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Unread 21-12-2012, 09:01
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Re: Motion Profiling

Quote:
Originally Posted by AustinSchuh View Post
I disagree with this statement.
I think you're right -- I was making an assumption that I did not state in my post. I was assuming that the velocity feedforward gain (your Kv) is sufficient to cause essentially zero steady-state error without an integral component -- if it is less, than it is possible to have no overshoot. Also, I was not claiming that it would be unstable -- it would overshoot once then return to the setpoint in a perfectly stable manner.

Here's where I'm coming from, assuming Kv is as described above (i.e. would cause approximately 0 steady state error with no integral component):

Say you're moving steadily (tracking a target trajectory) at a velocity of 1 (arbitrary units) -- your P, I, and D terms are all approximately zero, since you are at steady state. The Kv term is the majority of your control signal.

Now suppose the target trajectory changes to a velocity of 2 -- this could happen either smoothly or instantaneously. Due to the system's inertia, it will find itself at less than the desired position. Therefore, the control system will correct, trying to bring the state towards the new setpoint.

During this time, the previously-small I term will be growing as the errors accumulate. However, due to the Kv term, the necessary I term to maintain zero steady state error at the setpoint is approximately zero. Since the I term will not begin decreasing until it has overshot, it is guaranteed to overshoot.

This overshoot may or may not be acceptable. Additionally, if Kv is less than the value I've described, then it would only decrease the Ki value necessary to prevent overshoot, and decrease the rise time of the controller, which may be desirable.
 


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