PD Control Second Order Type 1 Step response and Root locus
The applets here show the step and ramp response of a type 1 second
order system with PD control.
The continuous system is discretised by a back difference
approximation to the derivative and a ZOH transformation of the
system transfer function. The continuous system is always stable.
eg parameters (10.0, 3.0, 0.0, 0.1, 2.0). This shows the step
response with P control. This response is unsatisfactory because of the damped oscillations. Adding D control can remove the transients. eg increasing Td from 0.0 to 1.0 damps out the
transient and changing the complex conjugate poles to real poles.
eg parameters (K, 3.0, 0.0, 0.2, 2.0). System without PD control.
For K =0.1 locus is very close to the unit circle and crosses
unit circle when = 10.0. Increasing Td to 0.8 pulls the locus away from the unit circle because of the introduced zero and keeps the system
stable for K up to 30.8.
Gif image below show how the applet should appear.
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COPYRIGHT © 2006 Cuthbert Nyack.