Question

Problem 1 Rooting the Locus (25pts) In this problem you will design function a basic root-locus visualizer. a. (100%) Design a function rootlocus(G) that takes an open-loop transfer function and re- turns a plot of the root-locus, showing the zeros and the open-loop poles. By definition, the root-locus gives all the solutions of the characteristics equation $1 + KG(s) = 0$ on the s-plane for $0 \le K < \infty$, so to plot the root-locus, you can solve for the roots of the char- acteristics polynomial numerically by varing the value of K and plotting the result. You can use MATLAB's built-in pole() and zero() commands. Helpful questions: - How many root-locus segments do you have? - How many arrays do you need to store the results of pole locations, as you vary K? - Compare your result with MATLAB's built-in rlocus()

          Problem 1
Rooting the Locus (25pts)
In this problem you will design function a basic root-locus visualizer.
a. (100%) Design a function rootlocus(G) that takes an open-loop transfer function and re-
turns a plot of the root-locus, showing the zeros and the open-loop poles.
By definition, the root-locus gives all the solutions of the characteristics equation $1 + KG(s) = 0$
on the s-plane for $0 \le K < \infty$, so to plot the root-locus, you can solve for the roots of the char-
acteristics polynomial numerically by varing the value of K and plotting the result.
You can use MATLAB's built-in pole() and zero() commands.
Helpful questions:
- How many root-locus segments do you have?
- How many arrays do you need to store the results of pole locations, as you vary K?
- Compare your result with MATLAB's built-in rlocus()

Problem 1
Rooting the Locus (25pts)
In this problem you will design function a basic root-locus visualizer.
a. (100%) Design a function rootlocus(G) that takes an open-loop transfer function and re-
turns a plot of the root-locus, showing the zeros and the open-loop poles.
By definition, the root-locus gives all the solutions of the characteristics equation 1 + KG(s) = 0
on the s-plane for 0 ≤ K < ∞, so to plot the root-locus, you can solve for the roots of the char-
acteristics polynomial numerically by varing the value of K and plotting the result.
You can use MATLAB's built-in pole() and zero() commands.
Helpful questions:
- How many root-locus segments do you have?
- How many arrays do you need to store the results of pole locations, as you vary K?
- Compare your result with MATLAB's built-in rlocus()

Added by Jacob A.

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