IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 59, NO. 11, NOVEMBER 2012 4197 Real-Time Implementation of Bi Input-Extended Kalman Filter-Based Estimator for Speed-Sensorless Control of Induction Motors Murat Barut, Member, IEEE, Ridvan Demir, Emrah Zerdali, and Remzi Inan Abstract—This paper presents the real-time implementation of a bi input-extended Kalman filter (EKF) (BI-EKF)-based estima- tor in order to overcome the simultaneous estimation problem of the variations in stator resistance R s and rotor resistance R ′ r aside from the load torque t L and all states required for the speed-sensorless control of induction motors (IMs) in the wide speed range. BI-EKF algorithm consists of a single EKF algorithm using consecutively two inputs based on two extended IM models developed for the simultaneous estimation of R ′ r and R s . There- fore, from the point of real-time implementation, it requires less memory than previous EKF-based studies exploiting two separate EKF algorithms for the same aim. By using the measured stator phase voltages and currents, the developed estimation algorithm is tested with real-time experiments under challenging variations of R s , R ′ r , and t L in a wide speed range; the results obtained from BI-EKF reveal significant improvement in the all estimated states and parameters when compared with those of the single EKFs estimating only R ′ r or R s . Index Terms—Extended Kalman filter, induction motors (IMs), load torque estimation, rotor and stator resistance estimation, sensorless control. I. I NTRODUCTION T HE performance of speed-sensorless control of induction motors (IMs) relies upon how accurately state estimations of IM are performed. In fact, these estimations are adversely affected by the temperature and frequency-dependent variations of R ′ r and R s as well as unknown load torque. Thus, for a suc- cessful speed-sensorless control application of IM, estimation algorithms must be robust against those variations; this fact can be discovered by inspecting the excellent papers such as [1]–[3]. Various estimation methods based on modified conventional methods [4], model reference adaptive system [5], neural net- work [6], sliding mode [7], and adaptive full-order Luenberger Manuscript received November 1, 2010; revised August 5, 2011 and September 13, 2011; accepted October 27, 2011. Date of publication December 7, 2011; date of current version June 19, 2012. This work was supported by the Scientific and Technical Research Council of Turkey (Türkiye Bilimsel ve Teknolojik Ara¸ stırma Kurumu–TÜBÍTAK) under the research grant of EEEAG-108E187. M. Barut, E. Zerdali, and R. Inan are with the Department of Electrical and Electronics Engineering, Nigde University, 51245 Nigde, Turkey (e-mail: muratbarut27@yahoo.com; mbarut@nigde.edu.tr; ezerdali@nigde.edu.tr; rinan@nigde.edu.tr). R. Demir is with the Electrical and Energy Department, Bor Voca- tional School, Nigde University, 51700 Nigde, Turkey (e-mail: ridvandemir@ nigde.edu.tr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIE.2011.2178209 observer [8] have been proposed very recently in the literature. Among these studies, [4]–[6] are sensitive to the variations in R ′ r and R s , while [7] and [8] are easily affected by the R s or R ′ r variations, respectively; thus, they still need improved performance under both resistance uncertainties. On the other hand, Faiz and Sharifian [9] declare that the simultaneous estimation of R ′ r and R s causes instability. Considering the studies [10]–[13], which attempt to perform both R s and R ′ r estimations in a speed-sensorless case, reported so far, Karanayil et al. [10] do not present the result of R ′ r estimation together with that of R s and angular velocity, ω m , in the speed-sensorless case. In [11], R s and ω m estimations cannot be simultaneously conducted at no load or when the load torque is not sufficiently high, and a high-frequency signal is also injected on the magnetizing current command in order to perform R ′ r estimation. Moreover, the estimation algorithms in [12] and [13] are only applicable whenever the speed-sensorless control system is in steady state, which is declared by authors. On the other hand, extended Kalman filter (EKF)-based solutions have been also investigated by the studies such as in [14]–[17] for the simultaneous estimation problem of R ′ r , R s , and ω m regardless of load conditions. For the solution of the problem, Barut et al. [14] and Bogosyan et al. [15] use braided EKF algorithms tested with real-time experiments while Barut et al. [16] utilizes switching EKF algorithm con- firmed by simulations. For the same purpose, Barut [17] also introduces a novel estimation technique called as bi input- EKF (BI-EKF) which is only verified by some simulation tests. Both braided/switching EKF and BI-EKF provide an accurate estimation of an increased number of parameters than would be possible with a single EKF algorithm, but braided/switching EKF uses two separate EKF algorithms in a braided/switching manner while BI-EKF includes a single EKF algorithm with the consecutive operation of two inputs obtained from two ex- tended IM models developed for the simultaneous estimation of R ′ r and R s . In other words, BI-EKF includes a single standard EKF with consecutive use of two inputs calculated from the two extended IM models. Thus, it differs from the past EKF- based studies [14]–[16] involving the successive utilization of two EKF algorithms. Thus, BI-EKF technique has an important advantage over those studies [14]–[16] because it reduces by approximately two times the required memory area of the studies in [14]–[16] for embedding observer algorithm and it provides easier debugging and design than the studies in [14]– [16]. These advantages make BI-EKF more attractive from the 0278-0046/$26.00 © 2011 IEEE