Hysteresis Nonlinearity Research Articles

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.

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.

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.

Inversion-based fuzzy adaptive control with prespecifiable tracking accuracy for uncertain hysteretic systems

Inversion-based control strategies have the outstanding effectiveness in the compensation for hysteresis nonlinearities. However, when the plant is driven by smart material-based actuator with the information absence of hysteresis output, there still exist technical gaps in the construction of hysteresis inverse controller. Therefore, this study aims to address this gap by proposing a novel control scheme. Technically, a novel hysteresis inverse algorithm, significantly reducing computational burden, has been proposed based on a novel adaptive estimation method for the unknown parameter (density function) in the Preisach-typed hysteresis nonlinearity. Furthermore, the inverse compensation error, the nonlinearities and uncertainties appeared in the controlled plant are accommodated by the innovative adaptive fuzzy feedback controller. With our scheme, it can ensure that the closed-loop stability, predefined steady-stated tracking performance and the convergence of algorithms including inverse algorithm and adaptive updating laws. In addition to theoretical analysis, we have validated the effectiveness of the proposed control scheme through simulation comparisons and experimental results conducted by the real-life piezoelectric actuator.

Modeling of dynamic characteristics and μ-synthesis control of piezoelectric positioning platform

Abstract The dynamic hysteresis nonlinearity and various uncertainties of the piezoelectric positioning platform are critical factors limiting its high-precision applications. To address this, the dynamic characteristics of the piezoelectric positioning platform under various loads are identified based on the linearization of the Prandtl-Ishlinskii inverse model. The inverse compensation error and load disturbances are attributed to model uncertainties, which are modeled in the frequency domain. A μ-synthesis controller is designed to improve the tracking accuracy of the piezoelectric positioning platform under uncertainty disturbances. Experimental results indicate that with the μ-synthesis controller, the piezoelectric positioning platform achieves a relative error (RE) of less than 2.71% when unloaded. The RE is less than 6.03% for load disturbances of 100g, 200g, and 300g, respectively. These results demonstrate that the designed controller meets the high-precision positioning performance requirements under various load disturbance conditions.

Residual Vibration Suppression of Piezoelectric Inkjet Printing Based on Particle Swarm Optimization Algorithm.

Piezoelectric inkjet printing technology, known for its high precision and cost-effectiveness, has found extensive applications in various fields. However, the issue of residual vibration significantly limits its printing quality and efficiency. This paper presents a method for suppressing residual vibration based on the particle swarm optimization (PSO) algorithm. Initially, an improved PI model considering the nonlinear hysteresis characteristics of piezoelectric ceramics is established, and the model is identified through a strain gauge circuit to ensure its accuracy in describing the nonlinear hysteresis characteristics. Subsequently, a dynamic model of the piezoelectric inkjet printing system is constructed, with precise parameter identification achieved using the self-induction principle. This enables precise simulation of residual vibration. Finally, the driving waveform is optimized based on the PSO algorithm, with iterative calculations employed to find the optimal combination of driving waveform parameters, effectively suppressing residual vibration while ensuring sufficient injection energy. The results indicate that this method significantly reduces the amplitude of residual vibration, thereby effectively enhancing printing quality and stability. This research offers a novel solution for residual vibration suppression in piezoelectric inkjet printing technology, potentially advancing its applications in printing and biofabrication.

Adaptive Nonsingular Fast Terminal Sliding Mode Control for Shape Memory Alloy Actuated System

