PD Control Second Order Type 1 Step response and Root Locus

Cuthbert Nyack

The applet here show the step response and root locus 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, 1.6, 0.05, 2.0). Good correspondence between continuous and sampled systems. Increased Td has damped out transient.
eg parameters (5.0, 3.0, 0.1, 0.05, 2.0).

Gif image below show how the applet should appear.

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