(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For the double integrator described with transfer function

[tex]G(s) = \frac{1}{s^2}[/tex]

the initial condition is zero. The double integrator is subjected to a unit‐feedback system where the controller is chosen as

1) a PI-controller with [tex]C(s) = k_p \left( 1 + \frac{1}{s} \right)[/tex], or

2) a PD-controller with [tex]C(s) = k_p \left( 1 + \frac{2}{3} s \right)[/tex].

Sketch root loci of the closed‐loop systems as k_p varies from 0 to +∞. Give the breakaway and break‐in points, the points where root loci cross the imaginary axis, and the relevant values of k_p at all these points.

2. Relevant equations

None

3. The attempt at a solution

I really have no idea where to start.

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# Homework Help: Root loci

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