PI velocity control of brushless DC motors using the extended dq transformation

This paper is concerned with velocity control in brushless direct current (BLDC) motors. Our control scheme is composed of a classical proportional–integral velocity controller and a proportional electric current controller computed in the extended dq coordinate system. We employ a finite time estimator that has been previously proposed in the literature intended to estimate the unknown back electromotive forces. This estimator has been proven previously to converge locally to the true values. This control strategy is proposed to eliminate torque ripple produced by the fact that back electromotive forces in BLDC motors are nonsinusoidal. We present, for the first time, a formal stability result for this control scheme: (a) the state has an ultimate bound provided that the estimate of the back electromotive forces is close to the true values, and (b) this ultimate bound can be rendered arbitrarily small when the estimate of the back electromotive forces converges to the true values. This result stands when starting from any initial condition such that the finite time estimator is ensured to converge to the true values. We verify our findings through simulations.