Hysteresis Nonlinearity Research Articles

Active alignment control system for thin disk regenerative amplifier.

We present an active alignment and stabilization control system for laser setups based on a thin-disk regenerative amplifier. This method eliminates power and pointing instability during the warm-up period and improves long-term stability throughout the entire operation. The alignment method is based on a four-mirror control system consisting of two motorized mirrors placed within the regenerative amplifier cavity, two additional motorized mirrors external to the amplifier cavity, and four camera detectors. The implemented stabilization system achieves significant performance improvements, increasing the power stability from 1.87% to 0.79% RMS and the peak-to-peak stability from 7.43% to 3.88%. Furthermore, the system significantly enhances beam positional stability, achieving up to a sixfold improvement in certain sensor measurements. The advantage of this method is the removal of long-term pointing instability by adding a second controlled motorized mirror to the cavity, in addition to using only one cavity end mirror for optimizing the overlap with the pump spot on the cavity medium. To achieve higher precision in pointing, the nonlinear hysteresis effect of the piezoelectric actuator is mitigated. Although the power and pointing stability of the cavity are secured, pointing instability at the input of the compressor occurs. This issue is resolved by two additional controlled motorized mirrors external to the cavity.

Effect of Nonlinear Hysteresis Details of Isolation System on In-Structure Response Spectra

To evaluate the seismic safety of components in a structure, an in-structure response spectrum (ISRS) must be obtained, and this also applies to seismically isolated structures. The main variables for designing seismic isolators are effective stiffness and effective damping, which can be given as the characteristic strength and secondary stiffness in seismic isolators for nonlinear behaviors. Many studies on the ISRS of isolated structures have been conducted to evaluate the effects of these two variables of isolators, but the effect of other variables related to the hysteresis curve of isolators also needs to be studied. This study focused on the effect of the initial stiffness of isolators on an ISRS because there were no clear criteria for determining the initial stiffness in isolator design standards, which has an effect on the ISRS that cannot be ignored. As a result, the initial stiffness contributed significantly to the ISRS not only at the natural frequency of the structure but also at low frequencies. An analysis was also performed in terms of the uncertainty of each variable. The sharpness of the yield point in the hysteresis curve was implemented using the Bouc–Wen model, and its impact was analyzed. In addition, the frequency content of the ISRS depending on the seismic intensity, which can considerably change the nonlinear hysteresis behavior, was examined. Through this study, although secondary stiffness and characteristic strength are the most important characteristics of seismic isolation design, it was confirmed that other variables also have a significant impact on the frequency content of an ISRS. Based on this study, the considerations when developing the ISRS of an isolated structure can be established.

Characterizing nonlinear piezoelectric dynamics through deep neural operator learning

Nonlinear hysteresis modeling is essential for estimating, controlling, and characterizing the behavior of piezoelectric material-based devices. However, current deep-learning approaches face challenges in generalizing effectively to previously unseen voltage profiles. This Letter tackles the limitation of generalization by introducing the notion of neural operators for modeling the nonlinear constitutive laws governing inverse piezoelectric hysteresis, specifically focusing on the relationship between voltage inputs and displacement responses. The study utilizes two neural operators—Fourier neural operator and the deep operator network—to predict material responses to unseen voltage profiles that are not part of the training data. Numerical experiments, including butterfly-shaped hysteresis curves, show that in accuracy and generalization to unseen voltage profiles, neural operators outperform traditional recurrent neural network-based models, including conventional gated networks. The findings highlight the potential of neural operators for modeling hysteresis in piezoelectric materials, offering advantages over existing methods in varying voltage scenarios.

Cyclic Lateral Response of Large‐Diameter Monopiles in Soft Clays Using Bounding Surface‐Based Analytical p‐y Curves

ABSTRACTThe p‐y curve method provides a relatively simple and efficient means for analyzing the cyclic response of horizontally loaded piles. This study proposes a p‐y spring element based on a bounding surface p‐y model, which can be readily implemented in Abaqus software using the user‐defined element (UEL) interface. The performance of these p‐y spring elements is validated by simulating field tests of laterally loaded piles documented in the literature. The developed spring element effectively replicates the nonlinear hysteresis, displacement accumulation, and stiffness degradation observed in soft clay. Subsequently, a finite element model of a large‐diameter monopile is established using the proposed spring element. A comprehensive numerical investigation is conducted to explore both the monotonic and cyclic responses of large‐diameter monopiles in soft clays. The results are presented and discussed in terms of pile head load–displacement curves, the evolution of rotation angles at the mud surface, and cyclic p‐y curves. Additionally, empirical formulas are proposed to predict the evolution of cumulative rotation angles and peak bending moments under both one‐way and two‐way cyclic loading conditions. The results provide valuable insights into the mechanism of pile–soil interaction under lateral cyclic loading.

