有色噪声背景下的正交子空间辨识

针对传统子空间辨识中存在的有色噪声干扰问题,本文提出一种正交子空间辨识方法.首先,根据子空间辨识算法机制构建含有色噪声的扩展状态空间模型.然后,结合有色噪声的相关性分析,研究了传统子空间辨识方法的有偏性问题,并重新设计了投影向量和正交投影方式,用以消除有色噪声干扰.最后,对投影后的数据矩阵进行奇异值分解,获取广义能观测矩阵,进而求得系统的状态空间模型参数.仿真结果表明该方法在有色噪声干扰下是一致无偏的,并且具有渐进二阶统计特性.结合陀螺仪的具体实验结果表明,该算法在实际应用中具有比传统子空间辨识法更高的辨识精度.     

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.     

递推子空间模型辨识算法的研究与仿真

为了很好的解决在线辨识系统模型问题，在对子空间模型辨识研究的基础上，结合递推最小二乘算法和子空问状态辨识方法。推导了子空间状态辨识的递推算法。该算法不仅解决了在线辨识问题，而且算法简单，计算方便，很好地克服了在线辨识时子空间矩阵维数的变化问题。经仿真研究表明，该递推算法克服了一次完成算法在大批量数据运算时，耗时大，专用内存多的缺点，而且对于测量和过程均有噪声干扰的多输入多输出系统，有很好的辨识效果，有较为广阔的应用前景。     

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。     

基于子空间辨识的状态空间模型预测控制

针对无法从工业过程中获得准确状态空间模型的问题,提出一种基于子空间辨识的状态空间模型预测控制方法。利用子空间辨识方法得到的状态空间模型作为系统模型,给出约束条件下的预测控制算法。以CD播放器机械臂系统为例,通过状态空间模型预测控制方法实现对系统输出的跟踪控制,仿真结果表明,该方法控制效果良好。     

基于小波子空间法的MIMO系统辨识研究

针对线性时不变多输人多输出(MIMO)系统的输出存在随机噪声情况下,提出直接利用小波域的输入输出数据,辨识MIMO系统的方法.子空间状态空间法是时域辨识MIMO系统的主要方法,通过数据矩阵投影,对数据矩阵进行QR分解和奇异值分解,辨识出系统的阶数和系统的状态方程矩阵.运用小波变换,将时域信号转换为小波域的信号,利用小波子空间状态空间辨识算法对MIMO系统辨识,通过仿真,得到辨识的结果与时域子空间状态空间法相比较,证明提出方法是有效的.     

用改进子空间辨识法建立航空发动机模型

研究一种采用改进子空间辨识法建立用于航空发动机故障诊断与控制系统设计的小偏差状态变量模型方法.首先,利用发动机非线性模型的输入输出数据序列,在离散域下基于子空间辨识法建立指定阶数、无噪声干扰的状态变量模型,然后将其转化到连续域下进行相似变换,从而获得具有明确物理意义的发动机状态变量模型.这样,不仅避免了那些基于最优化思想方法所带来的一系列问题,即非线性迭代优化、对初始值敏感、计算时间长、系统矩阵参数规律性差等,而且不受模型阶次影响,并具有实现简单等特点.应用于建立某型涡扇发动机的小偏差状态变量模型,并与改进拟合法在拟合精度、计算时间、参数变化三个方面进行比较,从而验证了改进子空间辨识方法的优点与有效性.     

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.     

子空间盲辨识的改进算法

针对单输入多输出(SIMO)系统模型参数的盲辨识问题进行了研究,基于二阶统计量,提出一类改进的子空间辨识算法.依据协方差阵的秩对该矩阵进行分块,在此基础上考虑了实际系统中存在的噪声误差,利用总体最小二乘(TLS)得到一个与噪声子空间相关的量,最后对该量进行标准正交化,得到了噪声子空间.与传统子空间方法相比,改进算法不需要对协方差矩阵进行特征值分解,可以减弱噪声及不确定因素的影响,减少了运算量,仿真实验结果表明了该算法的有效性.     

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。     

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.     

A PMF-based subspace method for continuous-time model identification. Application to a multivariable winding process

This paper presents a methodology for system identification of continuous-time state-space models from finite sampled input-output signals. The estimation problem of the consecutive time-derivatives and integrals of the input-output signals is considered. The appropriate frequency characteristcs of a linear filtering based on the Poisson moment functionals in regards to the derivative or integral estimation problem is shown. The proposed method combines therefore the Poisson moment functionals technique with subspace based state-space system identification methods. The developed algorithm is based on a generalized singular value decomposition to compensate the noise colouring caused by the linear prefiltering of the input-output data. Rules of thumb are presented to choose the design parameters and new regards to the selection of the Poisson filter cut-off frequency are introduced. Finally, the proposed method is applied to a multivariable winding processes. The experimental results emphasize the applicability of the developed methodology.     

