1664 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 54, NO. 3, JUNE 2007 Sensorless Indirect-Rotor-Field-Orientation Speed Control of a Permanent-Magnet Synchronous Motor With Stator-Resistance Estimation Mohamed Rashed, Peter F. A. MacConnell, A. Fraser Stronach, and Paul Acarnley Abstract—Efficient and precise sensorless speed control of a permanent-magnet synchronous motor (PMSM) requires accu- rate knowledge of rotor flux, position, and speed. In the litera- ture, many sensorless schemes have been presented, in which the accurate estimation of rotor flux magnitude, position, and speed is guaranteed by detecting the back electromotive force (EMF). However, these schemes show great sensitivity to stator resistance mismatch and system noise, particularly, during low-speed opera- tion. In this paper, an indirect-rotor-field-oriented-control scheme for sensorless speed control of a PMSM is proposed. The rotor-flux position is estimated by direct integration of the estimated rotor speed to reduce the effect of the system noise. The stator resistance and the rotor-flux speed and magnitude are estimated adaptively using stable model reference adaptive system estimators. Simple stability analysis and design of the estimators are performed using linear-control theory applied to an error model of the PMSM in a synchronous rotating reference frame. The convergence of rotor position- and speed-estimation errors to zero is guaranteed. Experimental results show excellent performance. Index Terms—Parameters identification, permanent-magnet synchronous motor (PMSM), sensorless control, speed control. NOMENCLATURE ψ r Rotor-flux space vector. i s Stator-current space vector. u s Stator-voltage space vector. ω r Rotor angular speed in electrical radians per second. ρ r Rotor position. ω e Synchronous rotating-reference-frame speed in electri- cal radians per second. ρ e Position of synchronous rotating reference frame in elec- trical radians. ψ r Actual rotor (magnet)-flux magnitude. R s Stator-winding resistance. L s Stator-winding inductance. Manuscript received April 6, 2005; revised January 3, 2006. M. Rashed is with the Electrical Engineering Department, Mansoura Univer- sity, Mansoura 35516, Egypt (email: m.rashed@eng.abdn.ac.uk). P. F. A. MacConnell is with the School of Engineering and Physical Sciences, University of Aberdeen, Aberdeen, AB24 3UE, U.K. A. F. Stronach was with the School of Engineering and Physical Sciences, University of Aberdeen, Aberdeen, AB24 3UE, U.K. He is now with Genbase Information Systems, Aberdeen, AB24 3UE, U.K. P. Acarnley is with the School of Engineering, Robert Gordon University, Aberdeen, AB10 1FR, U.K., and also with the University of Aberdeen, Aberdeen, AB24 3UE, U.K. Digital Object Identifier 10.1109/TIE.2007.895136 x, s Subscripts, real, and imaginary components in synchro- nous rotating reference frame. α, β Subscripts, real, and imaginary components in stator reference frame. I. I NTRODUCTION P ERMANENT-MAGNET synchronous motors (PMSMs) are known to provide higher torque per unit volume and better efficiency than induction motors, while improvements in the properties of permanent-magnet materials have increased their viability. Recently, sensorless PMSM drives have received increasing interest for industrial applications where there are limitations on the use of a position sensor. The elimination of the position sensor reduces the cost of the drive and increases the overall system ruggedness and reliability. High- performance operation of sensorless PMSM drives mainly re- lies on accurate knowledge of the rotor-magnet flux magnitude, position, and speed. The sensorless rotor-position estimation techniques can be classified into two major groups: the motor- model-based and the rotor-saliency-based techniques. The latter are suitable only for the interior PMSM (IPMSM). Most of the motor-model-based techniques detect the back-EMF vec- tor, which holds information about the rotor position and speed, using either open-loop estimators [1]–[3] or closed-loop estimators/observers [4]–[9]. In other motor-model-based tech- niques, the rotor-flux vector is directly estimated [10], [11]. Moreover, adaptive observers have been used to estimate the stator current, the rotor speed, and the rotor position [12]–[15]. Extended Kalman filters (EKF) have also been proposed for ro- tor speed and position estimation [16], [17]. Although the EKF algorithm is stable and well known, the EKF is computationally intensive and requires proper initialization. Furthermore, model reference adaptive system (MRAS) has been used extensively for combined rotor flux and speed estimation in induction motors [18]. In [1], open-loop back-EMF-based position and speed estimators have been considered. The scheme is sensitive to the system noise and to the stator resistance mismatch. In [4], the rotor-flux vector is estimated by direct integration of the calculated back EMF. The estimated rotor-flux vector is corrected adaptively by utilizing the error between measured and estimated stator currents to reduce the effect of integration drift. However, the scheme is not suitable for low-speed operation. On the other hand, in [12], an identity observer has been proposed to estimate the rotor speed by utilizing the 0278-0046/$25.00 © 2007 IEEE Authorized licensed use limited to: Newcastle University. 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