Suppose that I = 10 and c = 5 for the PI controller shown in Figure 10.6.2. The performance specifications require that = 2.

Suppose that I = 10 and c = 5 for the PI controller shown in Figure 10.6.2. The performance specifications require that τ = 2.
(a) Compute the required gain values for each of the following cases.
1. ζ = 0.707
2. ζ = 1
3. A root separation factor of 5
(b) Use a computer method to plot the unit-step command responses for each of the cases in part (a). Compare the performance of each case.