Lab 7a Tips: Brushless DC Motor

In-lab

A snapshot of phasevolt data.
A snapshot of sensor data.
When finding a relationship between v_ag and v_hall1, remember that the relationship depends on the value of V_DC as given in the MATLAB model. Your answer must account for this. In other words for the relationship v_ag=f(V_DC,v_hall1), find the function f.

The Fourier series of a 2π-periodic function f(x) that is integrable on [-π,π], is given by

where

and
To relate v_s to V_dc, you need to find the fundamental component of the Fourier series of the functions v_as, v_bs and v_cs. The fundamental component is the component with the lowest frequency, specifically

To solve for the coefficients a₀, a₁ and b₁ from the equations above, the integral must be broken down into a sum of integrals over continuous regions.
φ_v is the angle between V_as and e_as. To find this angle, compare zero-crossings near the middle of both curves. If you triggered the oscilloscope on channel 1, then V_as should be crossing zero with a rising edge in the exact middle of the plotted time. e_as will cross zero with a rising edge some small time after this point. Measure this difference in time and convert it from seconds to degrees or radians by dividing by the time in one period and multiplying by 360 (for degrees) or 2π (for radians).