Question

A unity negative feedback system has a loop transfer function $$ \begin{aligned} G_c(s) G(s) & =\frac{K\left(s^2+0.105625\right)}{s\left(s^2+1\right)} \\ & =\frac{K(s+j 0.325)(s-j 0.325)}{s\left(s^2+1\right)} . \end{aligned} $$ Sketch the root locus as a function of $K$. Carefully calculate where the segments of the locus enter and leave the real axis.

   A unity negative feedback system has a loop transfer function
$$
\begin{aligned}
G_c(s) G(s) & =\frac{K\left(s^2+0.105625\right)}{s\left(s^2+1\right)} \\
& =\frac{K(s+j 0.325)(s-j 0.325)}{s\left(s^2+1\right)} .
\end{aligned}
$$

Sketch the root locus as a function of $K$. Carefully calculate where the segments of the locus enter and leave the real axis.

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Modern Control Systems

Modern Control Systems

Dorf 11th Edition

Chapter 7, Problem 27

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Step 1

Step 1: Identify the poles and zeros of the transfer function The transfer function has a zero at $s=0$ and poles at $s=0$ and $s=\pm j$. Show more…

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A unity negative feedback system has a loop transfer function $$ \begin{aligned} G_c(s) G(s) & =\frac{K\left(s^2+0.105625\right)}{s\left(s^2+1\right)} \\ & =\frac{K(s+j 0.325)(s-j 0.325)}{s\left(s^2+1\right)} . \end{aligned} $$ Sketch the root locus as a function of $K$. Carefully calculate where the segments of the locus enter and leave the real axis.

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