Question

7. Use MATLAB root locus to analyze the system on the right. Marks 10 Show that the system is unstable for all values of K. Add a zero at s =-1, and show that this stabilizes the system. With the additional zero, determine the value of K such that the dominate pair of complex poles of the system has a damping ration of 0.5. Use Simulink to determine the step function of the uncompensated system. Use Simulink to determine the step function of the compensated.

Answer 1

(a) G(s)H(s)=k/[s^3+4s^2]

MATLAB code:

from the plot, the rootlocus moves in right half of s-plane for all values of gain(k), so finally system is unstable.

(b)

G(s).H(s)=[k(s+1)]/[s^3+4s^2]

MATLAB code:

by observing the plot, the root locus always moves in left half of s-plane.so the system is stable.

(d)

G(s).H(s)=k/[s^3+4s^2]

MATLAB code:

(e)

G(s).H(s)=[s+1]/[s^3+4s^2]

MATLAB code: