PD and Tachometer Control 2P 0T1, T1T2 Ramp Response

Cuthbert Nyack

Applet below compares the unit ramp response of P, PD and tachometer control. It also compares type 0 and 1 ramp responses.
Open and Closed loop transfer function for Tachometer control is,
G(s) = K/(s(T1s + 1)), G(s)H(s) = K(1 + Kcs)/(s(T1s + 1)), C(s)/R(s) = K/(T1s² + (1 + KKc)s + K)
And for PD Control is
G(s) = K(1 + Tds)/(s(T1s + 1)), C(s)/R(s) = K(1 + Tds)/(T1s² + (1 + KTd)s + K)

Both systems can follow a ramp with a steady error, but the PD controlled system has a smaller error. The error which appears at the input of the series controller is the same as for the PD controller so the feed back signal B(s) is t - 1/K as for the PD. However C(s) = B(s)/H(s) = B(s)/(1 + Kcs) so the tachometer controlled output is delayed by Kc relative to the PD controlled output.

Gif image below show how the applet should appear.

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