[scilab-Users] LTI SISO gain margin : weird results

[David PICARD]

I corrected the subject.

David PICARD a écrit :
> 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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