Lag Compensator Second Order Type 1, Ramp Response

Cuthbert Nyack
The applet here show the step and ramp response of a type 1 second order system with Lag Compensation.
The continuous system is discretised by the bilinear transform to get D(z) and a ZOH transformation of the system transfer function.

eg parameters (20.0, 0.5, 10.0, 1.0, 0.01, 0.2, 1.0) show the response of the uncompensated system.

eg parameters (20.0, 0.5, 10.0, 10.0, 0.1, 1.0, 1.0) show the response with lag compensation and reasonable agreement between the continuous and discrete systems.

eg parameters (20.0, 0.5, 10.0, 10.0, 1.0, 5.0, 1.0). Significant damped oscillation on the discrete response.

eg parameters (20.0, 0.8, 10.0, 10.0, 1.21, 5.0, 1.0). Discrete system oscillatory.
eg parameters (20.0, 1.5, 10.0, 10.0, 1.51, 5.0, 1.0). Discrete system unstable with growing oscillation.

Because of the slowing down effect of the lag compensator, this system can have larger sampling times than the system with the lead compensator.





Gif image below show how the applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.