PD Control 3P 0T1T2 Step Response and Root Locus

Cuthbert Nyack
Applet shows the root locus of a third order type 1 system with PD control. The parameter values (0.0, 1.0, 1.0, 0.0, 2.0) show the root locus with P control. This system can be unstable since the locus crosses the imaginary axis. Changing the parameters to (2.0, 1.0, 1.0, 0.0, 2.0) brings the closed loop poles on to the imaginary axis as verified by the oscillatory behaviour and the sharp peak in the frequency response.

The parameter values (0.0, 1.0, 1.0, 0.48, 2.0) show that the addition of a D contribution to the P controller brings the asymptote of the root locus onto the imaginary axis. Increasing the gain cannot bring the poles to the right of the imaginary axis to make the system unstable. The parameter values (2.0, 1.0, 1.0, 1.3, 2.0) show the effect of PD control on the root locus and also illustrates the limitation of having just one zero. Increasing the gain moves the closed loop poles parallel to the imaginary axis increasing the angle they make with the -ve real axis.

Gif image below show how the applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.