基于两步方法的闭环子空间辨识算法

闭环辨识算法具有广泛的工程应用前景,而子空间方法近年来应用于多个领域中,但子空间方法无法直接应用于闭环辨识,因此研究闭环子空间辨识算法具有重要意义.两步方法可用于辨识闭环系统,但计算量巨大,推导复杂,需要进一步改进.针对这种情况,提出了一种改进算法,使用将两步方法与正交投影相结合的方法,并利用QR分解实现,直接构建虚拟信号序列,大大减少了计算量,最后使用PI-MOESP辨识算法辨识模型.仿真实验将该算法与其他子空间辨识算法相比较,显示出该算法的有效性及计算量的显著减少.     

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.     

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．     

状态空间子空间方法处理闭环系统辨识

本文给出一个由闭环数据辨识状态空间模型的算法，此算法可辨识带有严重噪声干扰和延迟的稳定及不稳定系统，并已为数学理论及实验结果所验证。     

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。     

闭环子空间辨识方法的分析与比较

在实际应用中,辨识方法的辨识精度和辨识效率一直是人们关注的指标,也是人们选择辨识方法的主要依据。针对多种闭环子空间辨识方法的辨识精度和辨识效率问题的研究,首先归纳和总结了基于正交分解和基于正交投影闭环子空间辨识方法的理论和实现;然后扩展提出了基于正交分解的闭环子空间辨识方法 ORT_POMOESP、ORT_N4SID和基于正交投影的闭环子空间辨识方法 CSOPIM_W2;最后考虑系统输入输出测量噪声,针对过程噪声为白噪声和有色噪声两种情况下,通过仿真算例以数值分析的形式,对比研究了多种闭环子空间辨识方法的辨识精度和辨识效率。该研究不仅对子空间辨识方法应用于实际工业过程的建模具有实际的参考价值,而且对实际工程应用中闭环子空间辨识算法的选用具有一定的指导意义。     

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.     

基于子空间方法的精馏塔系统辨识建模研究

子空间辨识方法作为一种有效的针对多输入-多输出系统(MIMO)的辨识建模方法近年来受到广泛的重视.目前主要采用的子空间辨识算法只能适用于白噪声环境,而实际的工业现场数据很多是受到较大有色噪声干扰的.针对问题采用了一种新的子空间辨识算法,利用马尔可夫参数用于处理随机性部分,同时引入辅助变量用以去除噪声的干扰,能够适用于存在较大有色噪声干扰情况下的辨识建模,并可得到对象的无偏模型,建模的精度优于通常所采用的子空间辨识算法.通过对精馏塔仿真模型的辨识结果证明了该方法的可行性和有效性,以及在实际工业过程对象建模中良好的应用前景.     

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.     

An insight into instrumental variable frequency-domain subspace identification

In this paper, we study instrumental variable subspace identification of multi-input/multi-output linear-time-invariant, discrete-time systems from non-uniformly spaced frequency response measurements. A particular algorithm, which does not require noise covariance function to be known a priori is shown to be strongly consistent provided that disturbances have uniformly bounded second-order moments and the frequencies satisfy a certain regularity condition. Interpolation properties of this algorithm and a related one are also studied. A numerical example illustrating the properties of the studied algorithms is presented.     

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.     

Convergence analysis of instrumental variable recursive subspace identification algorithms

The convergence properties of recently developed recursive subspace identification methods are investigated in this paper. The algorithms operate on the basis of instrumental variable (IV) versions of the propagator method for signal subspace estimation. It is proved that, under suitable conditions on the input signal and the system, the considered recursive subspace identification algorithms converge to a consistent estimate of the propagator and, by extension, to the state-space system matrices.     

Closed-loop subspace identification using the parity space

It is known that many subspace algorithms give biased estimates for closed-loop data due to the existence of feedback. In this paper we present a new subspace identification method using the parity space employed in fault detection in the past. The basic algorithm, known as subspace identification method via principal component analysis (SIMPCA), gives consistent estimation of the deterministic part and stochastic part of the system under closed loop. Column weighting for SIMPCA is introduced which shows improved efficiency/accuracy. A simulation example is given to illustrate the performance of the proposed algorithm in closed-loop identification and the effect of column weighting.     

Closed-loop subspace identification: an orthogonal projection approach

In this paper, a closed-loop subspace identification approach through an orthogonal projection and subsequent singular value decomposition is proposed. As a by-product of this development, it explains why some existing subspace methods may deliver a bias in the presence of the feedback control and suggests a remedy to eliminate the bias. Furthermore, as the proposed method is a projection based method, it can simultaneously provide extended observability matrix, lower triangular block-Toeplitz matrix, and Kalman filtered state sequences. Therefore, using this method, the system state space matrices can be recovered either from the extended observability matrix/the block-Toeplitz matrix or from the Kalman filter state sequences.     

Necessary and sufficient convergence conditions of the instrumental variable method for identification

The consistency of the instrumental variable method is considered for a system driven by independent identically distributed input signals with zero mean. Necessary and sufficient conditions for convergence are developed with respect to the given model structure. The sufficient and necessary conditions are established for cases with and without data prefiltering. In this paper we extend on existing results such that the requirements on the degree of the instrumental variables can be relaxed. Numerical examples supporting the theoretical results are provided.     

The asymptotic model quality assessment for instrumental variable identification revisited

In this paper the problem of computing uncertainty regions for models identified through an instrumental variable technique is considered. Recently, it has been pointed out that, in certain operating conditions, the asymptotic theory of system identification (the most widely used method for model quality assessment) may deliver unreliable confidence regions. The aim of this paper is to show that, in an instrumental variable setting, the asymptotic theory exhibits a certain “robustness” that makes it reliable even with a moderate number of data samples. Reasons for this are highlighted in the paper through a theoretical analysis and simulation examples.     

An instrumental variable approach for rigid industrial robots identification

This paper deals with the important topic of rigid industrial robots identification. The usual identification method is based on the use of the inverse dynamic model and the least-squares technique. In order to obtain good results, a well-tuned derivative bandpass filtering of joint positions is needed to calculate the joint velocities and accelerations. However, we can doubt whether the bandpass filter is well-tuned or not. Another approach is the instrumental variable (IV) method which is robust to data filtering and which is statistically optimal. In this paper, an IV approach relevant for identification of rigid industrial robots is introduced. The set of instruments is the inverse dynamic model built from simulated data which are calculated from the simulation of the direct dynamic model. The simulation assumes the same reference trajectories and the same control structure for both the actual and the simulated robot and is based on the previous IV estimates. Furthermore, to obtain a rapid convergence, the gains of the simulated controller are updated according to IV estimates. Thus, the proposed approach validates the inverse and direct dynamic models simultaneously and is not sensitive to initial conditions. The experimental results obtained with a 2 degrees of freedom (DOF) planar prototype and with a 6 DOF industrial robot show the effectiveness of our approach: it is possible to identify 60 parameters in 3 iterations and in 11 s.     

Orthogonal projection based subspace identification against colored noise

In this paper, a bias-eliminated subspace identification method is proposed for industrial applications subject to colored noise. Based on double orthogonal projections, an identification algorithm is developed to eliminate the influence of colored noise for consistent estimation of the extended observability matrix of the plant state-space model. A shift-invariant approach is then given to retrieve the system matrices from the estimated extended observability matrix. The persistent excitation condition for consistent estimation of the extended observability matrix is analyzed. Moreover, a numerical algorithm is given to compute the estimation error of the estimated extended observability matrix. Two illustrative examples are given to demonstrate the effectiveness and merit of the proposed method.