PRZEGLĄD ELEKTROTECHNICZNY, ISSN 0033-2097, R. 92 NR 12/2016 249 Laaredj GHAOUTI 1 , Mohamed BOURAHLA 1 , Nadir BOUCHETATA 1 University of sciences and the technology of Oran -Mohamed Boudiaf - (USTO-MB) BP 1505 EL M’ naouer Oran, Algeria doi:10.15199/48.2016.12.64 Sensorless field oriented control of PMSM based on the extended KALMAN filter observer Abstract. in this paper, a study of sensorless field oriented control applied to surface-mount permanent-magnet synchronous motor is presented, the motor has been described in a stationary two-axes reference frame (α,β), to overcome the uncertainties the internal, measurement noises, the non zero initial rotor position and the dynamic nonlinearity of PMSM, the extended kalman filter (EKF) is used as a robust observer. The speed and rotor position estimation of PMSM drive are obtained through an EKF algorithm, by simply measurement of the stator line voltages and currents. Good state estimation with EKF observer is proved by the simulation results. Streszczenie. Artykuł poświęcony jest bezczujnikowemu sterowaniu silnikiem synchronicznym z magnesami trwałymi. Jako odporny obserwator jest użyty filtr Kalmana. Prędkość I pozycja wirnika są określane na podstawie algorytmu filtru prze pomiar napięcia I prądu stojanas. Bezczujnikowe sterowsanie silnikiem synchronicznym bazujące na filtrze Kalmana Keywords: Permanent magnet synchronous motor (PMSM), Field Oriented Control (FOC), Sensorless Speed Control, observer, observability, state estimator, Lie derivative, Extended Kalman Filter (EKF). Słowa kluczowe: silnik synchroniczny, sterowanie bezczujnikowe, filtr Kalmana Introduction Permanent Magnet Synchronous Machines (PMSM) are successfully used in different domains for their numerous advantages over other kinds of traditional motors such as DC motors or induction motors. These advantages include a simple structure, small size, high speed, high power density, high efficiency and large torque to inertia ratio, etc [1][4]. Despite of the advantageous features, high-performance PMSM drive characterized by the fast and precise speed response is still a difficult task, since the control performance is greatly affected by the uncertain motor parameters, load variation and nonlinear dynamical behaviour with strong coupling between the rotor speed and the stator currents [8][10]. Vector control technique is the most popular control strategy for the high performance control of PMSM in the synchronous frame, and three proportional–integral (PI) algorithms are conventionally adopted as speed and current controllers, one for the outer speed control loop and the other two for the inner current loops[2][11]. In vector control of a PMSM the rotor position must be known instantaneously. This can be achieved by using a position sensor. The cost of mechanical sensors, the difficulty to place them, and the lack of reliability of the motor encourage researchers to avoid their use [3][6]. There are different solutions to evaluate the mechanical variables of the motor, three different categories can be distinguished [3][9]: - Techniques based on the machine’s physical properties, - Back-EMF estimation based techniques, - State observers and extended Kalman filter (EKF). The EKF algorithm is a suboptimal recursive estimation algorithm for nonlinear systems. It processes all available measurements, to provide a quick and accurate estimate of the state variables, and also achieves a rapid convergence. This is done using the following factors: - A knowledge of the system and measurement device dynamics. - The statistical description of the system noises, disturbances, measurement errors, and uncertainties in the system model. - Any available information about the initial conditions of the state variables. - However the EKF algorithm is computationally intensive and all of the steps involved require vector and matrix operations. PMSM model for vector control In the dq axis coordinates, rotating synchronously with the rotor, the voltage, flux linkage, torque and mechanical equations of the PMSM are [5][7]: (1)                            r d d q q q s q q q d d d s d i L dt i d L i R v i L dt i d L i R v (2)         q q q r d d d i L i L    (3)     q d q d q r i i L L i p T          2 3 (4)     r q d q d q r T i i L L i p f dt d J             2 3 where, i d , i q , d- and q-axis components of armature current, v d , v q , d- and q-axis components of terminal voltage,  d ,  q , d- and q-axis components of flux linkage, L d , L q , d- and q- axis components of armature self inductance,  r flux linkage due to permanent magnet, R s armature resistance,  and Ω are the rotor electrical angle speed and the rotor mechanical speed respectively, p number of pole pairs, J rotor inertia, f viscous damping coefficient, T output torque and T r resistance torque. Vector control In FOC, the measured currents are firstly transformed into the d and q axes. The field orientation consists in setting i d = 0. Fig. 1. Then the torque of the PMSM is produced only by the constant flux ( r ) the permanent magnet and the torque generating current i q , as well as of the PMSM. A completely linear system results, and linear control theory applies [6]. Extended Kalman Filter observer designing The EKF is a suboptimal estimator of dynamic nonlinear systems states. To apply this algorithm, the nonlinear state motor nonlinear state equations are written in the following form [7][12]: (5)              ) ( ) ( ) ( ) ( ), ( ), ( k k k t v t x h t y t w t t u t x f dt dx