A Hybrid Compensation Scheme for the Input Rate-Dependent Hysteresis of the Piezoelectric Ceramic Actuators

A hybrid compensation scheme for piezoelectric ceramic actuators(PEAs)is proposed.In the hybrid compensation scheme,the input rate-dependent hysteresis characteristics of the PEAs are compensated.The feedforward controller is a novel input rate-dependent neural network hysteresis inverse model,while the feedback controller is a proportion integration differentiation(PID)controller.In the proposed inverse model,an input ratedependent auxiliary inverse operator(RAIO)and output of the hysteresis construct the expanded input space(EIS)of the inverse model which transforms the hysteresis inverse with multi-valued mapping into single-valued mapping,and the wiping-out,rate-dependent and continuous properties of the RAIO are analyzed in theories.Based on the EIS method,a hysteresis neural network inverse model,namely the dynamic back propagation neural network(DBPNN)model,is established.Moreover,a hybrid compensation scheme for the PEAs is designed to compensate for the hysteresis.Finally,the proposed method,the conventional PID controller and the hybrid controller with the modified input rate-dependent Prandtl-Ishlinskii(MRPI)model are all applied in the experimental platform.Experimental results show that the proposed method has obvious superiorities in the performance of the system.

Modeling and H_∞ Robust Control of a Smart Structure with Rate-dependent Hysteresis Nonlinearity

The performance of smart structures in trajectory tracking under sub-micron level is hindered by the rate-dependent hysteresis nonlinearity.In this paper,a Hammerstein-like model based on the support vector machines(SVM)is proposed to capture the rate-dependent hysteresis nonlinearity.We show that it is possible to construct a unique dynamic model in a given frequency range for a rate-dependent hysteresis system using the sinusoidal scanning signals as the training set of signals for the linear dynamic subsystem of the Hammerstein-like model.Subsequently,a two-degree-of-freedom(2DOF)H∞robust control scheme for the ratedependent hysteresis nonlinearity is implemented on a smart structure with a piezoelectric actuator(PEA)for real-time precision trajectory tracking.Simulations and experiments on the structure verify both the efectiveness and the practicality of the proposed modeling and control methods.

Rate-Dependent Hysteresis Modeling and Compensation of Piezo-Driven Flexure-Based Mechanism

Updating parameters according to the driving rate of input, the rate-dependent Prandtl-Ishlinskii （PI） model is widely used in hysteresis modeling and compensation. In order to improve the modeling accuracy, two PI models identified at low and high driving rates separately are incorporated through a combination law. For the piezo- driven flexure-based mechanism, the very low damping ratio makes it easy to excite the structural vibration. As a re- suit, the measured hysteresis loop is greatly distorted and the modeling accuracy of the identified P1 model is signifi- cantly affected. In this paper, a novel time-efficient parameter identification method which utilizes the superimposed sinusoidal signals as the control input is proposed. This method effectively avoids the excitation of the structural vibra- tion. In addition, as the driving rate of the superimposed sinusoidal signals covers a wide range, all the coefficients required for modeling the rate-dependence can be identified through only one set of experimental data. Hysteresis modeling and trajectory tracking experiments were performed on a 2-DOF piezo-driven flexure-based mechanism. The experimental results show that the combined hysteresis model maintains the modeling accuracy over the entire work- ing range of the flexure-based mechanism. The mechanism＇s hysteresis is significantly suppressed by the use of the inverse PI model as the feedforward controller; and better result is achieved when a feedback loop is also incorporated. The tracking performance of the flexure-based mechanism is greatly improved.

Operator-Based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems With PI Hysteresis

In this paper, operator based robust nonlinear control for single-input single-output(SISO) and multi-input multi-output(MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii(PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively.In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized.Finally, the effectiveness of the proposed method is confirmed by numerical simulations.

Coupled large earthquakes in the Baikal rift system: Response to bifurcations in nonlinear resonance hysteresis

The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation.The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures （RAS）.The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes,proximal in time but distant in space,may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors.The space-time distribution of coupled MLH ＞ 5.5 events has been stable for the period of instrumental seismicity,with the largest events occurring in pairs,one shortly after another,on two ends of the rift system and with couples of smaller events in the central part of the rift.The event couples appear as peaks of earthquake ‘migration＇ rate with an approximately decadal periodicity.Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation.The new knowledge,with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis,may be of theoretical and practical value for earthquake prediction issues.Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region,i.e.,there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.

