# MATLAB Root locus analysis of this diagram

Discussion in 'Homework Help' started by Kai Chiang, Jun 6, 2016.

1. ### Kai Chiang Thread Starter New Member

Oct 27, 2015
12
0

Is my code correct?
>> num=2*[1 2 1];
>> den = [1 0 0 0];
>> sys=tf(num,den);
>> rlocus(sys)

How do I type the saturation command for MATLAB so that I can do my root locus analysis?

2. ### Papabravo Expert

Feb 24, 2006
10,135
1,786
It is not clear to me that a root locus is valid with a non-linear element in the forward loop. If you limit the results to the linear range of the saturation element then -- maybe. This is typical of most analysis tools - they don't work with non-linear systems.

3. ### MrAl Well-Known Member

Jun 17, 2014
2,418
488
Hello there,

A while back (quite a while back) i had a non linear analysis book that talked about all kinds of non linear systems and how to do the analysis. When i moved, i put it into storage because i found that most of the non linear applications that came up could not be analyzed using those techniques anyway. That was a long time ago and all i remember was that the book was very expensive and most applications were not applicable. I do see them for sale on the web these days for maybe 100 bucks and up.

However, this particular system looks fairly simple. That's because it looks like there are only two modes: linear and non linear and they appear to be mutually exclusive. That's because when the system is not in saturation, it is linear (linear root locus applies) but when it goes into saturation it stays in saturation because the transfer function is made up of an integrator, a double integrator, and a ramp. These will cause the system to go into sat and stay there, and will eventually cause an output that is equal to the input exactly. So for a unit step the system will go into sat if the saturation limits are set to cause this, and once it goes into sat the output goes to 1 and stays there forever unless something on the input is changed. So the most important mode will be when the saturation limits are not exceeded, which keeps it in the linear mode.
You could solve for the time when the saturate limits are exceeded if you wanted to by computing the time domain function for the output of the gain stage.

There may be more advanced methods in one of those books however, so it might be a good idea to tack a look in at least one of them.

4. ### WBahn Moderator

Mar 31, 2012
17,715
4,788
I'll echo what the others have said -- Root Locus is predicated upon linear systems (just look at what the root locus plot means mathematically). As is often the case, techniques that apply to linear systems can be adapted to apply, within limits that are usually pretty restrictive, to nonlinear systems. But doing so usually requires quite a bit of care to retain a reasonable level of fidelity to the actual system response.