Identification of a class of Wiener and Hammerstein-type nonlinear processes with monotonic static gains

In this paper a non-iterative approach to identifying Wiener and Hammerstein models, including model structure and parameters, is proposed. A single symmetrical relay test is conducted to determine the structure and then the parameters of the block-oriented nonlinear model possessing a static nonlinearity and a linear process in cascade. The static nonlinearity block is represented by a memoryless and monotonic function and the linear process by a second order transfer function model. A relay with hysteresis induces the limit cycle output signal and one cycle data of the output signal is used to identify the block-oriented nonlinear model. The proposed identification method is simple and gives better performance than previous methods for processes with static nonlinearity.     

Identification of multivariable nonlinear systems in the presence of colored noises using iterative hierarchical least squares algorithm

This paper presents an efficient method for identification of nonlinear Multi-Input Multi-Output (MIMO) systems in the presence of colored noises. The method studies the multivariable nonlinear Hammerstein and Wiener models, in which, the nonlinear memory-less block is approximated based on arbitrary vector-based basis functions. The linear time-invariant (LTI) block is modeled by an autoregressive moving average with exogenous (ARMAX) model which can effectively describe the moving average noises as well as the autoregressive and the exogenous dynamics. According to the multivariable nature of the system, a pseudo-linear-in-the-parameter model is obtained which includes two different kinds of unknown parameters, a vector and a matrix. Therefore, the standard least squares algorithm cannot be applied directly. To overcome this problem, a Hierarchical Least Squares Iterative (HLSI) algorithm is used to simultaneously estimate the vector and the matrix of unknown parameters as well as the noises. The efficiency of the proposed identification approaches are investigated through three nonlinear MIMO case studies.     

电静液作动器精细化建模和特性分析

电静液作动器（Electro-hydrostatic actuator,EHA）是电驱液传的执行机构,具有体积小、重量轻、功率密度高、可控性好、维护性好、集成度高、可靠性高等优势。传统EHA的线性建模方法通常忽视电机和泵的强非线性,这种建模方式过于保守,导致模型精度降低,影响高性能控制及性能预测的准确性。为处理传统建模方式的保守性问题,建立考虑伺服电机和泵非线性的精细化模型：通过MATLAB/SIMULINK建立时变、非线性、强耦合、多变量的永磁同步交流电机（Permanent magnet synchronous motor,PMSM）模型,通过AMESim建立含流量脉动和外泄漏的定量柱塞泵模型,完善了EHA仿真模型;改变系统参数进行MATLAB-AMESim机电液联合仿真,通过多种仿真工况的结果对比,分析EHA系统的典型特性,揭示了系统参数对控制器跟踪性能的影响。建立精细化模型进行特性分析,为EHA系统参数对控制性能的影响度分析提供了理论支撑和仿真验证手段。     

电液位置伺服系统模型辨识与非线性控制

针对电液伺服系统非线性、参数时变的特点,为提高系统的性能,首先介绍了电液位置伺服控制系统的组成与工作原理,讨论了系统的非线性数学模型,利用实时工作间(RTW)的半实物仿真环境和MATLAB系统辨识工具箱,对电液位置伺服系统进行了系统模型辨识及验证。在此基础上,以辨识得到的模型为控制对象提出了一种Bang-Bang与模糊PID非线性控制方案,与传统PID以及模糊PID控制方法进行了仿真比较。结果表明,采用Bang-Bang与模糊PID复合控制,在系统参数变化、外界扰动的影响下,系统的快速性提高,稳态误差得到消除,具有较好的动态鲁棒性能。     

Limit cycle analysis of active disturbance rejection control system with two nonlinearities

Introduction of nonlinearities to active disturbance rejection control algorithm might have high control efficiency in some situations, but makes the systems with complex nonlinearity. Limit cycle is a typical phenomenon that can be observed in the nonlinear systems, usually causing failure or danger of the systems. This paper approaches the problem of the existence of limit cycles of a second-order fast tool servo system using active disturbance rejection control algorithm with two fal nonlinearities. A frequency domain approach is presented by using describing function technique and transfer function representation to characterize the nonlinear system. The derivations of the describing functions for fal nonlinearities and treatment of two nonlinearities connected in series are given to facilitate the limit cycles analysis. The effects of the parameters of both the nonlinearity and the controller on the limit cycles are presented, indicating that the limit cycles caused by the nonlinearities can be easily suppressed if the parameters are chosen carefully. Simulations in the time domain are performed to assess the prediction accuracy based on the describing function.     

