Design a pid compensator gc1s and a lead-lag compensator

Question

The feedback control system shown in Figure DP10.9 has the transfer function

Design a PID compensator G_c1(s) and a lead-lag compensator G_C2(s) such that, in each case, the closed-loop system is stable in the presence of a time-delay T = 0.1 s. Discuss the capability of each compensator to insure stability in the presence of an increase in the time-delay uncertainty of up to 0.2 second.