Hi, I am building some electronics to control a brushless motor (BLDC). I am studying the motor startup and I need the physical/mathematical model. My page at http://bldc.wikidot.com/p-esc-startup has some work on this subject but I think that something is wrong when I try to simplify the equations of x(t). Who can help? I need to obtain the time values for x=1,2,3,4,... but I am still looking for a good x(t) equation. Some calculus can be done with a 8 bit microcontroller so I can't use some functions...
The way I've seen this done is via a table of time deltas. The first one or two iterations may be backwards so the table takes this into account. After the frist two entries, the time deltas decrease as the array is incrementelly accessed, with the assumption that angular acceleration is constant (however in the real world, it turns out that this table has to be tuned a bit by trial and error). In our case, Bemf should have been present after 7 or 8 "blind" steps, and the switch was made. The iniitial algorithm started with a minimum voltage, then if the blind stepping failed to produce Bemf, the voltage was increased in small steps, and the blind step algorithm repeated. After a success full startup, the working voltage was reduced a bit to be used as the initial voltage for the next startup. There was some tweaking done of table values and voltage change during so the transition from blind to feedback loop was smooth, and by slowy adjusting the step timing versus the first sensing of Bemf.
I don't know that much about motor control, I was mostly observing and helping with the coding effort on how to use the table by another person who was good with motor control, but hadn't done much programming. It was years ago and I was just responding with the issues we encountered.