Lag Compensator Second Order Type 1, Step Response and Bode Plot
The applets here show the step response and Bode plot of a type 1 second
order system with Lag Compensation.
The continuous system is discretised by the bilinear transform to get D(z) and a ZOH transformation of the
system transfer function.
eg parameters (20.0, 0.5, 10.0, 1.0, 0.01, 0.2, 1.0) show the response of the uncompensated system.
eg parameters (20.0, 0.5, 10.0, 10.0, 0.1, 1.0, 1.0) show the response
with lag compensation and reasonable
agreement between the continuous and discrete systems. The phase margin of the cotinuous system is 48.5° and of the sampled system is
44.0°. The sampled system phase drops below -180° at ~5.5rad/s with a sampling frequency of 62.83rad/s.
eg parameters (20.0, 0.5, 10.0, 10.0, 1.0, 4.0, 1.0). Significant
damped oscillation on the discrete response. The sampled system
phase margin has dropped to 10.9°. The sampled system phase drops below -180° at ~1.8rad/s with a sampling frequency of 6.283rad/s.
eg parameters (20.0, 0.54, 10.0, 10.0, 1.68, 5.0, 1.0). Discrete system
oscillatory. Phase margin has dropped to ~0°, changing Ts show the closed loop poles are keeping close to the unit circle.
eg parameters (20.0, 0.6, 10.0, 10.0, 1.68, 5.0, 1.0). Discrete system
unstable with growing oscillation. Phase margin now -ve at -1.7°.
Applet below show the same information with the frequency axis being linear from 0 to half of the sampling frequency.
Gif images below show how the applets should appear.
Return to main page
Return to page index
COPYRIGHT © 2006 Cuthbert Nyack.