The system shown in Figure P6.16 has G₁(s) = 1/s(s + 2) (s + 4). Find the following:

a. The value of K₂ for which the inner loop will have two equal negative real poles and the associated range of K₁ for system stability.

b. The value of K₁ at which the system oscillates and the associated frequency of oscillation.

c. The gain K₁ at which a real closed-loop pole is at s = –5. Can the step response, c(t), be approximated by a second-order, underdamped response in this case? Why or why not?

d. If the response in Part d can be approximated as a second-order response, find the %OS and settling time, T_s, when the input is a unit step, r(t) = u(t).

R(s) + E(s) C(s) K1 G(s) K2 5 FIGURE P6.16