Lead, Lag and LagLead Ramp Response.

Cuthbert Nyack
The applets show the ramp response of Lead, Lag and LagLead compensators.

The Lead Compensator response is shown below. The parameters (20.0, 0.5, 0.3, 1.0, 1.0, 1.0) show the ramp response of the uncompensated system with initial transients. The orange curve shows an amplified view of the difference between the input ramp (magenta) and output ramp(pink).

The vertical scale for the ramp is -0.5 to 1.5 for hgain = 1.0.
Changing a to 0.1 reduces the transients. Reducing K increases the difference(velocity error).



The Lag Compensator response is shown below. The parameters (20.0, 0.5, 10.0, 1.0, 1.0, 1.0) show the ramp response of the uncompensated system with initial transients. The orange curve shows an amplified view of the difference between the input ramp (magenta) and output ramp(pink). The scale for the orange curve is different from the Lead compensator and is shown on the applet.

The vertical scale for the ramp is -0.5 to 1.5 for hgain = 1.0.
Changing b to 10.0 reduces the transients. Reducing K increases the difference(velocity error). Because the Lag compensator has a pole close to the origin, then the transient is slow to reduce to negligible levels. (Increase hgain to 5.0).



The LagLead Compensator response is shown below. The parameters (20.0, 0.5, 0.54, 18,3, 1.0, 1.0, 1.0) show the ramp response of the uncompensated system with initial transients. The orange curve shows an amplified view of the difference between the input ramp (magenta) and output ramp(pink).

The vertical scale for the ramp is -0.5 to 1.5 for hgain = 1.0. Gradient of ramp remains one as hgain is changed.
Increasing b reduces the transients. Reducing K increases the difference(velocity error). Because the Lag compensator has a pole close to the origin, then the transient is slow to reduce to negligible levels. (Increase hgain to 5.0 and reduce TG to see final steady state).



Gif images below shows how applets should appear when enabled.

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COPYRIGHT 2006 Cuthbert Nyack.