Harmonic approximation of velocity oscillations in electrical drives

The accuracy of an electrical drive moving at constant velocity significantly depends on the performance of the applied velocity estimation algorithm. In this paper, this dependence is investigated for estimation algorithms, which use digital filters and quantized encoder measurements. Assuming that the velocity controller, the estimation algorithm and the input-output behavior of the drive from desired torque to velocity are linear, the velocity controlled electrical drive is shown to have almost always no steady-state. Moreover, the velocity is found to be oscillating with a bounded oscillation amplitude. As the main result, a formula is derived which yields an approximation of the velocity oscillation in terms of Fourier series. The formula reveals the influence the encoder resolution and other electrical drive parameters have on the characteristics of the velocity oscillation. To verify the relations predicted by the formula, simulations of an electrical drive are performed.