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.

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