Test, Modeling, and Vibration Control of a Novel Viscoelastic Multi-Dimensional Earthquake Isolation and Mitigation Device

Earthquakes contain complex components in both the horizontal and vertical directions. However, most vibration control strategies work only in a single direction. The existing multi-dimensional isolation devices usually have complex designs and low damping ratios; hence, the stability of structures that incorporate the devices is currently insufficient. This study designs a novel multi-dimensional isolation and mitigation device based on viscoelastic damping technology (VE-MDIMD). The device consists of a core bearing and several cylindrical dampers, providing vibration control capacity in both the horizontal and vertical directions and a strong uplift resistance. To evaluate the device’s performance, a series of dynamic tests are conducted on the cylindrical damper utilized in the device. The results show that the damper’s mechanical properties exhibit a pronounced dependence on the frequency and amplitude, and its hysteresis curves become obviously nonlinear with increased deformation. Subsequently, to describe the behavior of the VE-MDIMD, a mechanical model is established which combines the construction of the device and the characteristics of the damper. Considering the limitations of existing models in fully capturing the nonlinear behavior of the damper, a novel multi-scale model is proposed based on the microstructure of viscoelastic material. The experimental verification confirms that the model can accurately capture the frequency and amplitude dependence, as well as the nonlinear hysteresis behavior, of the damper. Finally, the effectiveness of the VE-MDIMD is evaluated through the dynamic analysis of an actual structure. The arrangement of the device in the structure is optimized based on a multi-objective genetic algorithm available in Matlab (R2019b) and OpenSEES (Version 3.0.0). The results demonstrate the device’s superiority in controlling both horizontal and vertical vibrations in the superstructure.

A dynamic response prediction model of nonlinear hysteretic isolators based on quasi-static characteristics and dynamic compensations

Nonlinear hysteretic isolators are widely applied in the field of vibration isolation due to their excellent energy dissipation capacity. However, the dynamic response prediction of nonlinear hysteretic isolators highly depends on accurate modeling methods for nonlinear hysteresis under varying conditions. This paper proposes a dynamic response prediction model based on quasi-static characteristics to precisely characterize the dynamic properties of nonlinear hysteretic isolators. The model employs a normalized Bouc-Wen framework, extended by polynomials, to describe the possible nonlinear stiffness and asymmetric hysteretic behaviors under quasi-static loading conditions. Additionally, global nonlinear elastic and damping terms are introduced to further capture the dynamic hysteretic characteristics over a wider range of operating velocities. The model parameters can be identified through quasi-static cyclic loading experiments and dynamic sinusoidal experiments. Then, the parametric model representing the restoring force is integrated into the dynamic equation for dynamic response prediction of the isolation object. The effectiveness of the proposed model is experimentally validated using an assembled hysteretic isolator. With limited testing data at specific amplitudes and frequencies, the resonance frequencies under steady-state excitations and the root mean square values under stochastic excitations are predicted with average accuracies of 97.40% and 97.09%, respectively.

Performance analysis of position sensorless control of antagonistic shape memory alloy actuators

Abstract This paper presents a comprehensive performance analysis of position sensorless control of antagonistic shape memory alloy actuators (ASMAA), focusing on enhancing the sensorless position sensing capabilities and servo performance. The mechanisms and influencing factors of ASMAA self-sensing characteristics are comprehensively analyzed. A self-sensing model framework based on the constitutive model of ASMAA is proposed, and a self-sensing model based on differential resistance feedback is developed. An experimental platform based on the ASMAA motion mechanism is established to test and analyze SMA wires of two different materials under various pretension force conditions. The experimental results show that the antagonistic configuration mitigates hysteresis and improves linearity. A simple polynomial fitting is employed to establish the resistance-displacement relationship, achieving good accuracy with minimal residuals. The system identification is employed to avoid the parameter complexity and time-varying in the constitutive model. Based on the identified transfer function, a traditional PID controller is designed for position sensorless servo control. However, the inherent nonlinear hysteresis of ASMAA is difficult to suppress using a linear PID controller. Furthermore, a compound control strategy based on the Duhem model and PID controller is proposed, which utilizes the particle swarm optimization algorithm to identify the Duhem inverse model controller. Experimental results demonstrate that the compound controller significantly enhances position tracking accuracy and response speed compared to a standalone PID controller.

