Question about providing time responses of controllers

Hey Josh,

I'm a little confused about the section in this lab where we are asked to "provide the time responses of the three controllers when the additional external load is applied."

Is this something we are being asked to mathematically model? Or is this something we should use derive from our empirical data from the bicycle light measurements? The part of the lab where we pressed the eraser against the motor seems terribly informal and not suitable for analysis.

If I am correct about the above portion, how would we tackle the error analysis? I would assume that mathematical models are not subject to error. If the time response is supposed to be derived using discrete data, I am guessing we are simply supposed to curve fit the constants and plug them in to a general solution to a differential equation.

Actually I believe all the professors want here is just an direct comparison of the unloaded response to the loaded response of the motor, i.e. the settling time to reach the steady state speed. Additionally, you can compare the closed-loop time constants of the unloaded and loaded cases to get an idea of the motor responses of the controllers relative to one another.

You won't actually be using the data from the momentary disturbance test you conducted in the report, so you don't have to worry about that.

Similarly my question is can we get the loaded response times (ie finding time constants), straight from the data? What I mean by that is using the steady state value I can take 37% (meant 63%) of that and find a data point corresponding to that speed. This gives a time constant value, but is this method the intended way they want us to find the values for the loaded data?

That is one way to get the time constant, and another (the preferred) is the method from slide 21.