Several methods have been proposed to eliminate the low-frequency torque pulsations for BLDC motor drives such as Fourier series analysis of current waveforms and either iterative or least-mean-square minimization techniques. Most methods do not consider the flux linkage control, therefore possible high-speed operations are not feasible. In this work, a novel and simple approach to achieve a low-frequency torque ripple-free speed and flux control with maximum efficiency based on dq reference frame similar to the permanent magnet synchronous motor (PMSM) drives is presented. The electrical rotor position is estimated using winding inductance, and the stationary reference frame flux linkages and currents. Moreover, this method also permits to regulate the varying signals. Simple voltage vector selection look-up table is designed to obtain fast torque and flux control. Furthermore, to eliminate the low-frequency torque oscillations, two actual and easily available line-to-line back- EMF constants (kba and kca) according to electrical rotor position are obtained offline and converted to the dq frame equivalents using the new Line-to-Line Park Transformation. Then, they are set up in the look-up table for torque estimation.