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

Cuthbert Nyack
The Applet below compares P control, PD control and Tachometer(velocity feedback) control for a type 1 system. For a given overshoot, PD control has a smaller risetime than velocity feedback.

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)

The closed loop response of the PD control system has a zero while that of the tachometer controlled system does not. This zero reduces the risetime of the PD control system. The parameter values (4.0, 1.0, 0.5, 0.44, 0.58, 0.5) illustrates the early time responses of the 2 systems.

Gif image below show how the applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.