A periodic adaptive controller for the torque loop of variable speed brushless DC motor drives with non-ideal back-electromotive force

In this paper, an adaptive current controller is proposed for variable speed brushless direct current (BLDC) motor drives to minimize the output torque ripples caused by parametric and periodically varying uncertainties. Phase-to-phase non-ideal back-electromotive force (back-EMF) in BLDC motor changes periodically with respect to the shaft angle, and hence the period of these signals alters depending on the rotor frequency. To address these problems, the uncertain current dynamics of the BLDC motor is reformulated by transforming the time variable, then the periodic adaptive controller employing the instantaneous estimation values of the unknown periodic signal is developed to achieve the torque ripple reduction. The periodic estimation of the non-ideal back-EMF waveform is achieved considering the switching between conduction and commutation periods. Also, the update rules based on direct adaptation for parametric uncertainties are derived, and thus, hybrid differential-periodic adaptation rules are obtained considering the switching phenomenon. Asymptotic convergence of the phase currents to the reference values is proven by an appropriate Lyapunov-Krasovskii function depending on the angular position. Comprehensive numerical simulation studies have been successfully carried out to verify the performance and the effectiveness of the proposed controller for variable speed applications.