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.