I can't understand your solution. please more detail step-by-step solution

12.5. A PD controller is used in a control system having a first-order process and a measurement lag as shown in Fig. P12-5. (a) Find expressions for and for the closed-loop response. (b) If 1=1min and m=10s, find Kc so that =0.7 for the two cases (1) D=0s and (2) D=3s. (c) Compare the offset and period realized for both cases, and comment on the advantage of adding the derivative mode. FIGURE P12-5 12.5. A PD controller is used in a control system having a first-order process and a measurement lag as shown in Fig. P12-5. (a) Find expressions for and for the closed-loop response. (b) If 1=1min and m=10s, find Kc so that =0.7 for the two cases (1) D=0s and (2) D=3s. (c) Compare the offset and period realized for both cases, and comment on the advantage of adding the derivative mode. FIGURE P12-5