PD Control Second Order Type 1 Step and Frequency response

Cuthbert Nyack
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. As shown on the applet, the phase of the discrete system goes below -180° and the system may be unstable.
eg parameters (5.0, 1.0, 0.4, 0.1, 1.0). Good agreement between discrete and continuous system. The gain margin is ~20dB and the phase margin ~50°.
eg parameters (5.0, 1.0, 0.4, 0.3, 1.0). Damped oscillations appear on the discrete response, the gain margin is ~8dB.
eg parameters (11.0, 1.0, 0.4, 0.3, 1.0). Discrete system has become unstable.



Gif image below show how the applet should appear.

Return to main page
Return to page index
COPYRIGHT 2006 Cuthbert Nyack.