Lead Compensator Second Order Type 1, Step Response and Bode Plot
The applets below show the effect of sampling on the step response and bode plot of a type 1 second order system with Lead Compensation. The
function of the compensator is to increase the phase margin
at the gain crossover frequency without too large an increase
in the gain crossover frequency.
eg parameters (20.0, 0.5, 0.3, 1.0, 0.02, 0.2, 1.0).
With a = 1, the response is that of
the uncompensated system. The response shows damped oscillations,
a gain crossover frequency(cofk) ~ 6.16rad/s and a phase margin ~ 17.9°. The sampled system phase margin is 16.1°,
the sampling frequency is 628.3rad/s and the sampled phase
becomes less than -180° at ~ 19rad/s.
With parameters (20.0, 0.5, 0.28, 0.1, 0.01, 0.2, 1.0), the
transient response has improved, the gain crossover frequency has increased to ~ 11.06rad/s, the maximum
phase advance of ~54.9° occurs at 11.29rad/s and the new phase
margin of the cotinuous system ~ 65.1°. At this sampling frequency
628.3rad/s, the phase margin of the sampled system is ~ 61.9°. Reducing the sampling frequency to 83.8rad/s reduces the phase margin to ~ 40°
Reducing the sampling frequency to 34.9rad/s shows the phase margin dropping to ~0 and the system becoming oscillatory at ~ 12rad/s. The
pole of the continuous Lead compensator is at 35.7rad/s.
eg (20.0, 0.5, 0.28, 0.1, 0.18, 1.0, 1.0)
The applet below shows the linear frequency response from
zero to half the sampling frequency.
eg parameters (20.0, 0.5, 0.42, 0.56, 0.11, 0.5, 1.0) show
the sampled system becoming oscillatory at ~ 0.135
Gif images below show how the applets should appear.
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COPYRIGHT © 2006 Cuthbert Nyack.