How to find Phase angle?

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Io7
Io7 2022-4-10
回答： Star Strider 2022-4-10
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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回答（1 个）

Star Strider
Star Strider 2022-4-10
Ran in:
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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