LagLead Compensator Second Order Type 1, Step Response and Root Locus

Cuthbert Nyack
The applets here show the step response and Root Locus plot of a type 1 second order system with LagLead 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 (2.0, 1.5, 1.5, 8.0, 1.0, 0.2, 1.0) show the response of the continuous and sampled uncompensated system.
(10.4, 1.5, 1.5, 8.0, 1.0, 0.2, 1.0) show the sampled uncompensated system becoming unstable at ~0.08 of the sampling frequency.

eg parameters (20.0, 1.5, 1.5, 8.0, 10.0, 0.01, 0.2) show close correspondence between the cantinuous and sampled system with the sampling time of 0.01s.

eg parameters (20.0, 1.5, 1.5, 8.0, 10.0, 0.2, 0.2) show significant differences developing between the cantinuous and sampled system at small times with the sampling time of 0.2s.

eg parameters (20.0, 1.5, 1.5, 8.0, 10.0, 1.18, 3.0) show the sampled system becoming oscillatory at ~ 0.4 of the sampling frequency. For K = 10 oscillation at half the sampling frequency occurs at Ts = 1.85s.



Applet below show an expanded view of the rhs of the above.



Gif images below show how the applets should appear.

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COPYRIGHT 2006 Cuthbert Nyack.