2 Pole Sine Response

Cuthbert Nyack

The sinusoidal response of a 2 pole system is shown in the applet below.
The open and closed loop transfer function for the system is
G(s) = K/(s(T1s + 1)), C(s)/R(s) = K/(s(T1s + 1) + K))
and
G(s) = K/((T1s + 1)(T2s + 1)), C(s)/R(s) = K/((T1s + 1)(T2s + 1) + K))
Both responses goes through resonance type 1 can be seen with eg parameter values (20.0, 8.0, 8.0, 3.0, ~1.58, 0.2) and type 0 with (20.0, 8.0, 8.0, 3.0, ~0.53, 0.8). Type 1 resonance occurs at angular frequency ((K/T1)(1 - z²))^½ where z = (1/(4K*T1))^½ and type 0 at angular frequency ((1 + K)(1 - z²)/(T1 * T2))^½ where z = ((T1 + T2)/(4(1 + K)*(T1 * T2))^½).

Gif image below shows how applet should appear.

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