Due to its high power-to-weight ratio, low weight, and silent operation, shape memory alloy (SMA) is widely used as a muscle-like soft actuator in intelligent bionic robot systems. However, hysteresis nonlinearity and multi-valued mapping behavior can severely impact trajectory tracking accuracy. This paper proposes an adaptive nonsingular fast terminal sliding mode control (ANFTSMC) scheme aimed at enhancing position tracking performance in SMA-actuated systems by addressing hysteresis nonlinearity, uncertain dynamics, and external disturbances. Firstly, a simplified third-order actuator model is developed and a variable gain extended state observer (VGESO) is employed to estimate unmodeled dynamics and external disturbances within finite time. Secondly, a novel nonsingular fast terminal sliding mode control (NFTSMC) law is designed to overcome singularity issues, reduce chattering, and guarantee finite-time convergence of the system states. Finally, the ANFTSMC scheme, integrating NFTSMC with VGESO, is proposed to achieve precise position tracking for the prosthetic hand. The convergence of the closed-loop control system is validated using Lyapunov’s stability theory. Experimental results demonstrate that the external pulse disturbance error of ANFTSMC is 8.19°, compared to 19.21° for the comparative method. Furthermore, the maximum absolute error for ANFTSMC is 0.63°, whereas the comparative method shows a maximum absolute error of 1.03°. These results underscore the superior performance of the proposed ANFTSMC algorithm.

Adaptive neural chattering suppression pseudo inverse active control for a class of micromilling systems with multiaxis piezoelectric actuators

For a multi-axis nonlinear milling system with piezoelectric actuators, a pseudo inverse dynamic surface active control scheme with adaptive fuzzy output-feedback is developed. The main contributions can be characterized as following: (1) to overcome the hysteresis non-linearities in the piezoelectric actuators, the new hysteresis pseudo inverse compensators are established to replace the conventional hysteresis direct-inverse model construction, which is a very challenging or even impossible work. The hysteresis pseudo inverse means that the hysteresis direct-inverse model is no longer essential any more, instead, a search algorithm for the actual control signal from the designed hysteretic temporary control laws are proposed to alleviate the hysteresis nonlinearities effectively; (2) to realized high-precision tracking control and mitigate chattering suppression in the micromilling systems, the fuzzy logic systems, the novel dynamic surface control algorithms and the modified high-gain states observer are designed to approximise the unknown continuous functions of the micromilling systems, design the high performance controller and estimate the immeasurable states in the control system, respectively; (3) the hardware-in-loop simulation platform is constructed and the experiments of tracking control and chattering suppression are implemented to validate the effectivity of the developed control scheme.

Piecewise modified Prandtl-Ishlinskii model for precise nano-positioning

Piezoelectric ceramic, an indispensable micro-nano actuator, has advantages of small size, high sensitivity and strong controllability, which is widely applied in various fields like micro-nano processing, medicine, chemistry and materials. However, its nonlinear and asymmetric hysteresis features directly affect its positioning accuracy. The classical and generalized Prandtl-Ishlinskii models with linear symmetry operators are commonly used to deal with these issues, but they still face difficulties in asymmetric systems. Therefore, a piecewise modified Prandtl-Ishlinskii (PMPI) model is proposed to compensate nonlinear and asymmetric hysteresis in this paper. The new nonlinear operator and piecewise nonlinear envelope function are introduced into the PMPI model. Independent right and left parts are adopted to describe hysteresis increasing and decreasing stages, while the threshold and weight vectors correspond to them. Weight vectors are extended and a new diagonal matrix is constructed for avoiding excessive parameters and computation. Simulations and experiments are shown that the PMPI model has good compensation performance and effectiveness, which has better fitting, higher accuracy, fewer parameters and computation, and can be well applied to the precise nano-positioning systems with less nonlinear and asymmetric errors.

Modelling and compensation of rate‐dependent hysteresis in piezoelectric actuators based on a modified Madelung model

AbstractBased on the principle of weight superposition, a modified Madelung model is proposed. By combining the signal delay response characteristics (SDRC), a dynamic model and its inverse model are established to describe and compensate for the rate‐dependent hysteresis phenomenon of the piezoelectric actuators (PEAs). The effectiveness of the proposed method is verified by experiments, and the results show that the hysteresis nonlinearity of the PEA is basically eliminated, with the normalized root‐mean‐square error of 0.64% under the excitation of multi‐frequency superposition signal.

