PD Control 2P 0T1, T1T2 Step Response

Cuthbert Nyack
The Applet below shows PD control of type 0 and 1 systems, compares P and PD control for a type 1 system and illustrates the relative contributions of the P and D controllers to the output for the type 0 system.
The P controller output is proportional to the error while the D controller output is proportional to the rate of change of the error.
For P control increasing K reduces the rise time but increases the overshoot and oscillatory behaviour. With PD the P controller works as with P control but now the D controller provides an additional variable Td for increasing the damping of the oscillations.
Open and Closed loop Transfer function for type 1 is
G(s) = K(1 + KTd)/(s(T1s + 1)), C(s)/R(s) = K(1 + KTd)/(T1s2 + (1 + KTd)s + K)
And for type 0 is
G(s) = K(1 + KTd)/((T1s + 1)(T2s + 1)), C(s)/R(s) = K(1 + KTd)/(T1T2s2 + (T1 + T2 + KTd)s + (1 + K))

Gif image below show how the applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.