Q3. (8 marks) A closed-loop system consists of proportional controller, a ZOH element, a first order plus time delay system. T u Gc(z) ZOH Gp(s) The open-loop pulse transfer function between y(z) and u(z) (incorporating the ZOH) is given by: (bz)z '" HG,(z) = G (2)=K 1 - az a) For specific case in which b=0.09, and a=0.86, find the maximum value of K, for which the closed-loop system remains stable if time delay m=0. (2 marks) b) Repeat part b) for time delay m=1. (4 marks) c) Based on the results obtained above, comment on the effect of time delays on the range of K. value required for closed-loop stability. (2 marks)