Applets show Bode plot for a first Order Type 0 system with a PI Controller .

eg parameters (K, 1.0, 1.5, Ts). The range of K for stability depends on Ts.

For Ts = 0.2, the closed loop response reaches its maximum at angular frequency 31.4rad/s(half the sampling frequency) with K = ~ 10.1. At this frequency the magnitude reaches 0dB and the phase is -180°. The system is unstable for K > 10.1.

For Ts = 0.16, the closed loop response reaches its maximum at angular frequency ~20rad/s(half the sampling frequency) with K = ~ 12.5. At this frequency the magnitude reaches 0dB and the phase is -180°. The system is unstable for K > 12.5.

For Ts = 0.471, T1 = 2.9, Ti = 0.2, the closed loop response reaches its maximum at angular frequency ~3.3rad/s(one quarter the sampling frequency) with K = ~ 5.8. At this frequency the magnitude reaches 0dB and the phase is -180°.

Gif images below show how the applets should appear.

COPYRIGHT © 2006 Cuthbert Nyack.