Question

Cons idet the characteris tic equafion fon Cons idesthe root locus for oe ks varioos values of Consider the range sps20 For N-L00l value« of p in this ranq e sketch te woot locu s How does the root locus change as p charges I particular what harpens to fhe asy ptofe inTersection As a fiaal case let tp) disappear.Ths ts equivalent- ta (etting-P→ce.

Answer 1

Conclusion:

1)As P value increase from 2 to 20, system becomes more relatively stable because root locus bends towards right half of the s- plane.

2)As increasing P value number of asymptotes are constant but centroid or intersection points moves left half of the s-plane

3)If P---infinite, s=-p, pole become insignificant and system becomes more relatively stable and system is critically damped rise time, delay time increases and system time constant increases.

Conclusion: 1)As P value increase from 2 to 20, system becomes more relatively stable because root locus bends towards right half of the s- plane. 2)As increasing P value number of asymptotes are constant but centroid or intersection points moves left half of the s-plane 3)If P---infinite, s = -p, pole become insignificant and system becomes more relatively stable and system is critically damped rise time, delay time increases and system time constant increases. Finding open loop transfer function from the given characteristic equation Delta (s) = (s + 1)^2 (s + 1) + k (s + 2) = 0 = 1 + 6 H (s) = 0 6 H (s) = ? 1 + k (s + 2)/(s + 1)^2 (s + p) = 0 6 H (s) = k (s + 2)/(s + 1)^2 (s + p) Range of P is 2 lessthanorequalto P lessthanorequalto 20 For P =