Robust Design of a LEM by Means of Interval Taylor Extension Biagio De Vivo, Patrizia Lamberti * and Vincenzo Tucci Dept. of Electrical and Electronic Engineering - University of Salerno - ITALY *Corresponding author: via Ponte Don Melillo, I-84084, Fisciano (SA) ITALY, plamberti@unisa.it Abstract: In this paper the Robust Design of a Linear Electric Motor (LEM) is performed. A Robust Design is a set of nominal parameters that satisfies the customer constraints with uncertain parameters. In particular it is possible to obtain the Most Robust Stationary Design (MRSD) of a Performance Function (PF) by looking at the minimum range of the Interval Extension of its Taylor’s series. Furthermore an analytic expression of the PF is required, and, if it does not exist, as in the case of electromagnetic systems design, a suitable Interpolation of the PF (IPF) is necessary. It can be obtained by means of a good and manageable FEM software. To this aim, the force of the LEM is rewritten as a MATLAB ® function of three geometric parameters and the communication with FEMLAB3.1 is used to perform the IPF. The MRSD is found as the nominal set that minimizes the variation of the IPF due to the uncertainty on the nominal parameters. Keywords: Robust design, uncertainty parameter, Interval Analysis, Electromagnetic module. 1. Introduction In this paper the Robust Design of a Linear Electric Motor (LEM) of the moving coil type given in the Electromagnetic Module of FEMLAB 3.1 is performed by using the Interval Taylor Extension [1]. A Robust Design is a set of nominal parameters that satisfies the customer constraints also in presence of a given tolerance on the parameters [2]. It can be obtained by looking at the range amplitude of the system Performance Function (PF): the lower is the range amplitude the grater is the robustness. A novel procedure has been recently introduced to obtain information about the range of a function by applying the Interval Arithmetic [3] on its Taylor series, i.e. by performing the so called Interval Taylor Extension (ITE) [4]. By looking at the minimum of the amplitude of the ITE it is possible to select the Most Robust Stationary Design (MRSD) of a system [5]. It corresponds to adopting a worst-case robustness index [6] in which the robustness of a nominal solution is linked to the range amplitude of the function that describes the system performance for a given parameter’s variation: the smaller is the amplitude of the range, i.e. the amplitude of the co-domain, the bigger is the robustness of the solution [7]. To apply the method an analytic expression of the PF is required but, unfortunately, in the design of electromagnetic systems this is rarely available and a numerical solution is requested. Furthermore, it is possible to make use of a suitable Interpolation of the PF (IPF) if a good and manageable FEM software is employed: a MRSD could be carried out on it by applying the ITE method. To this aim, the LEM solution is rewritten as a MATLAB ® function and the communication between FEMLAB3.1 and MATLAB ® is used to perform a Response Surface Method (RSM) [8] in order to obtain the IPF as a function of three geometric parameters: primary pole width l ps , secondary pole height h pi and primary pole height h ps . By applying on the obtained IPF the ITE, the MRSD is found as the nominal set of l ps , h pi and h ps that minimizes the variation of the force. The reliability of the results is then checked by using a Monte Carlo approach. 2. The IPF of the LEM’s force The Performance Function (PF) describes the device performance as a function of ν design parameters, ( ν x x x x , , , 2 1 L = . If the performance is obtained as a solution of a FEM software, it is known as discrete way data points on which a suitable intepolation can be performed. This is the case of the force of a LEM as a function of the geometric parameters. LEMs are electromechanic components performing linear motion without any conversion system from the rotational to linear moving form. They consist of a fixed primary system and a secondary moving part. The primary is a permanent magnet made up of a double line of magnets with alternate polarity, placed on a iron support with a U-form, corresponding to the pst part in Figure 1. The