How to find Phase angle?

How to find phase angle of a root loci using matlab. I would really appreciate any help.

Lets say you have the following transfer function

sys = tf([1 2],[1 4]);

rlocus(sys)

How to find the phase angle if you are given a desired pole location of S1= a+bj where a and b are any real number.

Answer 1

[Star Strider]

I am not certain that is possible for this system. since the roots are all real.

See if getting the ‘Gains’ and ‘Roots’ will do what you want —

sys = tf([1 2],[1 4]);

figure
[r,k] = rlocus(sys);
Roots = r

Roots = 1×52

-4.0000 -3.6000 -3.5747 -3.5483 -3.5207 -3.4920 -3.4622 -3.4313 -3.3993 -3.3664 -3.3325 -3.2977 -3.2621 -3.2258 -3.1889 -3.1514 -3.1134 -3.0752 -3.0367 -2.9981 -2.9595 -2.9210 -2.8828 -2.8449 -2.8075 -2.7706 -2.7343 -2.6988 -2.6641 -2.6303

Gains = k

Gains = 1×52

0 0.2500 0.2701 0.2918 0.3152 0.3405 0.3678 0.3974 0.4293 0.4637 0.5010 0.5412 0.5846 0.6316 0.6823 0.7371 0.7962 0.8602 0.9292 1.0038 1.0844 1.1715 1.2655 1.3672 1.4769 1.5955 1.7236 1.8620 2.0115 2.1730

Nominally, ‘Roots’ would be complex, so the phase angles would be:

PhaseAngles = angle(Roots)

Angles = 1×52

3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416 3.1416

That should get you started. See the documentation for rlocus for details.

.