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.     

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.     

AUV闭环系统可辨识性分析及算法实现

针对水下机器人闭环系统辨识问题,应用闭环系统辨识理论,本文给出了水下机器人闭环系统可辨识的充分条件.运用增广的Kalman滤波算法对某水下机器人进行闭环辨识.获得了该系统模型.验证了所提出充分条件的正确性及算法的可行性.     

一种无外部持续激励的子空间闭环辨识算法

传统的闭环系统可辨识性受到外部激励和控制器结构的限制,然而在实际辨识应用中,由于过程操作条件的限制或者经济原因不希望存在外部持续激励。讨论了在无外部激励下基于快采样的多变量子空间模型闭环可辨识性,提出了无外部持续激励条件下的闭环快采样子空间模型辨识方法,在常规采样的可辨识性条件不满足或部分满足的情况下,通过对闭环系统控制对象的输入输出变量快采样来实现对象模型辨识,并通过仿真实例验证了基于快采样的辨识算法的有效性。     

基于正交分解的递推子空间闭环辨识方法

为实现闭环系统在线辨识,提出递推正交分解闭环子空间辨识方法(RORT)。首先,根据闭环系统状态空间模型和数据间投影关系,构建确定-随机模型,并利用GIVENS变换实现投影向量的递推QR分解;然后,引入带遗忘因子的辨识算法,构建广义能观测矩阵的递推更新形式,以减少子空间辨识算法中QR分解和SVD分解的计算量;最后,针对某型号陀螺仪闭环系统进行实验。实验结果表明, RORT法的辨识拟合度高于91%,能够对陀螺仪闭环系统模型参数进行在线监测。     

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.     

Projection-based identification algorithm for grey-box continuous-time models

In this paper, a new identification method for continuous-time models, which can handle various grey-box structures and has strong robustness, is presented. The proposed method is based on an incremental model update scheme and the projection onto the subspace which reflects the model structure. By utilising these schemes, robustness of other continuous-time system identification methods and versatility of generic optimisation algorithms can be integrated into the proposed method. The effectiveness of the proposed method is demonstrated through numerical examples related to a grey-box model in closed-loop system and systems with unknown time-delay.     

Subspace identification with non-steady Kalman filter parameterization

Most existing subspace identification methods use steady-state Kalman filter (SKF) in parameterization, hence, infinite data horizons are implicitly assumed to allow the Kalman gain to reach steady state. However, using infinite horizons requires collecting infinite data which is unrealistic in practice. In this paper, a subspace framework with non-steady state Kalman filter (NKF) parameterization is established to provide exact parameterization for finite data horizon identification problems. Based on this we propose a novel subspace identification method with NKF parameterization which can handle closed-loop data and avoid assumption on infinite horizons. It is shown that with finite data, the proposed parameterization method provides more accurate and consistent solutions than existing SKF based methods. The paper also reveals why it is often beneficial in practice to estimate a bank of ARX models over a single ARX model.     

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.     

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.     

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.     

On the assessment of multivariable controllers using closed loop data. Part I: Identification of system models

Controller performance assessment of SISO and MIMO systems requires effective and systematic identification of the associated system models based on closed-loop data. In this work, a new methodology for the identification of the process, controller and disturbance models is presented for the purpose of enabling the evaluation of the performance of MIMO control systems. The methodology is based on subspace identification algorithms for the identification of the controller, process and disturbance models from closed-loop data. However, identification of the process model is enhanced by the estimation of the associated interactor matrix via the Variable Regression Estimation technique, the existence of which is mathematically proved. The proposed identification methodology is applied to two 2 × 2 systems utilizing both step-response and PRBS closed-loop data.     

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.     

Comparison of input signals in subspace identification of multivariable ill-conditioned systems

Ill-conditioned processes often produce data of low quality for model identification in general, and for subspace identification in particular, because data vectors of different outputs are typically close to collinearity, being aligned in the “strong” direction. One of the solutions suggested in the literature is the use of appropriate input signals, usually called “rotated” inputs, which must excite sufficiently the process in the “weak” direction. In this paper open-loop (uncorrelated and rotated) random signals are compared against inputs generated in closed-loop operation, with the aim of finding the most appropriate ones to be used in multivariable subspace identification of ill-conditioned processes. Two multivariable ill-conditioned processes are investigated and as a result it is found that closed-loop identification gives superior models, both in the sense of lower error in the frequency response and in terms of higher performance when used to build a model predictive control system.