This is what I have been saying.
I thought I previously posted that any thing less than ten samples per period will not be enough and anything more than a 100 times per period is over kill unless there is a real need. Ron has definately shown that 10X is marginal and less is not fast enough.
The simulator should update more often than .5 seconds. Try again with a .05 second update. After 20 scans per second your simulation is the limiting factor. To make it short. Your 20 and 30 PID updates/period examples are limited by the simulation and do not show the real improvement. I have my simulations update 10 to 100 times faster than the PID update rate.
PIDs do not have to take up a lot of time. 3 multiplies and adds with some limiting and you are done. The PLC is probably filtering data but this too can be merged with the PID's three multiply and adds.
In your examples you found the natural frequency is .0659 HZ or .414 rad/sec. Now if you can compute the damping factor, you can model a second order system in the form:
Gain
 ? WHAT DOES ONE WITH THAT?
s^2+2*d*s+w^2
Where d is the damping factor, s is the Laplace operator and w is the natural frequency in radians/second.
Hint, look at the overshoot!
Now what happens if the SP moves at with frequency components faster than the natural frequency of the system? Or slow must the ramp be to not have the system oscillate?
