(Solved): TryIt \( 8.2 \) PROBLEM: Given a unity feedback system that has the forward t ...

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TryIt \( 8.2 \) PROBLEM: Given a unity feedback system that has the forward transfer function Use MATLAB and the following statements to solve Skill-Assessment Exercise 8.2. do the following: \[ \begin{array}{l} \mathbf{s}=-3+0 j \\ \mathrm{G}=(\mathrm{s}+2) /\left(\mathrm{s}^{\wedge} 2+4^{*} \mathrm{~s}+13\right) \\ \text { Theta }=(180 / \mathrm{pi})^{*} \ldots \\ \text { ang } \ldots(\mathrm{e}(\mathrm{G}) \\ \mathrm{M}=\mathrm{abs}(\mathrm{G}) \\ \mathrm{K}=1 / \mathrm{M} \end{array} \] \[ G(s)=\frac{K(s+2)}{\left(s^{2}+4 s+13\right)} \] a. Calculate the angle of \( G(s) \) at the point \( (-3+j 0) \) by finding the algebraic sum of angles of the vectors drawn from the zeros and poles of \( G(s) \) to the given point. b. Determine if the point specified in a is on the root locus. c. If the point specified in a is on the root locus, find the gain, \( K \), using the lengths of the vectors. ANSWERS: a. Sum of angles \( =180^{\circ} \) b. Point is on the root locus c. \( K=10 \) The complete solution is at www.wiley.com/college/nise.