# How to find Phase angle?

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Io7 am 10 Apr. 2022
Beantwortet: Star Strider am 10 Apr. 2022
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.
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### Antworten (1)

Star Strider am 10 Apr. 2022
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.
.
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