Question

please do part D only the matlab. thank you

3. Consider the following system s(s2 +4s 13) (a) Draw the root locus. b) Use Routh's criterion to find the range of the gain K for which the closed-loop system is stable. (continued on next page) (c) The range of K for which the system is stable can also be obtained by finding a point of the root locus that crosses the Imaginary axis. When you have an Im-axis crossing, the point is given by s-jo. Find the values ofω and K at that crossing point. (Hint: The point s ja, must satisfy the closed-loop characteristic equation above since it's on the root locus) (d) Confirm your calculations with a Matlab root locus plot

Answer 1

$1 + K\frac{1}{s(s^2 + 4s+13)}$

the closed-loop poles are the roots of

h(s) = n(s) d(s) h(s) =

MATLAB script:

h = tf([1],[1 4 13 0]);
rlocus(h)
[k,poles] = rlocfind(h); %Click on the plot the point where you want the closed-loop pole to be.

Root Locus 20 15 ︵ 10 5 0 -5 E-10 -15 20 -10 20 -15 -5 10 Real Axis (seconds )