PD Control Second Order Type 1 Step and Ramp response

Cuthbert Nyack

The applets here show the step and ramp 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 (8.0, 3.0, 0.3, 0.5, 3.0). Both responses have damped oscillations.
eg parameters (8.0, 3.0, 0.3, 0.94, 3.0). Oscillates at 1/4 the sampling frequency.

Gif images below show how the applets should appear.

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