Consider a negative gain root locus for L (s) = k (s-1)/[s(s^2 + 4s + 8)] with a scale of 20mm = 1 unit.
i. Graphically, find the gain required to give dominant closed loop poles with zeta = 0.5.
ii. For the above value of gain, find natural frequency and hence sketch the expected reference to output step response, assuming that the system is low-passing and dominantly second order.
iii. Add a sketch of the positive gain root locus to the diagram.
Please see the attached file.
Consider the positive gain root locus for shown on the last page of the examination paper with a scale of 20mm=1unit.
i) Graphically, find the gain required to give dominant closed loop poles with .
ii) For the above value of gain, find ...
Solutions are shown with full calculations including formulas C(s)/R(s) = L(s)/(1-L(s)) = [k(s-1)]/[s^3 + 4s^2 + (8-k)s + k] and Laplace transform pairs. Sketched graph for (ii) is also included.