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

[David PICARD]

Well, I eventually came up to the conclusion that both p_margin() and 
g_margin() are buggy. I had to write my own code to replace them.

I can give details upon request.

Regards.


David PICARD a écrit :
> 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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