压电陶瓷执行器的非光滑三明治模型辨识与内模控制

压电陶瓷执行器中含有非光滑、多值映射、频率依赖的非线性迟滞特性,然而在实际应用中,压电器件的输入输出信号无法直接测量,常规方法难以进行有效的辨识和控制.本文采用三明治模型来精确描述实际对象,并提出一种基于退化激励信号的两步辨识法解决三明治迟滞模型的辨识问题.最后,基于已辨识的三明治模型,设计一个内模控制器,解决压电陶瓷执行器的精密轨迹控制问题.实验结果表明所提出的辨识和控制方案取得了令人满意的结果.     

大工业过程的稳态模型分散辨识及其强一致性分析

针对动态线性大工业过程,提出了获得其可分稳态模型强一致性估计的分散辨识方法.该方法仅使用设定点的阶跃信号作为输入激励信号,并且每个子过程的输入输出稳态模型辨识是在相应的局部单元完成的,因而大大减少了对过程的干扰和信息的交换量.所提出的方法简洁,并且辨识精度高,仿真结果说明了该辨识方法的有效性和实用性.     

基于GA和单纯形法的直流电机参数辨识

提出一种基于优化算法的非线性系统参数辨识的方法.针对直流电机非线性摩擦力和饱和特性,建立直流电机的非线性模型.利用遗传算法的全局寻优特性和单纯形法快速的收敛性,通过获取充分激励的实际系统运行的输入输出数据,辨识出包括非线性摩擦力在内的直流电机所有的8个模型参数.获取系统实际运行的输入输出数据,分别验证电机运行于死区、饱和区和线性区时,模型辨识的精度.这种方法可以方便地应用于其他非线性系统参数辨识中.     

基于稀疏表示的系统辨识方法

基于信号的稀疏表示理论提出一种线性时不变系统辨识方法.该方法利用线性调频信号作为线性时不变系统激励输入信号,在利用传统方法进行系统辨识前利用稀疏分解算法对系统输出信号进行噪声处理.线性调频信号具有较好的时频聚集特性,线性时不变系统的输出也将具有很好的时频特征,利用基于Gabor字典的稀疏分解将能有效地提取输出信号中的有效分量,滤除其中的噪声成分,提高系统辨识的精度.仿真实验表明,本文提出的方法在低信噪比情况下,辨识效果好于传统方法.     

基于偏差补偿递推最小二乘的Hammerstein-Wiener模型辨识

许多实际系统可以表示成一种中间为线性动态环节、输入输出端为非线性静态环节的Hammerstein-Wiener模型. 针对含过程噪声的Hammerstein-Wiener模型, 提出一种改进在线两阶段辨识方法. 第一步采用偏差补偿递推最小二乘法在线辨识含原系统参数乘积项的参数向量. 通过在递推最小二乘算法中引入一个修正项, 补偿过程噪声引起的估计偏差. 第二步采用基于张量积逼近的奇异值分解法分离出原系统各参数的值. 通过引入两个矩阵的张量积逼近加权最小二乘的权系数, 提高参数分离精度. 理论分析和计算机仿真验证了本文方法的有效性.     

一种频率依赖性迟滞的神经网络内模控制

针对压电陶瓷等智能材料存在的依赖输入频率的迟滞非线性问题,采用BP神经网络对迟滞非线性进行辨识,并通过内模控制方案来对其进行控制.在迟滞的建模上,构建了一种静态迟滞非线性环节串联一个对输入频率敏感的线性动态环节组成的Hammerstein模型.在此基础上,得出Hammerstein模型的逆模型,并通过构造的正、逆模型进行内模控制.实验结果说明,提出的建模方法与内模控制方案是有效的.     

线性时变反馈系统的状态空间模型和模态参数递推辨识

针对闭环系统中时变状态空间模型和模态参数的辨识问题, 提出一种递推辨识格式, 将这种格式与递推子空间方法结合, 得到一种辨识方法. 该方法通过重建输入输出数据之间的关系, 递推辨识得到闭环系统的时变状态空间模型和模态参数. 算例研究了系统在模态参数突变和周期变化两种情况下的辨识问题, 仿真结果表明, 所提出算法能有效辨识线性时变反馈系统的状态空间模型和模态参数.

     

基于坐标变换和仿射映射辨识迟滞非线性模型

运用坐标变换方法和仿射映射的有关原理,对迟滞系统的输入信号进行变换映射.利用集合理论证明了变换后,迟滞的输入输出集合是双射的,从而对在光滑周期信号作用下的一类迟滞非线性进行建模.不仅建立了动态迟滞模型,而且也建立了相应的动态逆模型.仿真试验验证了所提出方法的有效性.     

