Re: Root Locus plots

[Doug Stewart]

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.

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