Phase Lead Optimal Control.
This applet shows a second order system with phase lead compensator.
J can be used to attempt to find optimal values of TL and
To get an acceptable transient response, m
may also have to be adjusted.
One possible set of parameters is shown below. It uses
m = 1.0, fixes a = 0.1 and varies
TL to get a minimum TL = 0.12.
(20.0, 1.0, 0.5, 0.12, 0.1, 0.3, 1.0) minimum J = 5.020770 and fm
With these parameters, the compensated cross over frequency is
7.1rad/s while the lead compensator has maximum phase lead at
Parameters TL = 0.19, a = 0.12 gives
= 60.51° with J = 5.521575, only slightly more than the minimum.
The value of TL is not sensitive to m
Fixing TL and varying a produces a minimum
for a = 0.
Starting with a = 0.2 give TL = 0.12, minimum
J = 5.365278 and fm
Starting with a = 0.05 give TL = 0.12, minimum
J = 4.858187 and f m
Because of the approximation used for J, the result for J varies
with hgain but this does not affect the result. Smaller hgain gives
more accurate numbers for J.
For Comparison, the phase lead applet is shown below.
Gif images below shows how applets should appear.
Return to main page
Return to page index
COPYRIGHT © 2006 Cuthbert Nyack.