基于一种新模糊模型的非线性系统模糊辨识

提出一种基于新的模糊模型和加权递推最小二乘算法 (WRLSA)的非线性系统模糊辨识方法.新型的具有插值能力的模糊系统可以通过学习从输入输出采样数据中提取MISO系统模糊规则,它继承了Sugeno模型及其变化形式的许多优点.采用相应的模糊隶属函数,使得被辨识的模型可用若干局部线性模型来表示,然后利用WRLSA拟合这些线性模型.给出了详细的模糊辨识算法,为了验证该辨识方法的有效性,还给出了对熟知的Box-Jenkins数据的辨识结果.     

MPT系列微位移定位系统的辨识与控制

微位移精密定位系统中的压电陶瓷元器件具有非光滑特性,无法直接测得压电元器件的输入输出信号,常规方法难以对其进行有效的辨识和控制。文章采用三明治模型来描绘纳米微位移平台,并提出一种基于最小二乘支持向量机优化的辨识方法解决三明治迟滞模型的辨识问题。最后基于已经辨识的三明治模型,设计一个PID逆补偿控制器,解决定位系统的精密轨迹控制问题。     

Exact analytical inverse mapping of decomposable TS fuzzy systems with singleton and linear consequents

In this study, a new method is proposed for the exact analytical inverse mapping of Takagi–Sugeno fuzzy systems with singleton and linear consequents where the input variables are described by using strong triangular partitions. These fuzzy systems can be decomposed into several fuzzy subsystems. The output of the fuzzy subsystem results in multi-linear form in singleton consequent case or multi-variate second order polynomial form in linear consequent case. Since there exist explicit analytical formulas for the solutions of first and second order equations, the exact analytical inverse solutions can be obtained for decomposable Takagi–Sugeno fuzzy systems with singleton and linear consequents. In the proposed method, the output of the fuzzy subsystem is represented by using the matrix multiplication form. The parametric inverse definition of the fuzzy subsystem is obtained by using appropriate matrix partitioning with respect to the inversion variable. The inverse mapping of each fuzzy subsystem can then easily be calculated by substituting appropriate parameters of the fuzzy subsystem into this parametric inverse definition. So, it becomes very easy to find the analytical inverse mapping of the overall Takagi–Sugeno fuzzy system by composing inverse mappings of all fuzzy subsystems. The exactness and the effectiveness of the proposed inversion method are demonstrated on trajectory tracking problems by simulations.     

基于Preisach模型的迟滞系统建模与控制

针对一种复杂的非线性系统一迟滞系统，研究了基于KP算子Preisach模型对迟滞系统进行建模的方法。利用Preisach模型与其边界线之间的映射关系，建立了容易在线更新的迟滞模型。基于Preisach模型进行迟滞非线性系统的控制，采用PID方法来控制一类带有未知非线性特性迟滞的单输入单输出非线性系统。对迟滞非线性系统的建模与控制进行的数值仿真研究结果表明，该迟滞非线性系统的建模和控制方法具有理论意义和应用价值。     

Input and output constraints-based stabilisation of switched nonlinear systems with unstable subsystems and its application

This paper studies the problem of stabilisation of switched nonlinear systems with output and input constraints. We propose a recursive approach to solve this issue. None of the subsystems are assumed to be stablisable while the switched system is stabilised by dual design of controllers for subsystems and a switching law. When only dealing with bounded input, we provide nested switching controllers using an extended backstepping procedure. If both input and output constraints are taken into consideration, a Barrier Lyapunov Function is employed during operation to construct multiple Lyapunov functions for switched nonlinear system in the backstepping procedure. As a practical example, the control design of an equilibrium manifold expansion model of aero-engine is given to demonstrate the effectiveness of the proposed design method.     

Nonlinear system identification of a small-scale unmanned helicopter

This paper presents a comprehensive method for identifying the nonlinear model of a small-scale unmanned helicopter. The model structure is obtained by first principles derivation, and the model parameters are determined by direct measurement and system identification. A new adaptive genetic algorithm is proposed to identify the parameters that cannot be directly measured. To simplify the identification process, the overall system is divided into two subsystems for identification: the heave–yaw dynamics and the lateral–longitudinal dynamics. On the basis of the input–output data collected from actual flight experiments, these two subsystems are identified using the proposed algorithm. The effectiveness of the identified model is verified by comparing the response of the simulation model with the actual response during the flight experiments. Results show that the identified model can accurately predict the response of the small-scale helicopter. Furthermore, the identified model is used for the design of an attitude controller. The experiment results show that the identified model is suitable for controller design.     

