| Abstract: | Some analytical results concerning PI controller tuning based on integrator plus time delay models are
worked out and presented. A method for obtaining PI controller parameters, Kp =
k , and, Ti = ,
which ensures a given prescribed maximum time delay error, d max, to time delay, , ratio parameter
= d max
, is presented. The corner stone in this method, is a method product parameter, c = .
Analytical relations between the PI controller parameters, Ti, and, Kp, and the time delay error parameter,
, is presented, and we propose the setting, = c
a ( + 1), and, = a
+1, which gives, Ti = c
a ( + 1) ,
and, Kp = a
( +1)k , where the parameter, a, is constant in the method product parameter, c = . It also
turns out that the integral time, Ti, is linear in, , and the proportional gain, Kp, inversely proportional
to, + 1. For the original Ziegler Nichols (ZN) method this parameter is approximately, c = 2:38, and
the presented method may e.g., be used to obtain new modified ZN parameters with increased robustness
margins, also documented in the paper. |
