Root Loci of Double Integrator: PI & PD Controllers

[Logarythmic]

Homework Statement

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.

Homework Equations

None

The Attempt at a Solution

I really have no idea where to start.

 

[verafloyd]

Hi,

I see no particular challenge in the problem specified. Are you familiar with the root-locus concept? I guess you'd better first develop some primary insight on the subject through available resources. Do you have any access to the book "Modern Control Engineering" (Author: Ogata) or any other introductory control engineering book? It gives a procedure to draw root-locus. All you need to do is to apply the procedure to your system.

 

[piercas]

Can you please provide more context and information about the problem? What is the purpose of this exercise and what are you trying to achieve by sketching the root loci? Also, what is the expected outcome or conclusion from this exercise? Without this information, it is difficult for me to provide a proper response as a scientist.