Tutorial 4: Root Locus and Design of Digital Controller 1. A digital control system is shown in Figure B1. The system consists of a proportional controller with gain k, Zero-order-hold (ZOH) and an analogue plant GP(S). Given that the analogue plant Gp(s) = 25- (1-exp-5T) s(s+5) and sampling period T=0.1 s, a. Determine the discrete transfer function GHP(Z). b. Determine the open loop transfer function and draw the root locus of this system, assume that the break-away point z=+0.26 and the break in point z= -1.98. Label your drawing clearly and indicate its critical gain, zero and poles. c. Determine the characteristic equation of the system and using Jury's test, determine the range of gain k in which the system is stable. R(z) e(z) C(z) k ZOH Gp(s) e*(z) Sample/Hold Figure B1