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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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