基于辅助变量的闭环系统子空间辨识

提出一种基于辅助变量的子空间辨识方法,适用于控制器信息未知以及参考输入已知的闭环系统参数辨识.通过将输入-输出数据块正交投影到辅助变量的行空间,直接得到扩展观测矩阵垂空间的估计.由此可从闭环系统中提取出对象模型信息,同时由SVD分解得到扩展观测矩阵与下三角Toeplitz矩阵的估计.给出了系统参数矩阵,噪声矩阵的计算方法.将所提出的子空间辨识方法应用于闭环动态的系统参数估计,其结果表明了该方法的有效性.

     

基于ARMAX模型的子空间辨识算法

针对于子空间辨识算法辨识闭环系统时,由于输入信号与不可测噪声是相关的,往往会得到有偏估计的问题.提出一种采用自回归滑动平均模型(ARMAX)的闭环子空间辨识方法,通过扩展最小二乘方法(ELs)估计ARMAX模型中的马尔科夫(Markov)参数,使用预测的子空间辨识方法(PBSID)获取系统参数矩阵,避免了采用高阶自回归模型(ARX)所导致的过大的估计方差等问题.算法实例验证结果表明,改进方法能够获得较好的闭环系统一致性估计,辨识精度较高,有非常良好的应用前景.     

数据驱动闭环子空间预测控制方法研究与应用

提出一种完全数据驱动的闭环子空间辨识及预测控制器设计方法. 该方法完全由闭环系统的输入输出数据辨识子空间矩阵, 通过子空间矩阵的拆分, 排除了与扰动相关的模型输入, 进而获取子空间矩阵参数的无偏估计; 将辨识得到的闭环系统子空间矩阵描述直接作为预测模型, 设计预测控制器; 将其应用于某钢铁集团焦炉炭化室压力控制系统, 取得了良好的控制效果.

     

连续时间模型的闭环子空间辨识

本文对直接使用采样数据进行连续系统的闭环子空间辨识问题进行了研究．将线性滤波方法与基于主 元分析的子空间辨识相结合,利用参考输入或者外部激励信号的高阶滤波变换的正交投影变量作为辅助变量,提出 了一种新的连续时间系统闭环子空间辨识算法．数值仿真表明了与其他算法相比,本文提出的算法具有很好的辨识 效果．     

基于新息估计和正交投影的闭环子空间模型辨识

针对闭环控制系统提出一种基于新息估计和正交投影的闭环子空间模型辨识方法.首先采用最小二乘法对VARX模型（Vector autoregressive with exogenous inputs model）进行计算得到新息估计值,然后通过将由观测输入输出数据构造的Hankel矩阵正交投影到新息数据的正交补空间以消除噪声影响,从而在无噪声的输入输出数据奇偶空间中提取得到扩展可观测矩阵和下三角形Toeplitz矩阵.最后采用平移变换法得到系统矩阵.对该算法严格分析和证明了实现一致估计的条件.通过仿真实例验证了本文方法的有效性和优越性.     

基于输入扩张的闭环系统子空间辨识及其强一致性分析

针对闭环条件下的子空间辨识问题, 结合线性代数和几何学的基本概念, 将输入输出误差序列包含至输入子空间中, 基于输入扩张的状态空间构造方法, 提出一种新的闭环辨识算法；解决开环算法应用于闭环系统辨识时产生有偏估计, 甚至不能正确辨识的问题；实现闭环条件下对系统状态空间矩阵的强一致估计, 并理论证明该辨识算法的强一致性；最后通过仿真实例验证本算法的有效性.     

基于目标函数的递推子空间辨识算法

针对实际工程中要求对系统参数进行在线估计的问题, 提出一种递推子空间辨识的新方法. 通过引入辅助变量关系将递推子空间辨识问题转化为目标函数的迭代最小化问题. 采用递推最小二乘算法在线估计参数并由传播方法得到更新的广义能观性矩阵, 进而求得子空间辨识模型系统参数. 该算法简单有效且对初值具有鲁棒性. 最后, 通过仿真实例验证算法的有效性.     

有色噪声干扰下多变量系统的辅助模型辨识方法

针对有色噪声干扰的多输入多输出系统模型辨识问题,提出了多变量系统的FIR辅助模型辨识方法;其辨识思想是把传递函数矩阵中的子模型等价成辅助模型—有限脉冲相应(FIR)模型,然后利用辨识得到的辅助模型估计输出向量的子子模型,最后利用递推最小二乘算法或帕德近似化方法得到子子模型的参数估计,并通过仿真来验证算法的性能。     

脉冲响应模型的闭环子空间辨识方法

针对实际情况中难以采集控制系统开环数据的问题，对脉冲响应模型的闭环辨识问题进行了研究，提出了一种基于正交分解理论的脉冲响应模型闭环子空间辨识方法。通过使用正交分解得到联合输入输出信号的确定部分（Deterministic Components），把闭环问题转化成开环问题。利用Toeplitz矩阵下三角结构形式，对由脉冲响应模型系数组成的子空间矩阵分块分解，通过求取子空间矩阵元素的平均值来获取脉冲响应模型参数的估计。通过采用PID控制器的单输入单输出（SISO）数值仿真、多输入多输出（MIMO）数值仿真和Wood-Berry蒸馏过程仿真实验3个仿真实例，对比研究了所提方法与PBSID_OPT、CVA三种方法。仿真结果表明了所提出的方法具有良好的辨识性能。对于实际工业过程的建模问题，该研究所提的闭环子空间辨识方法具有实际的参考价值和一定的指导意义。     

基于主元分析的子空间辨识算法

子空间辨识算法作为一种优良的多变量系统辨识算法,最近在国内发展很快.但是现在国内介绍的大多数子空间辨识算法在变量有误差(errors-in-variable)时和闭环辨识时辨识结果却是有偏的,这是因为大多数子空间辨识算法都假设输入变量是没有噪声及辨识算法中存在的一个投影过程.文中介绍了一种新的子空间辨识算法,这种算法利用主元分析(PCA)来获取系统矩阵,避免了其他算法中的投影过程,因此该算法在闭环辨识和变量有误差(errors-in-variable)的情况下,辨识结果也是无偏的.最后给出一个仿真例子说明这种辨识算法的辨识效果良好.     

