What does my Root Locus response mean? Why is it different?
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Right at the moment I am learning about Root Locus of the system and how they are normally used for damping/oscillating systems. I often see Magnetic Levitation Papers use these to determine the root locus, which I guess must be to determine the oscillations in their system. However, unlike their ones, mine is a bit different, only sitting at the real axis. Is this alright? I mean it does make sense since both my roots exist on the real plane, but I'm curious and want to know more as I cannot find any relevant info about MagLevs and root locuses anywhere else.
sys = tf([-19008],[960.704 0 -2376000])
Both Taken from IEEE:
Paul on 31 Mar 2022
Hello @Joel Okanta
The root locus is much more general than as suggested in the Question. Given a system described by an open loop transfer fuction L(s), the root locus are all values of s that solve, i.e., are the roots of, the equation
D(s) = 1 + K*L(s) = 0
as the scalar K varies over the range -inf < K < inf. Often the root locus is plotted only for 0 < K < inf ( the default for rlocus() ), but don't forget that sometimes we need to consider K < 0.
That equation is critical becase the roots of D(s) are the closed loop poles of a system with open loop transfer function K*L(s), and the closed loop poles determine the modes of the system. So the root locus technique applies to much more than just dampled oscillator systems, as the example in the Question illustrates with the closed loop poles one the real axis.