基于KP模型的气动肌肉迟滞建模方法

为了辨识气动肌肉运动过程中的迟滞非线性特性,在气动肌肉位移/气压迟滞特性实验的基础上,分别采用KP模型和多项式模型对其位移/气压迟滞展开了建模研究,并采用递推最小二乘法分别对两种模型中的未知参数进行了辨识,研究不同算子个数和多项式次数对模型建模精度的影响。参数辨识结果发现,KP模型拟合精度明显优于多项式模型,随着算子个数的增加,KP模型的精度显著提高,多项式模型的建模精度也随着多项式次数的增加而提高。     

基于粗糙集神经网络的非线性系统动态参数预测

为建立非线性系统辨识和预测模型,利用粗糙集和人工神经网络方法进行动态参数预测.考虑非线性系统中影响因子之间的高度非线性和不确定性,结合粗糙集和人工神经网络的优点,提出了一种动态参数预测的新方法.该方法充分考虑了学习样本的数据特性,简化了决策规则从而降低了网络拓扑结构规模,计算速度快,容错能力强,误差小,精度高.计算结果表明,该方法用于非线性系统动态参数分析是有效可行的.     

电液驱动3-UPS/S并联稳定平台的动力学参数辨识

以电液驱动并联稳定平台为研究对象,对平台惯性参数和驱动关节液压缸摩擦参数进行了基于实验的辨识研究。利用关键点旋量等效原则和虚功原理构建了平台惯性参数辨识模型,以五次多项式改进的傅里叶级数构造了激励轨迹,并进行了优化;基于液压缸摩擦力模型,分离出模型中固有的摩擦参数,建立了摩擦参数辨识模型,并规划了辨识轨迹。通过辨识实验得到了惯性参数及摩擦参数的辨识结果,利用任意轨迹实验对结果进行了验证。     

Time-frequency characterization of nonlinear normal modes and challenges in nonlinearity identification of dynamical systems

Presented here is a new time-frequency signal processing methodology based on Hilbert-Huang transform (HHT) and a new conjugate-pair decomposition (CPD) method for characterization of nonlinear normal modes and parametric identification of nonlinear multiple-degree-of-freedom dynamical systems. Different from short-time Fourier transform and wavelet transform, HHT uses the apparent time scales revealed by the signal's local maxima and minima to sequentially sift components of different time scales. Because HHT does not use pre-determined basis functions and function orthogonality for component extraction, it provides more accurate time-varying amplitudes and frequencies of extracted components for accurate estimation of system characteristics and nonlinearities. CPD uses adaptive local harmonics and function orthogonality to extract and track time-localized nonlinearity-distorted harmonics without the end effect that destroys the accuracy of HHT at the two data ends. For parametric identification, the method only needs to process one steady-state response (a free undamped modal vibration or a steady-state response to a harmonic excitation) and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. A nonlinear two-degree-of-freedom system is used to illustrate the concepts and characterization of nonlinear normal modes, vibration localization, and nonlinear modal coupling. Numerical simulations show that the proposed method can provide accurate time-frequency characterization of nonlinear normal modes and parametric identification of nonlinear dynamical systems. Moreover, results show that nonlinear modal coupling makes it impossible to decompose a general nonlinear response of a highly nonlinear system into nonlinear normal modes even if nonlinear normal modes exist in the system.     

含磁滞补偿的电液伺服系统预设性能跟踪控制

针对电液伺服系统普遍存在的参数不确定性、不确定非线性(磁滞、摩擦、外干扰等),提出一种基于自适应鲁棒控制的含磁滞补偿的预设性能跟踪控制策略。以阀控单出杆液压缸位置伺服系统为例,首先建立了含磁滞非线性的系统数学模型,然后通过定义预设性能函数,实现了对跟踪误差收敛速率、最大超调量和稳态精度的预先规划,基于规划后的转换误差设计了自适应鲁棒控制器,并提高了稳态和瞬态跟踪性能。仿真对比结果表明：该控制策略可以减小磁滞对系统跟踪精度的影响,提高跟踪误差的收敛速度,减小最大超调量,最终实现优良的跟踪性能。     

液压挖掘臂关节伺服系统非线性动态特征研究

为有效分析挖掘臂关节伺服控制系统,提高控制精度,通过机理建模分析了系统存在的非线性特性——比例阀死区、阀控非对称液压缸动态特性不对称特性、液压缸非线性摩擦力、非线性液压弹簧力及挖掘臂关节非线性动力学。通过实验验证了系统中各项非线性特性对其控制性能的影响。结果表明,以上几种非线性特性对系统动态响应均存在不利影响。     

