N4SID and MOESP Algorithms to Highlight the Ill-conditioning into Subspace Identification

• Published in: International journal of automation and computing Vol. 11; no. 1; pp. 30 - 38
• Main Authors: Hachicha, Slim, Kharrat, Maher, Chaari, Abdessattar
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.02.2014; Springer Nature B.V
• Subjects: Algorithms; CAE) and Design; Computer Applications; Computer simulation; Computer-Aided Engineering (CAD; Control; Decomposition; Engineering; error; identifcation; identifcation(MOESP); identifcation(N4SID); Identification; Identification methods; Ill-conditioned problems (mathematics); ill-conditioning; induction; Induction motors; Linear algebra; Mathematical analysis; Mathematical models; Matlab; Mechatronics; Methods; motor; multivariable; numerical; oblique; Optimization algorithms; orthogonal; output; Parameter estimation; Parameter identification; Projection; Robotics; Robustness (mathematics); space; state; State space models; Subspace; Subspaces; system; System identification; multivariable output error state space model identification (MOESP); orthogonal projection; ill-conditioning; Subspace identification; induction motor; oblique projection; algorithms numerical subspace state space system identification (N4SID)
• ISSN: 1476-8186; 2153-182X; 1751-8520; 2153-1838
• DOI: 10.1007/s11633-014-0763-z

In this paper,an analysis for ill conditioning problem in subspace identifcation method is provided.The subspace identifcation technique presents a satisfactory robustness in the parameter estimation of process model which performs control.As a frst step,the main geometric and mathematical tools used in subspace identifcation are briefly presented.In the second step,the problem of analyzing ill-conditioning matrices in the subspace identifcation method is considered.To illustrate this situation,a simulation study of an example is introduced to show the ill-conditioning in subspace identifcation.Algorithms numerical subspace state space system identifcation(N4SID)and multivariable output error state space model identifcation(MOESP)are considered to study,the parameters estimation while using the induction motor model,in simulation(Matlab environment).Finally,we show the inadequacy of the oblique projection and validate the efectiveness of the orthogonal projection approach which is needed in ill-conditioning;a real application dealing with induction motor parameters estimation has been experimented.The obtained results proved that the algorithm based on orthogonal projection MOESP,overcomes the situation of ill-conditioning in the Hankel s block,and thereby improving the estimation of parameters.