Quote:
Originally Posted by Tom Bottiglieri
You note that tau_d = tau_m/r. How does one find R? Do we just choose this? If so, what is a reasonable choice?
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Tom, tau_d is the time constant of your closed loop system.... and that is your choice... usually it is driven by the timing constraints of the shooter design. As in the example at the end of my note we wanted the shooter to be within 5% (I had a typo of 1%) of the target speed in one second. Since this is a first order exponential response the output will have a step response of
v_out = v_in*(1 - exp(- t/tau_d) .
The % error as a function of time is err% = 100*exp(-t/tau_d);
t= tau_d , err%= 37
t=2*tau_d, err% = 14
t=3*tau_d, err% = 5
t=4*tau_d, err% = 2
t=5*tau_d, err% = .7
So to meet the 5% in 1 second we needed 3 time constants to elapse which means 1 sec = 3*tau_d. So tau_d = .333 seconds and that in turn drives r the ratio of tau_m/tau_d.
It is important to note that you must have excess torque to take advantage of the gain increase caused by the PID loop. Our nominal target speed for the key is around 2000 rpm. So we designed the the max speed to be 2.5 times the nominal.
In general, you have a feeling for how much you want to speed up the response of your system. It is this ratio that determines r. Of course r has bounds like any amplified system. I like to keep it under 5 and nominally about 3.
Edit:
The pole/zero placement method I described gives you a lot of gain margin so usually the limiting factor is not stability but rather system saturation caused by large command changes or noise in the command signal. Saturation makes the system nonlinear and the response can no longer be predicted by tau_d. High frequency noise is amplified by KP and can be unevenly rectified by saturation causing a bias offset the error signal and unwanted current transients. So it is difficult to generalize about what gains are tolerable. I know 254 has lots of experience with PID loops and you might share what your experiences are relative to tolerable gains in a velocity loop.