Question

2. (40 pts) The open loop transfer function of a unity feedback control system is given as $G(s)H(s) = \frac{K(s+2)}{s(s^2+4)}$ (a) (12 pts) Draw the root locus of the system for K > 0, indicating all particulars such as asymptotes and their centroid, angles of arrival or departure, crossing points, break in/away points, etc. Draw the root locus neatly; neatness will be graded. (b) (3 pts) Determine the range of positive K values for which the system is stable. (c) (5 pts) In one sentence, explain why using a single PI controller will not make this system stable. (d) (10 pts) Suppose you use a PD controller $G_c(s) = K_d(s+8)$. Determine the range of $K_d$ values for which the system is stable. (e) (10 pts) Let $G_c(s) = K_d(s-z)$. Determine the range of z for which the system can be stabilized for all $K_d$ values. Explain your work in detail.

          2. (40 pts) The open loop transfer function of a unity feedback control system is given as
$G(s)H(s) = \frac{K(s+2)}{s(s^2+4)}$
(a) (12 pts) Draw the root locus of the system for K > 0, indicating all particulars such as asymptotes
and their centroid, angles of arrival or departure, crossing points, break in/away points, etc.
Draw the root locus neatly; neatness will be graded.
(b) (3 pts) Determine the range of positive K values for which the system is stable.
(c) (5 pts) In one sentence, explain why using a single PI controller will not make this system stable.
(d) (10 pts) Suppose you use a PD controller $G_c(s) = K_d(s+8)$. Determine the range of $K_d$ values
for which the system is stable.
(e) (10 pts) Let $G_c(s) = K_d(s-z)$. Determine the range of z for which the system can be stabilized
for all $K_d$ values. Explain your work in detail.

2. (40 pts) The open loop transfer function of a unity feedback control system is given as
G(s)H(s) = (K(s+2))/(s(s^2+4))
(a) (12 pts) Draw the root locus of the system for K > 0, indicating all particulars such as asymptotes
and their centroid, angles of arrival or departure, crossing points, break in/away points, etc.
Draw the root locus neatly; neatness will be graded.
(b) (3 pts) Determine the range of positive K values for which the system is stable.
(c) (5 pts) In one sentence, explain why using a single PI controller will not make this system stable.
(d) (10 pts) Suppose you use a PD controller Gc(s) = Kd(s+8). Determine the range of Kd values
for which the system is stable.
(e) (10 pts) Let Gc(s) = Kd(s-z). Determine the range of z for which the system can be stabilized
for all Kd values. Explain your work in detail.

Added by Jennifer R.

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