How should be change ROOT LOCUS asymmetric?

Task is find stabil interval. (root locus)

Code:

num=[1 0 0 0]
den=[1 0 5 10 1.5]
Hs=tf(num,den)
rlocus(Hs)

Result:

num =

       1     0     0     0

den =

    Columns 1 through 3

      1.0000         0    5.0000

    Columns 4 through 5

     10.0000    1.5000

Transfer function:
          s^3
------------------------
s^4 + 5 s^2 + 10 s + 1.5

Plot is asymmetric: http://i.imgur.com/v8dQD.png

Who can me help to solve symetrical plot?

[Azzi Abdelmalek]

xy, you've added a comment, then don't use answer (use comment).

What do you want exactly to do? Your question and your comment are not coherents

Answer 1

[Azzi Abdelmalek]

k=-1000:0.1:1000;
rlocus(Hs,k)

Answer 2

[Jonathan Epperl]

That's interesting, that harmless looking transfer function really seems to be problematic for Matlab.

You have already noted that the root locus your are getting is certainly wrong -- it is not symmetric wrt the real axis, and also the real axis left of the pole at -1.3 has to lie on the root locus entirely.

Two solutions I can offer:

• As Azzi has suggested, supply a vector of gain values with higher resolution, I suggest

       rlocus(Hs, linspace(0,40,5e3));

• Instead of drawing the root locus and eyeballing it, do some math to find the imaginary-axis crossings. The Routh-Array and Hurwitz Criteria are favorites here.

Answer 3

[x y]

Thi is not same ,but in this task is good,is symethric:

            s^3
  ------------------------
  s^4 + 5 s^2 + 10 s + 0.5

s^4 + K s^3 + 5 s^2 + 10 s + 0,5 = 0
omega^4 - K j omega^3 - 5 omega^2 + 10 j omega + 0,5 = 0

omega ^4 - 5 omega^2 + 0,5 = 0
- K j omega^3 + 10 j omega = 0  =>  k = 10 / omega^2 

>> omega=roots([1 0 -5 0 0.5]);
>> k=10./omega.^2
k =
    2.041684766872804e+000
    2.041684766872800e+000
    9.795831523312707e+001
    9.795831523312721e+001

>> r1=rlocus(g,k(1))
r1 =
     8.049116928532385e-016 +2.213123530591180e+000i
     8.049116928532385e-016 -2.213123530591180e+000i
    -1.990396370317212e+000                         
    -5.128839655559203e-002  

>> r2=rlocus(g,k(3))
r2 =
    -9.790828968598125e+001                         
     2.359223927328458e-016 +3.195062414783789e-001i
     2.359223927328458e-016 -3.195062414783789e-001i
    -5.002554714585826e-002

but i dont know how to get this:

s^4 + K s^3 + 5 s^2 + 10 s + 0,5 = 0
* omega^4 - K j omega^3 - 5 omega^2 + 10 j omega + 0,5 = 0*

 * omega ^4 - 5 omega^2 + 0,5 = 0
  - K j omega^3 + 10 j omega = 0  =>  k = 10 / omega^2 *