Robust Stability of Nonlinear Plants with a Non-symmetric Prandtl-Ishlinskii Hysteresis Model

In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.

A novel extended Tsypkin criterion for discrete-time descriptor systems with ferromagnetic hysteresis nonlinear physical phenomenon

This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity conditions of hysteresis operator, that is the input-output relation of the transformed operator is passive. The bound condition of the solution of the ferromagnetic hysteresis model is given. Through the framework of loop transformation, an augmented discrete-time descriptor system model is established for the stability analysis. A new extended Tsypkin criterion for the absolute stability of discrete-time descriptor systems with hysteresis is presented based on the linear matrix inequalities technique. A numerical example is given to illustrate the effectiveness of the extended criterion.

Active control for a flexible beam with nonlinear hysteresis and time delay

A new active control method is presented to attenuate vibrations of a flexible beam with nonlinear hysteresis and time delay. The nonlinear and hysteretic behavior of the system is illustrated by the Bouc-Wen model. By specific transformation and augmentation of state parameters, we can convert the motion equation of the system with explicit time delay to the standard state space representation without any explicit time delay. Then the instantaneous optimal control method and Runge-Kutta method in fourth-order are applied to the controller design with time delay. Finally, in order to verify the effectivity of the time-delay controller proposed, numerical simulations are implemented. It is indicated by the simulation results that the control performance will deteriorate if neglect the time delay in process of the controller design and proposed time delay controller works well with both small and large time delay problems.

Empirical modeling of nonlinear and hysteresis characteristics of the shock absorber

An empirical hybrid shock absorber model capable of capturing nonlinear and hysteresis characteristics of shock absorbers is built.The nonlinear characteristics are modeled by algebraic function and the hysteresis effects between shock force and shock velocity are modeled by neural network.To develop the empirical hybrid shock absorber model,a Mazda CX-7 front shock absorber is tested by a displacement-controlled hydraulic shock absorber testing machine.The hybrid shock absorber model is built and validated using the experimental shock absorber data.The RMS value for the hybrid shock absorber model is 60.28N at the velocity range from-1.3m/s to 1.3m/s.

Bifurcation and chaos characteristics of hysteresis vibration system of giant magnetostrictive actuator

Chaotic motion and quasi-periodic motion are two common forms of instability in the giant magnetostrictive actuator(GMA).Therefore,in the present study we intend to investigate the influences of the system damping coefficient,system stiffness coefficient,disc spring cubic stiffness factor,and the excitation force and frequency on the output stability and the hysteresis vibration of the GMA.In this regard,the nonlinear piezomagnetic equation,Jiles-Atherton hysteresis model,quadratic domain rotation model,and the GMA structural dynamics are used to establish the mathematical model of the hysteresis vibration system of the GMA.Moreover,the multi-scale method and the singularity theory are used to determine the eo-dimensional two-bifurcation characteristics of the system.Then,the output response of the system is simulated to determine the variation range of each parameter when chaos is imposed.Finally,the fourth-order Runge-Kutta method is used to obtain the time domain waveform,phase portrait and Poincare mapping diagrams of the system.Subsequently,the obtained three graphs are analyzed.The obtained results show that when the system output is stable,the variation range of each parameter can be determined.Moreover,the stability interval of system damping coefficient,system stiffness coefficient,and the coefficient of the cubic stiffness term of the disc spring are obtained.Furthermore,the stability interval of the exciting force and the excitation frequency are determined.

Structural-Identification Aspects of Decision-Making in Systems with Bouc-Wen Hysteresis

Considering the structural analysis problem of systems properties with Bouc-Wen hysteresis (BWH), various approaches are proposed for the identification of BWH parameters. The applied methods and algorithms are based on the design of parametric models and consider a priori information and the results of data analysis. Structural changes in the BWH form a priori. Methods for the Bouc-Wen model (BWM) identification and its structure estimation are not considered under uncertainty. The study’s purpose is the analysis the structural problems of the Bouc-Wen hysteresis identification. The analysis base is the application of geometric frameworks (GF) under uncertainty. Methods for adaptive estimation parameters and structural of BWM were proposed. The adaptive system stability is proved based on vector Lyapunov functions. An approach is proposed to estimate the identifiability and structure of the system with BWH. The method for estimating the identifiability degree based on the analysis of GF is considered. BWM modifications are proposed to guarantee the system’s stability and simplify its description.

