Third Order 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
(2.0, 1.0, 0.5, 1.3, 1.0, 3.0, 1.0) show the ramp response of the
uncompensated system with transients (K = 3.0 produces
oscillations). 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 0.03 reduces the transients.
For Kv = 2.0 the ramp error(velocity error) is 0.5. Reducing Kv increases the error.
The Lag Compensator response is shown below. The parameters
(2.0, 1.0, 0.5, 10.0, 1.0, 1.0, 6.0, 1.0) show the ramp response of the
uncompensated system with initial transients (K = 3.0 produces
oscillations).. 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 b to 5.0 "reduces" the transients. When K = 2, then the velocity error settles to a steady value of 0.5 for t > ~ 45s.
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.
The LagLead Compensator response is shown below. The parameters
(2.0, 1.0, 0.5, 2.0, 10.0, 1.0, 5.0, 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.
Increasing b to 4.0 "reduces" the transients. When K = 2, then the velocity error settles to a steady value of 0.5 for t > ~ 45s.
Reducing K increases the difference(velocity error). Because the LagLead
compensator has a pole close to the origin, then the transient is slow
to reduce to negligible levels.
Gif images below shows how applets should appear when enabled.
Return to main page
Return to page index
COPYRIGHT © 2006 Cuthbert Nyack.