LTI SISO phase margin : weird results
David PICARD
d.picard at opgc.univ-bpclermont.fr
Mon Mar 8 10:58:49 CET 2010
I get weird results when I try to calculate gain margin for transfer
functions. For example, this one :
-->Hbo=syslin(1.0,(0.263-0.656*z+0.206*z^2+0.3*z^3)/(-0.263+0.656*z+0.28*z^2-1.674*z^3+z^4))
Hbo_s =
2 3
0.263 - 0.656z + 0.206z + 0.3z
----------------------------------
2 3 4
- 0.263 + 0.656z + 0.28z - 1.674z + z
It is a digital controller open loop transfer function.
Phase margin : p_margin(Hbo_s) returns 65.62, which is correct (checked
with both a book and Matlab).
Gain margin : g_margin(Hbo_s) returns -41.06, which I is not what I expect.
So, I plot the frequency response with :
-->show_margins(Hbo_s,'nyquist')
to try to figure out the gain margin graphically.
The gain margin is the inverse of the gain of the transfer function when
the phase is -180°).
The curve crosses the X axis at -0.368, which leads to gain_margin =
1/0.368 = 2.7, which is the value given in my book and returned by
Matlab (margin() ).
In addition, the blue line that I assume, shows the gain margin, extends
way beyond -0.368, probably as far as -41.06.
Did I get something wrong here ? Thanks.
My configuration : Scilab 5.2.1, Windows XP SP3
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