Phase Lag Optimal Control.

Cuthbert Nyack

This applet shows a second order system with phase lag compensator. J can be used to attempt to find optimal values of TG and b.
To get an acceptable transient response, m may also have to be adjusted.

One possible set of parameters is shown below. It uses m = 0.4, fixes TG = 10.0 and varies b to get a minimum at b = 12.7.
(20.0, 0.4, 0.5, 10.0, 12.7, 1.0, 1.0) J = 0.930028 and the phase margin of the system is 52.59°.
Starting with TG = 6.0 gives a minimum J for b = 12.6, f_m = 49.77°. With TG = 16.0, b = 12.8, f_m = 54.26°.

With m = 1.0 and starting with TG = 10.0 gives a minimum J = 1.342245 for b = 20.3 with f_m = 59.68°.
With m = 0.3 and starting with TG = 10.0 gives a minimum J = 0.835238 for b = 10.9 with f_m = 50.00°.

For Comparison the Phase Lag applet is shown below.

Gif images below shows how applets should appear.

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