MATLAB: How to plot a root locus for an open loop system

Control System Toolboxopen loop systemroot locus

Hi,

I need help in plotting an open loop system for the following equation:

G(s)=K / s[(Is+a)(Hs+R) +K^2]

To find the root locus of G=1/(10s+5), use the following code:

s=tf('s'); G=tf(1/(10*s+5)); rlocus(G)

This should be enough to get you going.

The root locus of an (open-loop) transfer function is a plot of the locations (locus) of all possible closed loop

poles with proportional gain K and unity feedback.

Independently from K, the closed-loop system must always have n poles, where n is the number of poles of the

open loop transfer function. The root locus must have n branches, each branch starts at a pole of the Open Loop

Transfer Function (OLTF) and goes to zero of OLTF. If OLTF has more poles than zeros (as is often the case), m <

n and we say that the OLTF has zeros at infinity. In this case, the limit of OLTF as s → infinity is zero. The number

of zeros at infinity is n-m, the number of poles minus the number of zeros, and is the number of branches of

the root locus that go to infinity (asymptotes). Since the root locus is actually the locations of all possible closed

loop poles, from the root locus we can select a gain such that our closed-loop system will perform the way we

want. If any of the selected poles are on the right half plane, the closed-loop system will be unstable. The poles

that are closest to the imaginary axis have the greatest influence on the closed-loop response, so even though

the system has three or four poles, it may still act like a second or even first order system depending on the

location(s) of the dominant pole(s).

If G(p) is your system transfer function, The transfer function of your system in a closed loop with gain k is Gc(p)=G(p)/(1+k.G(p))

%you are looking for closed loop system poles depending on k vakues

G=tf([1 10],[1 2 1]) % your system in open loop
k=0:0.1:100; % k values
rlocus(G,k);  % your poles in closed loop

%or

rlocus(G);