PD Control Second Order Type 1 Step and Frequency response
Cuthbert Nyack
The applet here show the step and frequency response of a type 1 second
order system with PD control. The continuous system is always stable
The transfer functions of the controller Gc(s) and system Gs(s)
are combined with a sampler and ZOH to obtain a forward
transfer function:-
G(z) = (1 - z-1)Z{Gc(s)Gs(s)/S}
The closed loop transfer function is then:-
Gcs(z) = G(z)/(1 + G(z).
eg parameters (5.0, 3.0, 0.8, 0.05, 0.5). Good correspondence between
continuous and sampled systems.
eg parameters (13.0, 3.0, 0.05, 0.26, 1.5). Sampled system oscillatory
at ~0.085 of the sampling frequency. The open loop gain is 0dB
and the phase is -180° at this frequency.
eg parameters (13.0, 3.0, 0.85, 0.26, 1.5). Increased derivative
time has made the closed loop poles real and reduced transients.
Gif image below show how the applet should appear.
Return to main page
Return to page index
COPYRIGHT © 2006 Cuthbert Nyack.