Optimization and prediction of step response of brushless DC motor based on grey system theory

Brushless DC motors are widely used in industrial control, automation equipment and other fields, and their response performance plays a decisive role in the overall operation of the system. In order to explore the effect of capacitance C, resistance ${\mathrm {R_{x}}}$ and resistance ${\mathrm {R}}_{1}$ parameters on the response of brushless DC motor, multiple orthogonal test schemes were set up in Multisim simulation software with step signal as input signal and system response characteristics (peak time ${\mathrm {t_{p}}}$, rise time ${\mathrm {t}}_{{\mathrm {r}}}$, maximum overshoot $\sigma \%$) as objective function. At the same time, the gray characteristic of the step response of the brushless DC motor is introduced, the correlation coefficient and correlation degree of the objective function are calculated, and the parameters are optimized by multi-objective optimization, and the optimal circuit design parameters are obtained. The results show that when $\mathrm{C}=3500 \mu \mathrm{~F}$, ${\mathrm {R}}_{{\mathrm {x}}}=2.5 \mathrm{k} \Omega, {\mathrm {R}}_{1}=600 \mathrm{k} \Omega$, the motor response speed and stability state are optimal. In the optimal state, the peak time, rise time and maximum overshoot are $\mathrm{1 7 . 3 3 6 m s}, \mathrm{1 6 . 9 3 3 m s}$ and $0.26 \%$ respectively. The GM ($0, \mathrm{~N}$) grey prediction model is established to accurately predict the step response characteristics of the motor, and the relative error is less than $10 \%$, which is simple and fast.