Consider the closed-loop system shown in the figure with \[ G(s) = \frac{K(s^2 - 2s + 2)}{s^2 + 2s + 5}. \] The root locus for the closed-loop system is to be drawn for \( 0 \leq KLt;\infty \). The angle of departure (between \( 0^\circ \) and \( 360^\circ \)) of the root locus branch drawn from the pole \( (-1 + j2) \), in degrees, is (rounded off to the nearest integer).
Consider the closed-loop system shown in the figure with \[ G(s) = \frac{K(s^2 - 2s + 2)}{s^2 + 2s + 5}. \] The root locus for the closed-loop system is to be drawn for \( 0 \leq KLt;\infty \). The angle of departure (between \( 0^\circ \) and \( 360^\circ \)) of the root locus branch drawn from the pole \( (-1 + j2) \), in degrees, is (rounded off to the nearest integer).
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Correct Answer: 4 - 8
Solution and Explanation
Step 1: Calculate the angle of departure
The angle of departure from a complex pole is given by:
\[ \theta = 180^\circ - \sum (\text{angles to other poles}) + \sum (\text{angles to zeros}) \]
Step 2: Perform the calculation
Substituting the given pole and zero locations into the formula, the angle of departure is found to be approximately:
\[ \theta \approx 4^\circ \text{ to } 8^\circ \]
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