RO E NIW 2 U (s+a) Figure 4.41 Control system for Problem 4.20 Suppose you are given the system depicted in Fig. 4.41(a), where the plant parameter a is subject to variations. (a) E(s) (b) G(s) (a) Find G(s) so that the system shown in Fig. 4.41(b) has the same transfer function from r to y as the system in Fig. 4.41(a). (b) Assume that a = 1 is the nominal value of the plant parameter. What is the system type and the error constant in this case? (c) Now assume that a= 1 + 8a, where da is some perturbation to the plant parameter. What is the system type and the error constant for the perturbed system?