Question

11. Given the transfer function in root locus form $L(s) = K \frac{s + 6}{s^2 + 4s + 100}$, (a) (5 points) Find the poles and zeros of the transfer function in root locus form; use the method of least squares to solve for the roots of the quadratic equations. (b) (5 points) Do a pole-zero plot of the transfer function in root locus form as close to scale as possible on the complex plane. (c) (10 points) Determine the point(s) at which the root locus enters or leaves the real axis. (d) (10 points) Give the formula for determining the angle of departure for the pole in the second quadrant and calculate the departure angle. (e) (10 points) Plot the root locus for this transfer function in root locus form on the complex plane, in the process explaining your procedure. Your plot and explanation must demonstrate your knowledge of plotting a root locus.

          11. Given the transfer function in root locus form
$L(s) = K \frac{s + 6}{s^2 + 4s + 100}$,
(a) (5 points) Find the poles and zeros of the transfer function in root locus form; use the method of
least squares to solve for the roots of the quadratic equations.
(b) (5 points) Do a pole-zero plot of the transfer function in root locus form as close to scale as
possible on the complex plane.
(c) (10 points) Determine the point(s) at which the root locus enters or leaves the real axis.
(d) (10 points) Give the formula for determining the angle of departure for the pole in the second
quadrant and calculate the departure angle.
(e) (10 points) Plot the root locus for this transfer function in root locus form on the complex plane,
in the process explaining your procedure. Your plot and explanation must demonstrate your
knowledge of plotting a root locus.

11. Given the transfer function in root locus form
L(s) = K (s + 6)/(s^2 + 4s + 100),
(a) (5 points) Find the poles and zeros of the transfer function in root locus form; use the method of
least squares to solve for the roots of the quadratic equations.
(b) (5 points) Do a pole-zero plot of the transfer function in root locus form as close to scale as
possible on the complex plane.
(c) (10 points) Determine the point(s) at which the root locus enters or leaves the real axis.
(d) (10 points) Give the formula for determining the angle of departure for the pole in the second
quadrant and calculate the departure angle.
(e) (10 points) Plot the root locus for this transfer function in root locus form on the complex plane,
in the process explaining your procedure. Your plot and explanation must demonstrate your
knowledge of plotting a root locus.

Added by Brittney E.

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