Induction motors are the basis elements in industrial applications thanks to their economic cost, judicious size, and easy maintenance [1] [2] . However, these motors are complex and have a strongly nonlinear system. It is often hard to determine an adequate model that represents all the dynamic behavior of this machine.

Modeling is an essential initial step in the industrial process control. This fundamental step is necessary either for a control law development or for the development of a diagnosis procedure. Modeling a process consists in establishing relationships between its characteristics variables and in representing the dynamic behavior of this process in a particular field of operation.

Based on a priori knowledge of the studied process, many modeling types are used. The increasing complexity of industrial process pushes many researchers to develop modeling techniques that exploit linear systems tools. Hence, in this paper we will consider the modeling based on multimodel approach that recently, has been implemented in various science and engineering domains, concerning application to modeling, control and fault diagnosis [3] -[10] .

The multimodel approach consists in replacing the unique nonlinear model by a set of simpler linear models to create a model-base. Generally, each model of this base contributes to the whole description of the considered system through weighed functions or validities functions.

The modeling via this approach needs to follow up a scheme of four steps that are database acquisition, clustering, structural and parametric identification and fusion.

For clustering, many algorithms are adopted in literature [11] -[14] , in this paper we will focus on three fuzzy clustering algorithms that are subtractive, C-means and K-means clustering algorithms. The subtractive algorithm is used to determine the cluster number, whereas the C-means and the K-means will be exploited to generate the cluster centers then to construct the clusters. Thus, we will compare two modeling methods, the first is based on the association of subtractive-C-means algorithm and the second is based on the association of subtractive-K-means algorithm.

The two proposed modeling method are experimentally implemented to an induction motor.

The organization of this paper is as follows. The second part consists in describing the modeling with multi- model approach, the third part develops the application of the two modeling methods based on the two clustering algorithm to the induction motor. The part four is a comparative study of the two modeling method and finally the conclusion is in the fifth part.

To obtain a multimodel, we have to follow a strategy of four stages that are database acquisition, data clustering, structural and parametric identification and local models fusion.

The system is considered as a black box. Thus, it is exited via a rich frequency input. The collected data is consisting of a set of input/output measurements. Then the collected data will be divided into N clusters through clustering algorithms. Later, three clustering algorithms will be developed: the subtractive, C-means and K-means algorithm. Next, structural and parametric identification follow the clustering to obtain the local models. The structural identification is achieved using the general procedure of order estimation and the Instrumental determinant ratio (IDR). For the parametric identification, the generalized recursive least square is implemented.

The obtained local models are combined through weighted functions that are calculated based on residue approach [5] -[8] .

Two strategies are adopted. The first is based on the C-means clustering algorithm and the second is based on K-means clustering method as shown in Figure 1 and Figure 2.

Clustering data consists of organizing and collecting similar data points into group or cluster. The similarity is estimated by a function that computes the distance between the data points, usually, the Euclidean distance.

In literature, various clustering algorithm was proposed to deal with clustering problem [11] -[14] . Subtractive, C-means and K-means are among the most commonly-used clustering algorithm

We propose in this section to modeling the IM by the two multimodel modeling strategies previously described.

Firstly, we have to collect a rich data base from the measurement of input/output of the IM. The electric motor is 1 kw squirrel cage Induction motor.

The training data set is generated through an experimental set-up that is described by Figure 3. It is used with the help of Matlab/Simulink and DSpace system with DS1104 controller board to collect the database.

The data collection requires the use of speed and current sensors. For that, Hall type sensors are exploited to measure stator currents and an incremental encoder position sensor delivering 1024 pulses per revolution is mounted on the shaft to measure the IM speed.

To test the robustness of the modeling approach we propose to vary the IM parameter and to apply a wide range of loads.

The load is a resistive bank fed by a DC generator that is connected to the IM.

To vary the stator resistances, three variable resistors are linked in series to the motor phases.

A large data set is selected out after input/output measurements at an operating point of 600 rpm.

In this paper, the multimodel modeling strategy is described. Two strategies are developed. The first is on the basis of C-means clustering algorithm and the second is based on K-means clustering algorithm. The two methods are applied in real time to an induction motor at an operating point of 600 rpm submissive to load insertion and parameter variation. A comparative study helps to confirm that the method based on K-means is the most convergent. In future work, to improve the modeling performance the modeling should take into account the total behavior of the induction motor.