Suppose that I = c = 4 for the PI controller shown in Figure 10.6.2. The performance specifications require that = 0.2. (a) Compute

Suppose that I = c = 4 for the PI controller shown in Figure 10.6.2. The performance specifications require that τ = 0.2.
(a) Compute the required gain values for each of the following cases.
1. ζ= 0.707
2. ζ = l
3. A root separation factor of 10
(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.