Rockwell's Pos & Vel PID Forms

I've got quite a few questions to fire.



In the velocity form, why does the P term now act like the D term in the positional form?


The D term in the velocity form is a nifty equation, but is this an example of second derivative tuning? Can it be extended to n-3?


I just had a hard time explaining to someone that with this velocity form you have to tune I like P and now P like D and P doesn't exist now, but D now does this cool acceleration thing... etc.
Would the attached have redundant terms or would this keep the classic PID understanding?


Do you guys have any resources that have other error terms or algorithm forms?


(Edit) Just to get it out of the way, I know t should probably be squared in that last term.

With the possible exception of how anti-windup is done, roundoff-error in the sixth or seventh decimal place, and how the tuning is done (e.g. Ki vs. Ti, although that is usually a dependent gains vs. independent gains difference), Rockwell's Positional and Velocity forms of the PID equation are arithmetically, and behave, exactly the same.

Cf. this link.


And this link and this link also.

Taylor Turner said:

In the velocity form, why does the P term now act like the D term in the positional form?

Click to expand...

This works because the P term is being integrated.

The D term in the velocity form is a nifty equation, but is this an example of second derivative tuning? Can it be extended to n-3?

Click to expand...

Yes, this is necessary for underdamped hydraulic systems. The RMC has a second derivative gain which is applied to errors between the target and actual accleration.

I just had a hard time explaining to someone that with this velocity form you have to tune I like P and now P like D and P doesn't exist now, but D now does this cool acceleration thing... etc.

Click to expand...

Sometimes explaining the difference between the two forms of PID is hard.
drbitboy is correct. The I, P and D gains are tuned the same way and usually provide the same results.

Would the attached have redundant terms or would this keep the classic PID understanding?

Click to expand...

Keep the same understanding.

Do you guys have any resources that have other error terms or algorithm forms?

Click to expand...

Again, we have a second derivative gain that is multiplied by the difference between the target and actual acceleration. The problem with this is calculating the actual acceleration

(Edit) Just to get it out of the way, I know t should probably be squared in that last term.

Click to expand...

??