Subspace identification using instrumental variable techniques

Subspace-based algorithms for system identification have lately been suggested as alternatives to more traditional techniques. Variants of the MOESP type of subspace algorithms are in addition to open-loop identification applicable to closed-loop and errors-in-variables identification. In this paper, a new instrumental variable approach to subspace identification is presented. It is shown how existing MOESP-algorithms can be derived within the proposed framework, simply by changing instruments and weighting matrices. A noteworthy outcome of the analysis is that an improvement of an existing MOESP method for errors-in-variables identification can be proposed.     

Indirect closed-loop identification by optimal instrumental variable method

Recently, a new bias-compensating least-squares (BCLS) method was proposed for the identification of a closed-loop system with high-order controller. The major feature of this method is that it can achieve consistent parameter estimation without modelling the coloured noises acting on the system. This paper studies the connection between the BCLS method and the instrumental variable (IV) family. It is shown that the BCLS method is a kind of weighted instrumental variable (WIV) method whose results do not depend upon the order of the controller.     

基于辅助变量的压缩采样匹配追踪闭环系统辨识方法

针对被控对象和反馈通道均具有未知时滞的闭环系统,提出一种基于辅助变量的压缩采样匹配追踪辨识方法.该方法利用辅助变量方法对压缩采样匹配追踪算法进行改进,获得过参数化辨识模型稀疏参数向量的估计,根据稀疏向量的结构得到前向通道的参数估计和时滞估计,进而根据模型等价原理获得反馈通道的参数估计.仿真结果表明,所提出方法仅需少量的迭代即可获得这类闭环系统参数与时滞的有效估计.     

Closed-loop subspace-based identification algorithm using third-order cumulants

The problem of closed-loop system identification for coloured noise system without any knowledge of feedback controller is considered. We develop a solution to this problem in the framework of subspace identification based on high-order cumulants. The key of the developed algorithm is using the properties that the third-order cumulants are insensitive to any coloured Gaussian noises. By post-multiplying a suitable instrumental variable to the noise terms, the cross third-order cumulants are constructed that become zero when the noises are Gaussian distributed, and meanwhile the column rank of extended observability matrix is maintained. Thus, the standard subspace identification algorithms can be extended to closed-loop system corrupted by arbitrary coloured noises. A numerical simulation is presented to demonstrate the proposed algorithm.     

Improved closed-loop subspace identification with prior information

It has been proven that combining open-loop subspace identification with prior information can promote the accuracy of obtaining state-space models. In this study, prior information is exploited to improve the accuracy of closed-loop subspace identification. The proposed approach initially removes the correlation between future input and past innovation, a significant obstacle in closed-loop subspace identification method. Then, each row of the extended subspace matrix equation is considered an optimal multi-step ahead predictor and prior information is expressed in the form of equality constraints. The constrained least squares method is used to obtain improved results, so that the accuracy of the closed-loop subspace can be enhanced. Simulation examples are provided to demonstrate the effectiveness of the proposed algorithm.     

Iterative motion feedforward tuning: A data-driven approach based on instrumental variable identification

Feedforward control can significantly enhance the performance of motion systems through compensation of known disturbances. This paper aims to develop a new procedure to tune a feedforward controller based on measured data obtained in finite time tasks. Hereto, a suitable feedforward parametrization is introduced that provides good extrapolation properties for a class of reference signals. Next, connections with closed-loop system identification are established. In particular, instrumental variables, which have been proven very useful in closed-loop system identification, are selected to tune the feedforward controller. These instrumental variables closely resemble traditional engineering tuning practice. In contrast to pre-existing approaches, the feedforward controller can be updated after each task, irrespective of noise acting on the system. Experimental results confirm the practical relevance of the proposed method.     

一种新的辅助变量法——重复实验辅助变量法

本文提出了一种新的辅助变量(IV)法--重复实验辅助变量(TRIV,Test-Repeat IV) 法.这种方法不但适用于闭环系统辨识,而且具有精度高、速度快、算法简单及易于判阶等优 点.在理论上分析了这种方法的一致性,并通过Monte Carl1o仿真实验证实了这种方法的有 效性.     

Instrumental variable methods for closed-loop system identification

In this paper, several instrumental variable (IV) and instrumental variable-related methods for closed-loop system identification are considered and set in an extended IV framework. Extended IV methods require the appropriate choice of particular design variables, as the number and type of instrumental signals, data prefiltering and the choice of an appropriate norm of the extended IV-criterion. The optimal IV estimator achieves minimum variance, but requires the exact knowledge of the noise model. For the closed-loop situation several IV methods are put in an extended IV framework and characterized by different choices of design variables. Their variance properties are considered and illustrated with a simulation example.     

Instrumental variable scheme for closed-loop LPV model identification

Identification of real-world systems is often applied in closed loop due to stability, performance or safety constraints. However, when considering Linear Parameter-Varying (LPV) systems, closed-loop identification is not well-established despite the recent advances in prediction error approaches. Building on the available results, the paper proposes the closed-loop generalization of a recently introduced instrumental variable scheme for the identification of LPV-IO models with a Box–Jenkins type of noise model structures. Estimation under closed-loop conditions with the proposed approach is analyzed from the stochastic point of view and the performance of the method is demonstrated through a representative simulation example.