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

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.

Model variables identification of a gas turbine using a subspace approach based on input/output data measurements

This paper deals with a state model identification of a gas turbine used for gas transport, using a subspace approach of the state space model. This method provides a reliable and robust state representation of the model, taking advantage of its benefits in the control, monitoring, and supervision of this machine. The model for each variable is set so that the state matrices associated with the gas turbine model are determined from their real input/output data. The comparison of the obtained identification results with those of the actual turbine operation serves to validate the proposed model in this work. This numerical algorithm of the subspace identification method is full of information and more accurate in terms of residual modeling error, and expresses a very high level of confidence in the identified turbine system dynamics. Hence, the controllability and observability tests of turbine operation for different input/output variables allowed to validate the real-time operating stability of the turbine.