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

[David PICARD]

Look at bug reports 6744 and 6745 at http://bugzilla.scilab.org

6744 has an  attachment with my own functions. Probably not perfect as 
well !


Vladímir Rodríguez a écrit :
> El mar, 09-03-2010 a las 16:39 +0100, David PICARD escribió:
>   
>> 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
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>         
>>>
>>>       
> I am interested in every detail about it, I am going to use these
> function in clases.
> Thanks
>   
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