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Root Locus plots


From: dontguess
Subject: Root Locus plots
Date: Thu, 18 Mar 2010 10:35:23 -0700 (PDT)

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.
 
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