A new subspace identification approach based on principal component analysis

Principal component analysis (PCA) has been widely used for monitoring complex industrial processes with multiple variables and diagnosing process and sensor faults. The objective of this paper is to develop a new subspace identification algorithm that gives consistent model estimates under the errors-in-variables (EIV) situation. In this paper, we propose a new subspace identification approach using principal component analysis. PCA naturally falls into the category of EIV formulation, which resembles total least squares and allows for errors in both process input and output. We propose to use PCA to determine the system observability subspace, the A, B, C, and D matrices and the system order for an EIV formulation. Standard PCA is modified with instrumental variables in order to achieve consistent estimates of the system matrices. The proposed subspace identification method is demonstrated using a simulated process and a real industrial process for model identification and order determination. For comparison the MOESP algorithm and N4SID algorithm are used as benchmarks to demonstrate the advantages of the proposed PCA based subspace model identification (SMI) algorithm.     

System identification method inheriting steady-state characteristics of existing model

In this paper, we propose an identification method to construct a state-space model that inherits steady-state characteristics from an existing model. It is assumed that in prior to an identification experiment, a designer has a model which accurately expresses steady-state characteristics of an actual system responding to certain inputs. The characteristics are extracted and inherited to a reconstructed state-space model via the combination with a subspace identification method. By applying a change-of-variable technique, the combined identification problem, which is formulated as nonlinear optimisation, is reduced to a least squares problem. Finally, we show the effectiveness of the proposed method in three different numerical simulations.     

Modeling of a dynamic dual-input dual-output fast steeringmirror system

A modeling method is proposed for a dynamic fast steering mirror (FSM) system with dual inputs and dual outputs. A physical model of the FSM system is derived based on first principles, describing the dynamics and coupling between the inputs and outputs of the FSM system. The physical model is then represented in a state-space form. Unknown parameters in the state-space model are identified by the subspace identification algorithm, based on the measured input-output data of the FSM system. The accuracy of the state-space model is evaluated by comparing the model estimates with measurements. The variance-accounted-for value of the state-space model is better than 97%, not only for the modeling data but also for the validation data set, indicating high accuracy of the model. Comparison is also made between the proposed dynamic model and the conventional static model, where improvement in model accuracy is clearly observed. The model identified by the proposed method can be used for optimal controller design for closed-loop FSM systems. The modeling method is also applicable to FSM systems with similar structures.     

Subspace identification of MIMO LPV systems using a periodic scheduling sequence

A novel subspace identification method is presented which is able to reconstruct the deterministic part of a multivariable state-space LPV system with affine parameter dependence, in the presence of process and output noise. It is assumed that the identification data is generated with the scheduling variable varying periodically during the course of the identification experiment. This allows to use methods from LTI subspace identification to determine the column space of the time-varying observability matrices. It is shown that the crucial step in determining the original LPV system is to ensure the obtained observability matrices are defined with respect to the same state basis. Once the LPV model has been identified, it is valid for other nonperiodic scheduling sequences as well.     

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.     

非线性CSTR过程预测控制器设计

针对非线性CSTR(continuously stirred tank reactor)过程,提出一种新的预测控制的设计与仿真实现.在对一类特殊非线性过程分析的基础上,从系统的输入输出数据出发,基于子空间辨识算法建立双线性系统模型来近似描述被控系统;设计新的预测控制算法实现对CSTR过程的跟踪控制;为补偿模型失配以消除控制中的稳态误差,将积分作用包含在预测控制器的设计中,实现对控制输出的良好跟踪性能;最后通过一个仿真实例验证算法的有效性.     

Simultaneous state estimation and parameter identification in linear fractional order systems using coloured measurement noise

In the present paper, the identification and estimation problem of a single-input–single-output (SISO) fractional order state-space system will be addressed. A SISO state-space model is considered in which parameters and also state variables should be estimated. The canonical fractional order state-space system will be transformed into a regression equation by using a linear transformation and a shift operator that are appropriate for identification. The identification method provided in this paper is based on a recursive identification algorithm that has the capability of identifying the parameters of fractional order state-space system recursively. Another subject that will be addressed in this paper is a novel fractional order Kalman filter suitable for the systems with coloured measurement noise. The promising performance of the proposed methods is verified using two stable fractional order systems.