Modeling and identification of magnetostrictive hysteresis with a modified rate-independent Prandtl-Ishlinskii model

This paper presents a modified rate-independent Prandtl-Ishlinskii （MRIPI） model based on the Fermi-Dirac distri- bution for the asymmetric hysteresis description of magnetostrictive actuators. Generally, the classical Prandtl-Ishlinskii （CPI） model can hardly describe the asymmetric hysteresis. To overcome this limitation, various complex operators have been developed to replace the classical operator. In this study, the proposed MRIPI model maintains the classical operator while a modified input function based on the Fermi-Dirac distribution is presented to replace the classical input function. With this method, the MRIPI model can describe the asymmetric hysteresis of magnetostrictive actuators in a relatively simple mathematic format and has fewer parameters to be identified. A velocity-based sine cosine algorithm （VSCA） is also proposed for the parameter identification of the MRIPI model. To verify the validity of the MRIPI model, experiments are performed and the results are compared with those of the existing modeling methods.

The effects of cold region meteorology and specific environment on the number of hospital admissions for chronic kidney disease:An investigate with a distributed lag nonlinear model

Objective:To explore the effects of daily mean temperature(°C),average daily air pressure(hPa),humidity(%),wind speed(m/s),particulate matter(PM)2.5(μg/m3)and PM10(μg/m3)on the admission rate of chronic kidney disease(CKD)patients admitted to the Second Affiliated Hospital of Harbin Medical University in Harbin and to identify the indexes and lag days that impose the most critical influence.Methods:The R language Distributed Lag Nonlinear Model(DLNM),Excel,and SPSS were used to analyze the disease and meteorological data of Harbin from 01 January 2010 to 31 December 2019 according to the inclusion and exclusion criteria.Results:Meteorological factors and air pollution influence the number of hospitalizations of CKD to vary degrees in cold regions,and differ in persistence or delay.Non-optimal temperature increases the risk of admission of CKD,high temperature increases the risk of obstructive kidney disease,and low temperature increases the risk of other major types of chronic kidney disease.The greater the temperature difference is,the higher its contribution is to the risk.The non-optimal wind speed and non-optimal atmospheric pressure are associated with increased hospital admissions.PM2.5 concentrations above 40μg/m3 have a negative impact on the results.Conclusion:Cold region meteorology and specific environment do have an impact on the number of hospital admissions for chronic kidney disease,and we can apply DLMN to describe the analysis.

腐蚀疲劳交替下2A12-T4航空铝合金的寿命分析研究

基于飞机服役期间经历“地面腐蚀与空中疲劳”的交替损伤模式,考虑载荷间的相互作用,研究了航空铝合金2A12-T4在预腐蚀与“腐蚀+疲劳”交替模式下疲劳寿命的退化与损伤累积规律。同级加载条件下提出利用腐蚀疲劳耦合损伤指数和迟滞载荷用来描述考虑交替腐蚀疲劳损伤模式,用各级疲劳损伤间的相互影响及腐蚀损伤与疲劳损伤在服役工作期间的耦合作用来描述腐蚀、疲劳间的相互促进、加速劣化的现象。基于损伤力学和非线性累积理论,考虑载腐蚀疲劳耦合指数与迟滞载荷对传统的Miner线性累积损伤理论进行修正。建立了飞机结构材料的寿命计算模型,并将模型计算结果与试验结果进行对比验证。确定了腐蚀实验中的腐蚀耦合损伤,并利用低载锻炼效应理论得出均匀分布的迟滞载荷。计算结果表明,本文提出的寿命计算模型的结果与实验结果比较吻合。

磁流变阻尼器Bingham力学模型改进及参数辨识

磁流变阻尼器不仅具有阻尼快速响应、良好的温度稳定性、内部结构简单等优势,而且可以通过调节控制电流使阻尼器的出力值连续变化,实现阻尼力可控。由于磁流变阻尼器阻尼特性与内部磁流变液的磁流变效应有关,具体表现非常复杂,现有力学模型目精度不足,无法精确描述磁流变阻尼器的阻尼特性。在磁流变阻尼器力学性能测试基础上,应用分段拟合函数方法同时结合反正切函数模型改进模型,并辨识改进后力学模型中各参数。将改进后的Bingham模型与实际测试出力值进行对比,结果表明改进后的Bingham模型能够很好地解决Bingham力学模型在非线性滞回阶段出力值曲线与实际测试数据不符的问题,改进后模型总体出力值曲线与阻尼器实际出力值基本相同,模型精度大幅提升。此种改进方法为磁流变阻尼器建立高精度力学模型提供参考。

