Any mismatch between the real and tuned values of the stator resistance (R8) leads to a degraded performance of the direct torque control (DTC) strategy. The underestimation of R8causes an error in the stator flux and torque estimations, thereby weakening the DTC performance; however, an overestimation of R8can make the DTC unstable. The main objective of this paper is to present a novel estimator based on the model reference adaptive system (MRAS) for online estimation and tracking of R8in the DTC of six-phase induction motors (6PIMs). Voltage and current vectors of 6PIM are mapped into α - β, z1- z2, and o1- o2subspaces, where only the α - β components are related to electromechanical energy conversion. The proposed technique uses additional degrees of freedom, i.e., the z1- z2subspace to estimate R9. The attained merits include simplicity, low computation burden, and low sensitivity to other parameters of the 6PIM. The adaptation law is derived from the Lyapunov stability theory and Popov hyperstability theory. The proposed technique is applied under a duty cycle control based DTC, where z1- z2currents possess reduced amplitudes in comparison with the conventional DTC. The validity of the proposed system is verified by simulation and experimental results.
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Holakooie et al. (2018) studied this question.
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