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

In this paper, an analysis for ill conditioning problem in subspace identification method is provided. The subspace identification technique presents a satisfactory robustness in the parameter estimation of process model which performs control. As a first step, the main geometric and mathematical tools used in subspace identification are briefly presented. In the second step, the problem of analyzing ill-conditioning matrices in the subspace identification method is considered. To illustrate this situation, a simulation study of an example is introduced to show the ill-conditioning in subspace identification. Algorithms numerical subspace state space system identification (N4SID) and multivariable output error state space model identification (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 effectiveness 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.