Comparative analysis and optimization of nonlinear hysteresis models for a magnetorheological fluid dual-clutch of an electric vehicle transmission

Comparative analysis and optimization of nonlinear hysteresis models for a magnetorheological fluid dual-clutch of an electric vehicle transmission

Robust PID controller design for positioning systems with hysteresis and time-varying delay

This paper presents Linear Matrix Inequalities (LMIs) conditions for designing Proportional-Integral-Derivative (PID) controllers that guarantee asymptotic stability with exponential convergence rate for positioning systems affected by hysteresis nonlinearity and time-varying delay. The hysteresis is modelled using the Prandtl-Ishlinskii operator, and the effects of both the time-varying delay and hysteresis are encapsulated into a bounded uncertain parameter confined within a known convex polytope. Numerical results support the theoretical developments, confirming that the controller effectively mitigates the effects of disturbances while suppressing both the hysteresis and time-varying delay influences.

Nonlinear resonant bar of approximate Ramberg–Osgood type modulus defect

This study investigates the nonlinear vibration of a material bar with a modulus defect that causes observable hysteresis in the elastic regime. The Ramberg–Osgood equation is used to obtain an approximate model of the quasi-static stress–strain relationship for such a material, from which a phenomenological dynamic hysteresis function of arbitrary order is constructed. The nonlinear hysteresis is described with two parameters. Applying the hysteresis function leads to a nonlinear wave equation which is then solved for the longitudinal vibration of the bar using a perturbation method. The leading-order solution provides the strain-dependent resonance frequency and damping factor which are the two quantities measured in the nonlinear resonance ultrasound spectroscopy (NRUS). It is shown that the resonance frequency shift and damping increment hold, in general, a power-law dependence on the strain amplitude and the conventional linear dependence is a special case for the quadratic hysteresis. The derived formula is applied to existing data from bending and torsional NRUS-type experiments where the conventional linear fit appears to be clearly inadequate. Experimental resonance frequency shift data are fitted to determine the two hysteresis parameters, both of which vary with the changes in the material state. It is shown that the nonlinear damping ratio is a more general measure of the energy dissipation due to the increasing hysteresis and thus can be taken as a damage index. Consequently, this paper proposes a general procedure to analyze NRUS data for a wider range of materials. The present analysis is valid up to the yield strain which is sufficient to cover the strain amplitudes used in NRUS measurements.

Investigating the impact of extreme weather events and related indicators on cardiometabolic multimorbidity

BackgroundThe impact of weather on human health has been proven, but the impact of extreme weather events on cardiometabolic multimorbidity (CMM) needs to be urgently explored.ObjectivesInvestigating the impact of extreme temperature, relative humidity (RH), and laboratory testing parameters at admission on adverse events in CMM hospitalizations.DesignsTime-stratified case-crossover design.MethodsA distributional lag nonlinear model with a time-stratified case-crossover design was used to explore the nonlinear lagged association between environmental factors and CMM. Subsequently, unbalanced data were processed by 1:2 propensity score matching (PSM) and conditional logistic regression was employed to analyze the association between laboratory indicators and unplanned readmissions for CMM. Finally, the previously identified environmental factors and relevant laboratory indicators were incorporated into different machine learning models to predict the risk of unplanned readmission for CMM.ResultsThere are nonlinear associations and hysteresis effects between temperature, RH and hospital admissions for a variety of CMM. In addition, the risk of admission is higher under low temperature and high RH conditions with the addition of particulate matter (PM, PM2.5 and PM10) and O3_8h. The risk is greater for females and adults aged 65 and older. Compared with first quartile (Q1), the fourth quartile (Q4) had a higher association between serum calcium (HR = 1.3632, 95% CI: 1.0732 ~ 1.7334), serum creatinine (HR = 1.7987, 95% CI: 1.3528 ~ 2.3958), fasting plasma glucose (HR = 1.2579, 95% CI: 1.0839 ~ 1.4770), aspartate aminotransferase/ alanine aminotransferase ratio (HR = 2.3131, 95% CI: 1.9844 ~ 2.6418), alanine aminotransferase (HR = 1.7687, 95% CI: 1.2388 ~ 2.2986), and gamma-glutamyltransferase (HR = 1.4951, 95% CI: 1.2551 ~ 1.7351) were independently and positively associated with unplanned readmission for CMM. However, serum total bilirubin and High-Density Lipoprotein (HDL) showed negative correlations. After incorporating environmental factors and their lagged terms, eXtreme Gradient Boosting (XGBoost) demonstrated a more prominent predictive performance for unplanned readmission of CMM patients, with an average area under the receiver operating characteristic curve (AUC) of 0.767 (95% CI:0.7486 ~ 0.7854).ConclusionsExtreme cold or wet weather is linked to worsened adverse health effects in female patients with CMM and in individuals aged 65 years and older. Moreover, meteorologic factors and environmental pollutants may elevate the likelihood of unplanned readmissions for CMM.

