1551-3203 (c) 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2020.2964876, IEEE Transactions on Industrial Informatics IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. XX, NO. XX, XX XX 1 A Comprehensive Comparison of Extended and Unscented Kalman Filters for Speed-Sensorless Control Applications of Induction Motors Recep Yildiz, Student Member, IEEE, Murat Barut, Member, IEEE, and Emrah Zerdali, Member, IEEE Abstract—In this paper, the real-time comparison of extended and unscented Kalman filter algorithms, which estimate the stator stationary axis components of stator currents, the stator stationary axis components of rotor fluxes, the rotor mechanical speed, and the load torque including viscous friction term, are performed under different operating conditions for speed- sensorless control applications of induction motors (IMs). Thus, it is clarified which algorithm is more suitable for state and parameter (load torque) estimation problem of IMs. For this purpose, four different real-time experimental tests have been carried out, which examine the effect of noise covariance ma- trices, parameter changes, sampling time, and computational burdens on estimation performance of both algorithms. Unlike the current literature, remarkable comparison results have been obtained. Index Terms—Extended Kalman filter, Induction motor, Speed- sensorless control, State estimation, Unscented Kalman filter I. I NTRODUCTION S PEED-SENSORLESS control of induction motors (IMs) has long been in the interest of industries and nowa- days this attention has increased due to the electric vehicles. As well-known, estimation algorithms directly affects speed- sensorless drive performance. However, the performance of estimation algorithms deteriorates due to the changing IM parameters and unknown load inputs. To overcome those un- desired effects, different model-based methods such as open- loop estimators [1], model reference adaptive systems [2], [3], full-order observers [4], [5], Luenberger observers [6], [7], extended Kalman filters (EKFs) [8], [9], unscented Kalman filters (UKFs) [10], [11], sliding-mode observers [12], [13], etc., are introduced to the literature. Unlike the other methods, EKF and UKF algorithms pro- pose a stochastic approach to nonlinear state estimation prob- lems, and the uncertainties and nonlinear relations in the IM model harmony with the stochastic nature of EKF and UKF algorithms [14]. The difference between EKF and UKF algorithms is that EKF uses linearization process ignoring high-order terms in the Taylor series and requiring Jacobian matrix calculation while UKF utilizes the unscented transfor- mation (UT). There are a very limited number of studies [10], [11], [15]–[17] comparing both algorithms for state estimation problem of IMs. In [10], EKF and UKF algorithms, which use fifth-order IM model assuming the speed as a constant R. Yildiz, M. Barut, and E. Zerdali are with the Department of Electrical and Electronics Engineering, Ni˘ gde ¨ Omer Halisdemir University, Ni˘ gde, 51240 Turkey (e-mails: recep.yildiz@mail.ohu.edu.tr, mbarut@ohu.edu.tr, ezerdali@ohu.edu.tr) parameter, are compared both in simulation and experimental. It is emphasized that UKF is easier to implement and has a higher convergence. Moreover, it is stated that low sampling time can lead to unstable filter performance in EKF due to the linearization. Unlike [10], Kumar et al. [11] assumes the speed as a dynamic state instead of a constant state with the use of the equation of motion. Here, the information of load torque is required and it has been measured with a torque transducer in this paper. However, it does not seem like a logical option because of the fact that torque transducer is more expensive equipment than encoder. Also it increases size of drive and needs additional mechanical works and wiring. As a result, the authors are noted that EKF remains as the best alternative compared to UKF for speed-sensorless control of IMs. In [15], different from [11], the load torque is estimated as an additional constant state, instead of measuring. Furthermore, UKFs using four different UTs are compared with EKF and it is concluded that UKF provides more robust estimation performance according to EKF. The same IM model in [15] is used in [16] and the comparison of square root UKF (SRUKF), standard UKF, and EKF algorithms are performed. It is speci- fied that SRUKF and UKF have higher estimation performance than EKF, but require more computational load. In [17], it is emphasized that EKF and UKF based control algorithms provide similar dynamic performance under step variations; moreover, UKF has a higher estimation performance under stochastically varying load torque disturbance due to separate optimization of the covariance matrices for EKF and UKF by using both current and speed errors. Since meta-heuristic methods guarantee results close to optimum values in each run, different optimized covariance matrices have been found for both algorithms leading to performance differences in [17]. The main contribution of this paper is to compare EKF and UKF algorithms, which estimate the stator stationary axis components of stator currents (i sα and i sβ ), the stator stationary axis components of rotor fluxes (ϕ rα and ϕ rβ ), the rotor mechanical speed (n m ), and the load torque (τ l ), under different operating conditions; Differently from the existing studies [10], [11], [15]–[17], the comparisons in this paper are done to reveal and clarify the conflicts or disagreements in the literature. The first test involves the comparison of both algorithms using the same Q and R matrices under different operating conditions. The second test examines the effect of parameter changes on estimation performance of both algorithms. The third comparison investigates the effect of sampling time on the estimation performance of both