis behavior of piezoelectric actuators using a computationally efficient phenomenological model and modified cuckoo search algorithm

Hysteresis, an intrinsic characteristic of piezoelectric (PZT) actuators, has been demonstrated to dramatically reduce the capability and stability of the system. This paper proposes a novel computationally efficient model to describe nonlinear and hysteresis behaviors of PZT actuators. First of all, the model parameters are analyzed to investigate their effects on the output response. Then, a modified cuckoo search algorithm is used to identify the model parameters, without falling into the local optimum problems through introducing adaptive egg discovery probability and step length control factor. Further, the performance of the proposed model is validated using experimental data, via the comparison with classical Bouc-Wen and Prandtl-Ishlinskii hysteresis models. Finally, the rate-dependence of the parameters of proposed model is analyzed, which contributes to a generalized hysteresis model for the compensation control application of PZT actuators.