基于坐标变换和仿射映射辨识迟滞非线性模型

运用坐标变换方法和仿射映射的有关原理,对迟滞系统的输入信号进行变换映射。利用集合理论证明了变换后,迟滞的输入输出集合是双射的,从而对在光滑周期信号作用下的一类迟滞非线性进行建模。不仅建立了动态迟滞模型,而且也建立了相应的动态逆模型。仿真试验验证了所提出方法的有效性。     

Hammerstein-Wiener system estimator initialization

In nonlinear system identification, the system is often represented as a series of blocks linked together. Such block-oriented models are built with static nonlinear subsystems and linear dynamic systems. This paper deals with the identification of the Hammerstein-Wiener model, which is a block-oriented model where a linear dynamic system is surrounded by two static nonlinearities at its input and output. The proposed identification scheme is iterative and will be demonstrated on measurements. It will be proven that on noiseless data and in absence of modeling errors, the optimization procedure converges to the true system locally.     

A Wiener-type recurrent neural network and its control strategy for nonlinear dynamic applications

This paper presents a Wiener-type recurrent neural network with a systematic identification algorithm and a control strategy for the identification and control of unknown dynamic nonlinear systems. The proposed Wiener-type recurrent network resembles the conventional Wiener model that consists of a dynamic linear subsystem cascaded with a static nonlinear subsystem. The novelties of our network include: (1) the two subsystems are integrated into a single network whose output is expressed by a nonlinear transformation of a linear state-space equation; (2) the characteristics of the trained network can be analyzed by its associated state-space equation using the well-developed theory of linear systems; and (3) the size of the network structure is determined by the number of state variables (or the system order) of the unknown systems to be identified. To effectively identify a given unknown system from its input–output data, we have developed a systematic identification algorithm that consists of an order determination procedure, a parameterization procedure, and an online learning procedure. The false nearest neighbors algorithm was adopted to acquire a minimal embedding dimension from the input–output data as the system order, and then the eigensystem realization algorithm (ERA) was used to initialize a best-fit state-space representation according to the acquired system order. To improve the overall identification performance, we have derived an online parameter learning algorithm based on an ordered derivatives and momentum terms. Subsequently, a simple feedback linear controller was designed to control the unknown dynamic nonlinear systems without much complexity. Computer simulations and comparisons with some existing recurrent networks have conducted to confirm the effectiveness and superiority of the proposed Wiener-type network, identification algorithm and control strategy.     

一种非线性离散动态投入产出系统的最优控制

阐述了基于动态投入产出模型的最优控制理论,并对当前国内外的研究成果进行了对比研究。在分析其优缺点的同时,针对非线性离散动态投入产出系统的特点,提出了一种动态投入产出系统最优控制的逐次逼近方法。此方法首先将系统的最优控制问题转化为非线性两点边值问题族,然后通过构造线性两点边值问题族,将非线性两点边值问题转化为非齐次线性两点边值问题族;得到的最优控制律由精确控制项和非线性补偿项两部分组成,精确控制项可以通过求解Riccati方程求出其精确解,非线性补偿项由逐次逼近法求解一族线性伴随向量方程的解序列求得;最优控制律的最终目标是在规划期内使实际产出尽可能地与理想产出接近。实验仿真测试表明,采用逐次逼近法获得了非线性离散动态投入产出的最优系统控制,从而为最优控制问题的有效解决提供了参考和借鉴。     

基于组合式信号源的Hammerstein-Wiener模型辨识方法

针对含有有色噪声的非线性Hammerstein-Wiener模型,提出一种基于组合式信号源的辨识方法.通过利用可分离信号和随机信号组成的组合信号源实现有色噪声干扰下Hammerstein-Wiener模型各串联模块参数辨识的分离,简化辨识过程.首先,基于可分离信号的输入和输出,采用相关分析方法抑制过程噪声的干扰,辨识输出静态非线性模块和动态线性模块的参数;然后,基于辅助模型技术,利用辅助模型的输出和残差的估计值分别取代辨识模型中的不可测中间变量和噪声变量,推导辅助模型递推增广最小二乘方法,根据随机信号的输入输出数据辨识输入静态非线性模块和噪声模型的参数;最后,通过理论分析和仿真结果表明,所提出方法能够有效辨识有色噪声干扰下的非线性Hammerstein-Wiener模型,具有较好的鲁棒性.