[AustinSchuh]

Originally Posted by techhelpbb

Yeah okay. Now in reality when you set the I and D to zero whatever those units are supposed to be, not only does it not reach the set point even with a small value, but when you make the P value too large it overshoots and becomes unstable.

Physics dictates that this is true.

Here are the differential equations governing a motor, if you ignore the effect of the inductance in the motor (a pretty good assumption for most things.) I'll stick with differential equations to make it easier to follow rather than using the laplace transform.

V - Km * d/dt theta  = R I
Kt I =  torque

Lets connect that motor to a rotating mass, with a moment of inertia of J for simplicity.

torque = J * d^2/dt^2 theta

Lets then connect it up to a P controller.

V = P * (goal - d/dt theta)

Plug that into the system of equations above, and simplify a bunch.

P * goal - R / Kt * J * d^2/dt^2 theta = d/dt theta * (P + Km)

At steady state, d^2/dt^2 theta = 0, so this simplifies to

goal * P / (P + Km) = d/dt theta

This says that you will only get to the goal if you crank the P constant up to infinity, which isn't practical. When you break the assumption that you are working in continuous time with a perfect system, it goes unstable. So, the loop is behaving exactly like I would expect it to.

A similar analysis can be used to show that you absolutely need the I term in order to get 0 steady state error. I can go through that math if it isn't clear. Treat the I term when doing a velocity loop as if it were the P term when you tune a position loop, and the P term as though it were the D term when tuning a position loop.