Applet on this page compares the Closed Loop Pole Zero locations for the 2 methods, shown below, of deriving a sampled version of a type 0 first order system with PI control.

In the first case, the system below has a controller transfer function Gc(s) = K(1 + 1/(Tis)) and the system transfer function Gs(s) = 1/(T1s + 1).

The denominator coefficients for G(z) are the same for both approaches and are given by:-

eg parameters (4.0, 1.0, 2.0, 0.1). Here the difference is negligible.

eg parameters (4.0, 1.0, 2.0, 0.24). Here the difference is also negligible with both systems becoming unstable for K > 8.36.

eg parameters (K, 0.3, 0.2, 0.24). Here the difference is noticeable with the first system becoming unstable for K > 2.44 and the second becoming unstable for K > 2.64.

The applet indicates that only small differences occur when T1 and Ti are unusually small and then the second system performs marginally better.

Gif image below show how the applet should appear.

COPYRIGHT © 2006 Cuthbert Nyack.