The specification requires that the response to the unit-step disturbance be such that the settling time be 2 to 3 sec
and the system have a reasonable damping. We may interpret the specification as C = 0.5 and w, = 4 rad/sec for
the dominant closed-loop poles. We may choose the third pole at 5 = -10
so that the effect of this real pole on the response is small.
Then the desired characteristic equation can be written as