Universal Motor NN Modelling JOSÉ CARLOS QUADRADO DEEA, ISEL, R. Cons. Emídio Navarro, 1950-072 LISBOA, PORTUGAL CAUTL, Av Rovisco Pais, 1049-001 LISBOA, PORTUGAL Abstract: - The paper presents a hybrid modelling of electrical motors. To improve the performance, the analytical model is combined with Adaptive-Network-based Fuzzy Inference System (ANFIS) to compensate the modelling error. The architecture and hybrid learning procedure is presented. The method is applied to universal motors. In the first step, parameters of analytical model are identified by simple least-square method. Then, the modelling error is compensated by hybrid learning procedure, preserving the meaning of the physical parameters. The reliability of the obtained model is increased. Key-Words: - Modelling, universal motor, neuronal networks 1 Introduction This paper addresses modelling of an actuator unit. The unit consists of a universal motor and air turbine as load. Due to non modelled physical processes (hysteresis, core saturation,…), the analytical model is combined with a black-box model for compensating the modelling error. The identification of such hybrid model is based on a learning stage known from artificial neural networks theory. The structure is usually known in advance, while the parameters are determined by optimisation on input-output data of the process [1]. In the given example, the Adaptive-Network-based Fuzzy Inference System (ANFIS) [2] was used due to its relatively simple implementation in practice. The present paper is organised as follows. The second section describes the ANFIS method with the hybrid learning procedure. It is followed by modelling of the electrical motor in the third section. The analytical model, as well as the principle of modelling error compensation, is also given in this section. In section four some simulation results are presented. Conclusions follow at the end. 2 Adaptive Network Based Fuzzy Inference System 2.1 Structure Lets consider a system with two inputs x and y and one output z = f. The system can be described by two fuzzy rules of first-order Sugeno-Takagi type:  if x is A 1 and y is B 1 then f 1 =p 1 x+q 1 y+r 1  if x is A 2 and y is B 2 then f 2 =p 2 x+q 2 y+r 2 The same system can be represented as an Adaptive- Network-based Fuzzy Inference System (ANFIS) as shown on figure 1. Figure 1: ANFIS structure Adaptive nodes include parameters and are denoted as squares. In the learning procedure, the parameters change accordingly. Fixed nodes are denoted as circles and have no parameters. Their function is to perform the predefined operation. The directed neural networks include 5 levels. The structure and functions of particular levels are as follows: Level 1: Each node i on this level is adaptive with the membership function given by (1) (1) is a degree of membership of the variable x to linguistic terms A i , which are described by their membership functions. The membership functions µ A i (x) are usually defined as bell functions (2).