Let's say you have a closed loop power control system that is making adjustments every second proportional to the error from a target. Also, the readings it gets are delayed by ten seconds. For what values of the proportional factor is the system stable?
Any help is greatly appreciated.
Thank you.
As long as the loop gain is less than 1, a sustained echo is impossible. But the loop gain has to include the proportional gain factor, and the output signal to ultimate input signal factor.
For example, if 10% change on the output increase produces an eventual 30% input signal increase, then the proportional gain on error must be less than 1/3rd. This assumes that the loop delay is much larger than any time constant that rolls off high frequencies. A total loop gain of 1/2 is often near optimum for a dead time dominated loop. This is because each echo of a disturbance is half as large as the previous one.
If the controlled process includes, say, a 1 minute time constant, that filters the output step response as seen by the process measurement, then higher proportional gain is useful. For more details on this, you might read the original Ziegler and Nichols paper on the subject, reproduced here:
It depends on the signal that your trying to control. If its a slow moving signal then 10 seconds could be fine. If not then a lot could happen in that
10 seconds so that it actually makes it worse. Your signal might be -1 at time t = 0 and at time t = 10 its +1. Your control see's -1 but adds a to +1 making it larger. This could happen indefinately and one would get uncontrol oscillations unless there is some type of dampening(which eventually there will be). The "adjustments" could always be off and just make the signal grow without bound. If, say, you know the signal is always positive then this can't happen. It also can't happen if the frequency your sampling at is much larger than the bandwidth of the signal. If its periodic then it can work much better but you still might have issues.I'm not sure if I understand what your getting at though but maybe this is close.
Jon
looks like about .15 loop gain is the limit .04 seems optimal
no doubt there are equations to describe this system. I got my answers by plugging your description into a spreadsheet and duplicating it down 1000 rows and then graphing the result.
Bye. Jasen
Interesting. Is it possible to devise some type of transfer function to represent this system?
Thank you.
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