Slide 5 of 23
So our verification problem is this:
- stepper motor system parameters, and
- no stall exists in any possible acceleration scenario
We define a "stall" to be a deviation of pi/N radians from the current desired equilibrium, where N is the number of rotor teeth.
Note that our safety verification is concerned with a fixed initial time interval. (We thus call this an initial safety problem.)
We can simulate a single trajectory in seconds or less. Does this then leave us randomly testing acceleration scenarios in search of an unsafe stalling trajectory? No, we can easily do much better. From our definition of a stall, we have a simple measure of distance from stall: angular displacement from the nearest stall state. Thus we can heuristically rate the relative safety of stepper motor simulation trajectories using the minimum distance to a stall state over the course of the simulation.