Adaptive quantized tracking control for switched nonlinear systems with hysteresis nonlinearity using a novel predefined‐time stability criterion

AbstractThis article investigates the adaptive tracking control problem for switched nonlinear systems with input quantization and hysteresis nonlinearity. First, the hysteresis nonlinear phenomenon is considered and the Bouc–Wen hysteresis model is employed to address the complexities of controller design. Considering the time‐sampling mechanism may lead to the wastage of communication resources, a hysteresis quantizer is introduced to address this issue. Additionally, a command filter is constructed to relieve complexity explosion issues encountered during the backstepping process. Subsequently, compared with the conventional predefined‐time lemma, a novel predefined‐time lemma is proposed which can effectively adjust system performance even if the predefined‐time parameter is determined. In this case, a novel adaptive predefined‐time control scheme is devised by considering hysteresis properties and input quantization via the application of backstepping, which can track the reference signals within the predefined‐time frame. Finally, the flexibility and effectiveness of the proposed strategy are elaborated through numerical and practical examples.

Development of enhanced force models to analyze the nonlinear hysteresis response of miniaturized pneumatic artificial muscles

Miniaturized pneumatic artificial muscles (MPAMs), designed to replicate natural muscle actuation, offer unique attributes such as a high power-to-weight ratio, flexibility, easy integration, and compactness, making them favourable for many applications. The present paper aims at the development of an accurate semi-analytical force model considering the effect of the bladder material and friction terms to predict the nonlinear force-deformation response of MPAMs during contraction and expansion cycles. Existing force models for MPAMs exhibit limitations to accurately capturing the force-deformation behaviours due to several simplification factors. This study enhances these models by integrating correction terms to accurately address the nonlinearity and frictional effects exhibited by MPAMs. An analysis of the hysteresis loops resulting from the cyclic loading and unloading of MPAMs under specific pressures is undertaken to compare different methodologies in order to determine the most accurate correction terms. To investigate the nonlinear behaviour of MPAMs, the stress-strain relationship of the bladder material and results from force-deformation experimental tests on the entire actuator are considered and for the effect of friction term, theoretical and empirical approaches are investigated. Results suggest that the theoretical force model based on analytical and empirical friction forces, respectively, slightly overestimates and underestimates the force experienced by MPAMs during contraction while slightly underestimate and overestimates during expansion, respectively. A comparative analysis between MPAMs featuring Ecoflex-50 silicone and Ecoflex30 + PDMS mixture as bladder materials has also been conducted to further investigate the effect of bladder materials on their force and contraction outputs under inlet pressures ranging from 0 kPa to 300 kPa. It is shown that the MPAM feauting Ecoflex-50 bladder, exhibits lower dead-band pressure and an overall reduced blocked force in comparison to MPAM with bladder made of Ecoflex30 + PDMS while exhibiting a substantially enhanced free contraction capacity.