Question: Consider the system of Problem 8.10-10. (a) Plot the root locus for this system, and find the value of (K>0) for which the system is

Consider the system of Problem 8.10-10.

(a) Plot the root locus for this system, and find the value of $K>0$ for which the system is stable.

(b) Find the time constant for the system with $K=1$.

(c) Design a phase-lead controller such that the characteristic-equation root in part (b) moves to yield a time constant of $0.5 \mathrm{~s}$ for $K=1$.

(d) By computer, verify the design in part (c) yields the correct characteristic-equation zero.

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