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Re: Root Locus plots


From: dontguess
Subject: Re: Root Locus plots
Date: Thu, 18 Mar 2010 13:12:26 -0700 (PDT)

Just to clarify, should one make a root locus diagram for 

0 = Gol = Gc Gp

or

0 = 1 + Gol = 1 + Gc Gp

I think the second equation is quite common for process analysis.   However,
I cannot do this with Octave, because Kc appears in several, but not all
terms. 

For example, try the following. 
Gc = Kc ( tau_i s + 1 ) / (tau_i s + 0)
Gp = Kp / (tau_p s + 1)

and a 3rd order equation results, with Kc in some, but not all terms. 
-----------------------------------------------------------------------------


Doug Stewart-4 wrote:
> 
> I believe you are missing one point.
> 
> The (rlocus ) root locus uses the open loop poles and zeros not the closed
> loop system.
> 
> The root locus is the location of the system roots as you increase the
> loop
> gain, As the loop gain gos from 0 to infinity the system roots move from
> the
> open loop poles to the open loop zeros (some may be at infinity). Octave
> uses the open loop equations to draw the rlocus.
> 
> Doug
> 
> 
> 
> On Thu, Mar 18, 2010 at 1:35 PM, dontguess
> <address@hidden>wrote:
> 
>>
>> Just getting started with this tool.  As an example, I would like to make
>> a
>> root locus plot for a first order system with a PI controller. (No this
>> isn't homework; well, it is self-assigned homework).  Anyway, the closed
>> loop transfer function cannot be put into the form:  Kc * Num(s) / Den(s)
>> (at least by me.), which seems to be what the Ocatve documentation
>> describes.  Instead I have some variation of the following:
>>
>>      +
>> R --->    ----------------->  Gc   --------->  Gp  --------------------->
>> C
>>     -  |                                                            |
>>        |                                                            |
>>        -------------------------------------------------------------
>>
>> Gc = controller transfer function = Kc ( tau_i s + 1 ) / (tau_i s + 0)
>> Gp = process transfer function =   Kp / (tau_p s + 1)
>> Gcl = closed loop transfer function = Gc Gp / (1 + Gc Gp)
>>      = Kc ( tau_i s + 1) / (  tau_i tau_p / Kp s^2 + tau_i (1 + Kc Kp) /
>> Kp
>> s + Kc)
>>
>> Note there are two Kcs buried in the denominator of the transfer
>> function.
>>
>> So,  how to use Octave to make a root locus plot for the above system?
>>
>> Thanks for your help,
>>
>> Bob.
>>
>> --
>> View this message in context:
>> http://old.nabble.com/Root-Locus-plots-tp27948920p27948920.html
>> Sent from the Octave - General mailing list archive at Nabble.com.
>>
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-- 
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