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For a high dynamic performance induction machine (IM) control, parameters have to be precisely known. In this paper we propose a detailed study of the extensive recursive least squares (ERLS) method to estimate these parameters in real time. We use this algorithm with its various extensions to identify the parameters of the Autoregressive Moving Average with Extra Inputs (ARMAX) model associated to the IM. This method is based on the minimization of a quadratic criterion. As advanced technique, this paper proposes Genetic Algorithms (GA) to identify model parameters with biased estimations. A comparison of these two methods confirms the effectiveness of the last one.