Identification of nonlinear boundary effects using nonlinear normal modes

Local nonlinear effects due to micro-slip/slap introduced in boundaries of structures have dominant influence on their lower modal model. This paper studies these effects by experimentally observing the behavior of a clamped–free beam structure with local nonlinearities due to micro-slip at the clamped end. The structure is excited near one of its resonance frequencies and recorded responses are employed to identify the nonlinear effects at the boundary. The nonlinear response of structure is defined using an amplitude-dependent nonlinear normal mode identified from measured responses. A new method for reconstructing nonlinear normal mode is represented in this paper by relating the nonlinear normal mode to the clamped end displacement-dependent stiffness parameters using an eigensensitivity analysis. Solution of obtained equations results equivalent stiffness models at different vibration amplitudes and the corresponding nonlinear normal mode is identified. The approach results nonlinear modes with efficient capabilities in predicting dynamical behavior of the structure at different loading conditions. To evaluate the efficiency of the identified model, the structure is excited at higher excitation load levels than those employed in identification procedures and the observed responses are compared with the predictions of the model at the corresponding input force levels. The predictions are in good agreement with the observed behavior indicating success of identification procedure in capturing the physical merits involve in the boundary local nonlinearities.     

液压振动台非线性摩擦力测量与参数辨识

电液伺服振动试验系统低速和换向时的非线性摩擦力测量和补偿是提高运输环境试验和地震模拟试验等控制精度的重要途径。为了定量获取液压振动台的非线性摩擦力,基于Stribeck效应建立了改进的电液伺服振动试验系统非线性摩擦力理论模型,并结合液压振动台的力平衡方程建立了非线性摩擦力待辨识参数的目标函数。提出一种基于位移闭环控制的简便方法对不同速度下的液压振动台油缸压力差进行测量,得到振动台液压缸与活塞杆之间的摩擦力随速度变化的数值规律。采用基于拟随机序列的混合遗传算法对非线性摩擦力理论模型的4个参数进行了辨识。试验结果证明了本研究方法的可行性,为液压振动试验系统加速度波形失真补偿提供了一定参考。     

Nonlinear vibrational response of a single edge cracked beam

The nonlinear vibrational response of a breathing cracked beam was investigated. The study was done by using a new crack stiffness model to examine some of the nonlinear behaviors of a cantilever beam with a breathing crack. The quadratic polynomial stiffness equation of the cracked beam was derived based on the hypothesis that the breathing process of a crack depends on the vibration magnitude. The Galerkin method combined with the stiffness equation was used to simplify the cracked beam into a Single-degree-of-freedom (SDOF) lumped system with nonlinear terms. The multi scale method was adopted to analyze the nonlinear amplitude frequency response of the beam. The applicability of the stiffness model was discussed and parameter sensitivity studies on the dynamic response were carried out by the SDOF model for a cantilever beam. Results indicate that the new stiffness model provides an efficient tool to study the vibrational nonlinearities introuduced by the breathing crack. Therefore, it might be used to develop a nonlinear identification method of a crack in a beam.     

基于Hammerstein模型的GMAW-P焊接熔深自适应预测控制

针对脉冲熔化极气体保护焊(Pulsed gas metal arc welding,GMAW-P)过程中焊接熔深的实时控制,使用脉冲峰值期间的电压变化幅值(ΔU)来表征焊接熔深变化,并且通过测量和控制ΔU的大小来间接达到熔深控制的目的。建立了以ΔU为输出和脉冲基值电流为输入的单输入单输出熔深控制系统。系统输入输出之间的静态关系模型显示该熔深控制系统具有一定非线性,因此,采用加入干扰的Hammerstein模型描述该非线性系统。在基于该Hammerstein模型的经典预测控制算法基础上,在控制过程中加入递推最小二乘法在线辨识模型参数,从而实现焊接熔深自适应控制。控制算法仿真和实时焊接试验表明该熔深控制算法能够较好地实现GMAW-P焊接过程中的熔深控制。变散热试验结果验证了该控制算法的有效性和适应性。     

一类非线性系统的广义预测控制研究

提出一种针对双线性Hamm erste in模型的预测控制策略。该策略将双线性Hamm erste in模型中的无记忆非线性静态增益环节,改进成易于由中间变量求取控制量的环节,避免求解高阶方程根的困难,又对双线性环节采用双线性系统的广义预测控制。避免解非线性优化问题,使得到的中间变量的表达式具有解析形式。由于引入广义预测控制中多步预测的思想,抗噪声的能力显著提高。仿真结果验证了该策略的有效性。     