Analysis and Prediction of Nonlinear Hysteretic Behaviors of Graphite Magnetorheological Grease at Different Temperatures.

Magnetorheological grease (MRG) is considered a promising alternative to magnetorheological fluids as a smart material because of its higher stability and less leakage. To enhance yield stresses in various applications, graphite is incorporated as an additive, resulting in graphite magnetorheological grease (GMRG). However, the nonlinear hysteresis properties of this new material and its prediction methods have not been investigated. Therefore, in this work, the nonlinear hysteretic properties of GMRG at different temperatures, magnetic fields, and frequencies are systematically investigated and compared with those of MRG. The results of rheological experiments show that graphite enhances the shear stress of GMRG in the hysteresis curve through its reinforcing effect on the magnetic chains. The strain hardening, elasticity, and viscosity of GMRG are enhanced, but an increase in temperature decreases this efficacy. A prediction model based on the particle swarm optimization neural network algorithm (PSO-BP) is also proposed to efficiently and accurately control the nonlinear behavior of GMRG in engineering. The hysteresis curves of GMRG under different external excitations are characterized and predicted by the particle swarm optimization neural network approach. The statistical results show that the PSO-BP-based hysteresis characteristic estimates have satisfactory accuracy. In the test data, the PSO-BP model demonstrates improvements in RMSE, MAE, and SMAPE by 19.5%, 20.6%, and 21.0%, respectively, compared to the conventional BP network, which maintains an R2 value exceeding 0.95. This method provides an efficient solution for researchers to carry out reliable performance prediction in work such as genetic engineering of materials and related engineering applications.

Modeling linear and nonlinear viscoelastic oscillatory rheometric stress-strain hysteresis of asphalt binders

Understanding the complex stress-strain hysteresis behavior of asphalt binders under varied conditions is critical for optimizing pavement performance. This study addresses the challenge by analyzing and modeling asphalt binder responses in oscillating shear mode across different aging states (unaged, short-term aged, and long-term aged), stretch amplitudes, frequencies, and temperatures. Fifty-three stress-strain hysteresis loops were meticulously analyzed, revealing distinct stress paths relative to applied stretch levels. A nine-parameter parallel rheological framework model was developed, integrating a four-parameter eight-chain (FEC) hyperelastic model in one network and a FEC hyperelastic model with a linear viscoelastic flow element in series in another. This constitutive model was implemented in LS-DYNA finite element simulations to predict experimentally-measured stress-strain hysteresis loops accurately. The research demonstrates the model’s capability to simulate both linear and nonlinear viscoelastic responses of asphalt binders across a wide range of environmental and loading conditions. This approach significantly enhances our ability to capture and understand the stress-strain behavior critical for asphalt pavement durability and performance optimization.

Modeling and precise tracking control of spatial bending pneumatic soft actuators

In recent years, a variety of pneumatic soft actuators (PSAs) have been proposed due to the development of soft robots in biomimetic robots, medical devices, etc. At the same time, the modeling and control of PSAs remains an open question. In this paper, a spatial bending pneumatic soft actuator (SBPSA) modeling method based on the Prandtl–Ishlinskii (PI) model is proposed, and the inverse model is designed to compensate for hysteresis nonlinearity. Furthermore, an adaptive feedback controller combined with a hysteresis compensator is proposed for the precise control and tracking of SBPSAs. Finally, an experimental platform is built, and experimental results demonstrate the effectiveness of the proposed method for precise tracking.

Reinforcement Learning-Based Adaptive Optimal Control for Nonlinear Systems With Asymmetric Hysteresis.

This article investigates the adaptive optimal tracking problem for a class of nonlinear affine systems with asymmetric Prandtl-Ishlinskii (PI) hysteresis nonlinearities based on actor-critic (A-C) learning mechanisms. Considering the huge obstacles arising from the uncertainty of hysteresis nonlinearity in actuators, we develop a scheme for the conflict between the construction of Hamilton functions and hysteresis nonlinearity. The actuator hysteresis forces the input into a hysteresis delay, thus preventing the Hamilton function from getting the current moment's input instantly and thus making optimization impossible. In the first step, an inverse model is constructed to compensate for the hysteresis model with a shift factor. In the second step, we compensate for the control input by designing a feedback controller and incorporating the estimation and approximation errors into the Hamilton error. Optimal control, the other part of the actual control input, is obtained by taking partial derivatives of the Hamiltonian function after the nonlinearities have been circumvented. At the end, a simulation is given to validate the developed solution.