压电平台高精度自适应分数阶滑模跟踪控制

为了实现压电平台高精度指令跟踪控制,针对其存在的严重迟滞问题,本文提出了一种自适应分数阶滑模跟踪控制方法。首先,根据Duhem模型结构将分数阶算子和自适应律引入到滑模面的设计过程中,增加滑模面的自由度可变性并实现了滑模面参数的自适应调节;其次,利用不确定和干扰估计方法代替传统的滑模控制器切换项,解决了滑模控制器存在的抖振问题并提高了控制器的鲁棒性。最后,通过压电平台指令跟踪控制实验结果表明:相较于PID和传统的滑模控制方法,提出的自适应分数阶滑模控制器的指令跟踪误差减小了80%以上,在50 Hz参考指令信号下自适应分数阶滑模控制器将压电平台的平均跟踪误差降低到0.41μm。因此,自适应分数阶滑模控制方法具有更加优越的跟踪性能。

Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis

A new modeling approach for nonlinear systems with rate-dependent hysteresis is proposed. The approach is used for the modeling of the giant magnetostrictive actuator, which has the rate-dependent nonlinear property. The models built are simpler than the existed approaches. Compared with the experiment result, the model built can well describe the hysteresis nonlinear of the actuator for input signals with complex frequency. An adaptive direct inverse control approach is proposed based on the fuzzy tree model and inverse learning and special learning that are used in neural network broadly. In this approach, the inverse model of the plant is identified to be the initial controller firstly. Then, the inverse model is connected with the plant in series and the linear parameters of the controller are adjusted using the least mean square algorithm by on-line manner. The direct inverse control approach based on the fuzzy tree model is applied on the tracing control of the actuator by simulation. The simulation results show the correctness of the approach.

球型钢丝绳隔振器非对称迟滞模型

针对球型钢丝绳隔振器的非线性刚度和阻尼特性导致迟滞模型表征困难的问题,提出了非线性弹性因子和修正因子改进的归一化Bouc-Wen迟滞模型,结合Simulink仿真完善改进的迟滞模型,采用最小二乘法和遗传算法相结合的方法对改进模型进行参数识别。通过数值仿真绘制GGQ25-62L型球型钢丝绳隔振器在不同工况的迟滞环,并和实验数据进行对比。结果表明,参数识别方法准确可靠,实验数据和理论计算曲线具有较强的一致性,该模型能够有效地描述隔振器的动态特性。

基于粒子群算法的钢丝网垫隔振器参数识别

目的 证明粒子群优化算法对钢丝网垫隔振器参数识别的有效性和准确性。探究不同的加载条件对钢丝网垫元件力学性能的影响。方法 对钢丝网垫元件进行正弦加载试验,获取试验响应数据。以双折线模型对钢丝网垫的力学性能进行描述,建立隔振器的参数识别方程,应用粒子群算法和试验响应数据识别出模型参数,并研究不同加载条件下识别参数的变化规律。结果 用识别出的参数计算绘制的迟滞回线和试验结果吻合较好。改变激励幅值和频率,钢丝网垫的一次刚度、三次刚度、滑移刚度、等效阻尼均发生规律性变化,而改变钢丝网垫所受静载,曲线变化极为微小。结论 研究证明了粒子群优化算法对钢丝网垫隔振器参数识别的有效性和准确性,是一种有工程应用价值的参数识别方法。

空气舵绕轴转动动力学响应分析

针对空气舵绕舵轴转动动力学模型,考虑含转动间隙、Stribeck效应的干摩擦模型,建立含间隙、干摩擦空气舵转动受迫振动方程,应用平均法解析分析转动方向幅频特性,研究不同摩擦力矩系数及外激励频率对绕轴振动幅频响应的影响。结果表明:外激励频率变化时,绕轴振动幅频曲线呈现软硬不同的迟滞非线性特性,频域出现多解频带,且频域多解频带随摩擦力矩系数的增大而增大。