A certain plant has the transfer function
Gp (s) = 4p / (s2 + 4(s + 4) (s + p)
Where the nominal values of ( and p are ( = 0.5 and p = 1.
a. Use Ziegler-Nichols tuning to compute the PID gains. Obtain the resulting. Closed-loop characteristic roots.
b. Use the root locus to determine the effect of a variation in the parameter p over the range 0.4 ≤ ( ≤ 0.6.
c. Use the root locus to determine the effect of a variation in the parameter p over the range 0.5 p ≤ 1.5.