Hysteresis dynamic modeling of 4-SPS parallel all-metallic isolator with spherical joints considering nonlinear micro-collision and interfacial friction

This work aims to identify ways to model a high-accuracy hysteresis dynamic model for an innovative 4-SPS parallel all-metallic isolator. Firstly, a three-dimensional contact model of spherical joints under different conditions (stretching and compression) is proposed, referred to as the integrated model of nonlinear micro-collision and interfacial friction (INCF model). Simultaneously, in conjunction with the nonlinear elastic recovery force, nonlinear damping force, and nonlinear hysteresis damping force, the high-accuracy hysteresis dynamic model of the isolator is constructed. To validate the accuracy, dynamic experiments are conducted on the isolator at distinct frequencies (6–9 Hz) and amplitudes (0.6–0.9 mm). The results indicate that the hysteresis dynamic model constructed based on the INCF model exhibits a remarkably high level of precision compared to the classic model (R2=0.998). This increased accuracy is attributed to the consideration of influencing factors of the INCF model, such as micro-collisions between spherical joints and interfacial friction during the operation of the isolator. These variables are determined by the material properties and geometric dimensions of the spherical joint and can be adjusted in real time based on the isolator deformations to enhance the model's accuracy. The method of parameter identification applied to overall structure resolves challenge of measuring the internal deformation of spherical joints. Importantly, the INCF model is not limited to the isolators proposed in this work but can also be applied to similar isolators with Stewart structure-type connections that employ spherical joints. These research findings provide a robust theoretical support for the design and performance optimization of the isolator, with the potential to positively impact related engineering applications.

Enabling accurate simulations of the nonlinear magnetic hysteresis behavior in ferromagnetic materials

In this work, a stable node - based smoothed finite - element method algorithm is developed to address the lower accurate issues in the simulation of the magnetic hysteresis behavior in ferromagnetic materials, in which the inverse vector Jiles - Atherton model is intimately coupled. The improvement of the accuracy for hysteresis issues is achieved by linking the stable node - based smoothed finite - element method in the framework of the Newton - Raphson iteration and the Jiles - Atherton model. The optimal relaxation coefficient method is introduced to address the natural strong nonlinearity of the Jiles - Atherton model and to ensure the convergence of the model. The algorithm is validated against the experimental results, and several examples are presented for simulations of the ferromagnetic hysteresis issues to illustrate both the accuracy and expandability in the practical scenarios of ferromagnetic materials.

Dynamic modeling of thermo-sensitive hydrogel describing its complex energy conversion mechanism with hysteresis nonlinearity

Thermo-sensitive hydrogel (TSH) demonstrates a lot of promise for soft robots. However, the TSH presents challenges for modeling due to its complex energy conversion mechanism and hysteresis nonlinearity. To address this issue, a dynamic model consisting of an electro-thermal model and a thermo-deformation model is developed in this paper. In which, the electro-thermal model is established for describing the relationship between the driving voltage and the temperature of the TSH. The thermo-deformation model consisting of a Prandtl-Ishlinskii model, a polynomial model and a transfer function model is established between the temperature and the deformation of the TSH. In addition, the thermo-deformation model describes the asymmetric and rate-dependent hysteresis nonlinearity of the TSH. Moreover, due to the analytic inverse of the thermo-deformation model, it is convenient to design a model-based controller to achieve the high-precision deformation control of the TSH. Next, unknown parameters in the above models are determined based on the nonlinear least squares algorithm by using the data from the experiment. Finally, model validations are performed, and the fit values are all greater than 89.40 %. Thus, the established dynamic model can accurately describe the complex energy conversion mechanism with hysteresis nonlinearity of the TSH and has great generalization ability.

Validation of a three-dimensional finite element constitutive modeling approach for a thermoplastic polyurethane calibrated with uniaxial tests

This paper presents the three-dimensional finite element constitutive modeling validation for a Thermoplastic Poly-Urethane (TPU) material. The material parameters are those given in a previous study obtained by calibrating the constitutive model with uniaxial material-level test results (1-D tensile and compression tests). Confined compression tests were performed to estimate the bulk modulus for more accurate material characterization. The parameters were validated by comparing the results of experimental tests on TPU components with those obtained by its equivalent finite element simulations. The TPU component tests comprised cyclic compression tests of (i) a TPU cylinder, (ii) a solid 100 mm diameter TPU ball, and (iii) a 100 mm diameter TPU ball with an 80 mm steel core. In all tests, the constitutive model parameters showed an excellent performance in representing the mechanical behavior of the material observed in the tests, including the nonlinear stiffness and hysteresis. Finally, a brief case study is presented to illustrate the applicability of the validated constitutive model parameters in modeling a novel TPU damper for structural control before its manufacturing and experimental testing. The validated constitutive modeling approach and available material parameters will allow the performance of reliable and early-stage finite element simulations to prototype the mechanical behavior of TPU components of different shapes and boundary conditions and thus gain relevant insight into the component level response before manufacturing and testing.

Application of model predictive control scheme for piezoelectric ceramic micro-displacement

Abstract Currently, in the domain of micro-control technology, many operations need to meet the standard of nanometer-level positioning. As a high-precision micro-displacement element, piezoelectric ceramics are widely used in the field of micro-control due to their characteristics such as no need for transmission devices, high resolution, large output force, small size, and fast response speed. However, the inherent hysteresis nonlinearity of piezoelectric ceramics can lead to decreased displacement accuracy, oscillation, and even system instability. Therefore, eliminating the influence of nonlinear characteristics and improving displacement accuracy possess significant practical importance. In this paper, a model predictive control scheme is designed, which achieves faster response speed and higher accuracy compared to traditional control methods such as Proportional Integral Derivative control. Relevant simulations and tests have been conducted. In this scheme, hysteresis nonlinearity is first modeled and then compensated through feedforward, thereby simplifying the displacement control of piezoelectric ceramics into a more manageable linear problem. Subsequently, a linear model predictive control method is adopted to control the entire system. Both simulation and experimental results have verified the effectiveness of this control method.

Singularity-free practical finite-time force control for a compliant grinding mechanism subject to hysteresis nonlinearity and asymmetric time-varying air pressure constraints

Singularity-free practical finite-time force control for a compliant grinding mechanism subject to hysteresis nonlinearity and asymmetric time-varying air pressure constraints

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.

A nonlinear hysteresis compensation control of hydro-viscous drive in air transport operations

The Hydro-Viscous Drive (HVD) speed regulating system finds extensive application in air transport transmission systems to regulate the stepless speed or conduct overload protection. However, its intrinsic hysteretic behaviors, such as the asymmetric hysteretic and dead zone, could introduce inaccuracy and delay in control applications, posing challenges to system regulation. This paper investigates a Nonlinear Hysteresis Compensation Control (NHCC) that consists of two parts to control the HVD output speed by operating the valve under different engine operating conditions. In the first part, the Inverse Hysteresis Compensator (IHC) based on major loop data is introduced for the asymmetric hysteresis characterization and compensation of the HVD speed control system of the power generation and distribution, which aims to reduce the hysteresis and dead zone effect and expand the effective input range. In the second part, the Active Disturbance Rejection Controller (ADRC) is employed to mitigate the hysteresis effects of the compensated system and remove the steady-state error, which allows real-time compensation of the estimated perturbations as state feedback to achieve the required performance. An experimental laboratory station has been fabricated to evaluate the proposed method. The test results show that the NHCC method can regulate the fan speed to the desired value (|e|< 45 r/min at steady state) and broaden the effective input range to the full range under different engine conditions. Besides, the proposed control method can reduce the non-linearity of the input and output curves (from 18% to 4%) and compensate for the asymmetric hysteresis (from 38% to 5%).

Nonlinear hysteresis system control based on sliding mode neural network and observer

In this paper, a sliding mode neural network controller with observer is presented and employed in a nonlinear hysteresis system to eliminate the system’s unknown hysteresis and uncertainties. First, a sliding mode controller is proposed for trajectory tracking, which simplifies the computational complexity and ensures robustness. Second, radial basis function neural network is applied for approximating unknown nonlinear function in the control system. Then, an observer is utilized to estimate and observe the hysteresis nonlinearity and cancel the effect of the hysteresis phenomenon. Based on the proposed control scheme, the influence of hysteresis is suppressed, and the system has robust stability and achieves high output tracking performance. Finally, theoretical analysis and numerical simulations confirm the effectiveness of the designed control law.