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.

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COPYRIGHT 2006 Cuthbert Nyack.