DP10.9 Consider the feedback control system shown in Figure DP10.9. Design a PID compensator G s c1( )

and a lead-lag compensator G s c2( ) 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. 

FIGURE DP10.9 Feedback control system with a time-delay. Controller Plant 60 R(s) Ge(s) Y(s) (s+4s+6)(s+10) Time delay e-xT