I modified the software to sample the current at different offsets from the start of the duty cycle. After 2000 duty cycles, I get a complete picture of the current waveform over a single duty cycle. As long as the system is in a steady state, the waveform is quite repeatable. I used this program to examine the current waveform at different duty cycles and found out why the current measurements are way off during short duty cycles. Take a look at this graph of the current waveform at 25% duty cycle and no load.
Current waveform, 25% duty cycle, no load
From the graph, I realized there is a large positive current spike when the voltage turns on, and a large negative spike when the voltage turns off. When the duty cycle is short, the two spikes run together and make it impossible to measure the current during the on cycle. After studying it for a while, I decided the filtering capacitors I put on the motor terminals are most likely causing the spikes. There is a large current flow each time a capacitor is charged or discharged. I am going to try removing the capacitors to see if that improves the current waveform. It will be a challenge to remove them, though, because when I put them on I wound the wires around the terminals and put a huge blob of solder on them. I could cut them off easily, but then I wouldn’t be able to put them on again.