# Index of /skoge/publications/2003/tuningPID/smooth_tunings

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S. Skogestad,
"Tuning for Smooth PID Control with Acceptable Disturbance Rejection",
Ind. Eng. Chem. Res. 2006, 45, 7817-7822.
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You may be familiar with my SIMC tuning rules from my 2003-paper in Journal of Process Control.
For a first-order with delay plant (gain k, delay theta, time constant tau1), we get the PI-settings:
(1) Kc = (1/k) (tau1/(tauc+theta)),
(2) tauI=min[tau1,4(tauc+theta)],
For details see http://www.nt.ntnu.no/users/skoge/publications/2003/tuningPID/
There is one tuning parameter - the closed time constant, tauc.
In the 2003-paper I consider the case with "tight" tuning subject to achieving
reasonable robostness (Gain Margin about 3) and I recommend to use: tauc=theta = delay.
This is actually a minimum value, that is, the recommendation is
taucmin = theta
However, the choice tauc=taucmin=theta may be a bit aggressive,
so in practice one often uses a "smoother" tuning, that is, tauc > theta.
But tauc should not be too large, because otherwise the output y will go out of bound
when there are disturbances d.
This is the topic of the present 2006-paper.
The recoomendation is to use
Kc > Kcmin = u0/ymax
where ymax = max. allowed deviation in the output y
u0 = required input change to reject the disturbance(s) d
Subsituting Kcmin into (1) one can the obtain taucmax, and we end with a region for tauc:
taucmin ("tight") < tauc < taucmax ("smooth")
Please send me feedback on use of these rules - especially in industrial practice!
- Sigurd Skogestad