P Controllers G

The term "proportional band" (1/K) is often used to describe P controllers. When expressed as a % it represents the % change in the error which gives an output which is linearly proportional to the error.

Open and Closed loop transfer functions for 1st order is

G(s) = K/(T1s + 1), C(s)/R(s) = K/(T1s + (1 + K))

For 2nd order is

G(s) = K/((T1s + 1)(T2s + 1)), C(s)/R(s) = K/((T1s + 1)(T2s + 1) + K))

For 3rd order is

G(s) = K/((T1s + 1)(T2s + 1)(T3s + 1)), C(s)/R(s) = K/((T1s + 1)(T2s + 1)(T3s + 1) + K))

For 4th order is

G(s) = K/((T1s + 1)(T2s + 1)(T3s + 1)(T4s + 1)), C(s)/R(s) = K/((T1s + 1)(T2s + 1)(T3s + 1)(T4s + 1) + K))

For the parameter values (K, 1.0, 1.0, 1.0, 1.0, 2.0), the 4th order system becomes unstable for K > 4 and the third order becomes unstable for K > 8.0. For the ramp response, since all systems are type 0, then the offset increases linearly with t.

Gif images below show how 2 of the applets should appear.

COPYRIGHT © 2006 Cuthbert Nyack.