# Homework Help: Matlab Root Locus Analysis

1. Oct 20, 2008

### eh87

1. The problem statement, all variables and given/known data
I'm trying to analyze the root locus of this transfer function in Matlab to control a DC motor:

mysys=tf([0.022],[0.00000000007 0.0000000626 0.000493])

3. The attempt at a solution

Using:

%[Kp,P]=rlocfind(mysys)
%rltool(mysys)
rlocus(mysys)

I get a root locus that looks somewhat odd and I'm not really sure how to interpret it. It doesn't appear to be stable at all gains. Although, it does look a bit better when I add a zero in rltool to the right of that gap and then it seems stable at all gains.

Help? I'm lost.

2. Oct 22, 2008

### CEL

Your system has two poles in the LHP, so it is stable for all values of gain. Matlab should draw a root locus consisting of two vertical lines, starting in each of the two complex conjugate poles.
Since no part of the root locus goes to the RHP, the system is stable.
Can you please post the image of the RL?

3. Oct 22, 2008

### eh87

Yes, they are in the LHP but I don't think it's stable for all gains. I know that as long as they don't cross into the RHP it should be, but this is just confusing. Please see the attached picture.

In rltool, when I move the pink dots (gain) it seems like there's a limit that they won't cross, which makes me think this is not stable at high gains (?). I'm not sure really what it means, but that's my guess.

#### Attached Files:

• ###### ece456 root locus.jpg
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22.4 KB
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4. Oct 22, 2008

### CEL

I can't see your picture, because the authorization is pending. Anyway, the system is certainly stable for all gains.
I have tried to adjust the loop gain in rltool and reached 1.02e6, without problem, I stopped there, but could continue. For practical purposes this is infinity.

5. Oct 22, 2008

### eh87

Hmm. Maybe I did something wrong before.

Anyway, I checked on the response to a step function in rltool today and it seemed fine. I guess now I'll work on tweaking it to make it faster without losing stability, then re-post.

Thanks!