Parameter identification of the fatigue-testing rig

In this paper the dynamic parameter identification of the novel fatigue-testing rig is presented. The applied identification method assumes a priori a simple dynamical model for which parameters are identified through free and forced vibration tests. The rig is comprised of two base excited oscillators providing the dynamic excitation for a fatigue sample and two pneumatic actuators preventing a loss of contact between the oscillators and the sample. The actuators introduce strong nonlinearities. All parameters of the system apart from the pneumatic actuators identified through the free vibration tests using the linear model were in a good agreement with those obtained by the frequency analysis. Two models, a linear and the nonlinear with Coulomb friction, were dynamically interrogated by a random excitation. It was shown that the stiffness coefficient a, increases linearly with the pressure in the pneumatic cylinders, and the viscous damping coefficient b increases quadratically with the air pressure in the pneumatic cylinders. The predicted responses for the linear and nonlinear models correlate well with the experimental data.     

Digital Servo Control of a Robotic Excavator

An electro-hydraulic control system is designed and implemented for a robotic excavator known as the Lancaster University Computerised and Intelligent Excavator (LUCIE). The excavator is being developed to autonomously dig trenches without human intervention. Since the behavior of the excavator arm is dominated by the nonlinear dynamics of the hydraulic actuators and by the large and unpredictable external disturbances when digging, it is difficult to provide adequate accurate, quick and smooth movement under traditional control methodology, e.g., PI/PID, which is comparable with that of an average human operator. The data-based dynamic models are developed utilizing the simplified refined instrumental variable (SRIV) identification algorithm to precisely describe the nonlinear dynamical behaviour of the electro-hydraulic actuation system. Based on data-based model and proportional-integral-plus (PIP) methodology, which is a non-minimal state space method of control system design based on the true digital control (TDC) system design philosophy, a novel control system is introduced to drive the excavator arm accurately, quickly and smoothly along the desired path. The performance of simulation and field tests which drive the bucket along straight lines beth demonstrate the feasibility and validity of the proposed control scheme.     

Prediction and simulation errors in parameter estimation for nonlinear systems

This article compares the pros and cons of using prediction error and simulation error to define cost functions for parameter estimation in the context of nonlinear system identification. To avoid being influenced by estimators of the least squares family (e.g. prediction error methods), and in order to be able to solve non-convex optimisation problems (e.g. minimisation of some norm of the free-run simulation error), evolutionary algorithms were used. Simulated examples which include polynomial, rational and neural network models are discussed. Our results—obtained using different model classes—show that, in general the use of simulation error is preferable to prediction error. An interesting exception to this rule seems to be the equation error case when the model structure includes the true model. In the case of error-in-variables, although parameter estimation is biased in both cases, the algorithm based on simulation error is more robust.     

压电执行器动态迟滞建模与LQG最优控制器设计

为提高空间天文望远镜稳像系统中压电快摆镜(Fast Steering Mirror,FSM)的动态性能,对压电执行器(Piezoelectric Actuator,PZT)动态迟滞补偿和控制进行研究。鉴于基于广义Play算子Prandtl-Ishlinskii(PI)模型的求逆复杂性和迟滞曲线的非对称性,构造一种基于广义Stop算子PI逆模型来补偿压电执行器迟滞非线性。采用Hammerstein模型对压电执行器动态迟滞特性进行建模,以广义PI模型和自回归遍历模型(Auto-regressive Exogenous Model,ARX)分别表征Hammerstein迟滞模型中的静态非线性和率相关性,并针对迟滞率相关模型不确定性问题,提出一种前馈补偿和线性二次型Gauss最优控制算法(Linear Quadratic Gaussian,LQG)相结合的复合控制策略。利用自适应差分进化算法(Adaptive Differential Evolution algorithm,ADE)辨识和整定模型及控制器参数。实验结果表明:该动态迟滞模型能够有效描述1～100Hz频率范围内压电执行器迟滞曲线,拟合均方根误差为0.077 1μm(@1 Hz)～0.512 3μm(@100Hz),相对误差为0.31%(@1Hz)～2.09%(@100Hz);实时跟踪幅值为24.5μm的变频目标位移,LQG控制算法的跟踪精度相比于直接前馈控制和PID控制分别提高48.6%和27.02%。