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Question no 1: Get the transfer function C(s)/R(s) for system bellow:-. i. R(S) + V(s) Vz(s) V3(s) V4(5) Vs(s) C($) G) G2) G3() V-(8) Vo(s) H2(s) Hz(s) V.(5) H(s) Figure 1 ii. H3(s) R(3) C($) GS) G2(3) G3(5) G.) Hz(s) H(s) Figure 2

Disturbances dz d 12. yi Setpoint R(S) PID PID P2 Pi C(S) v telenom a prie Process Figure 3. 0.005 5 Where : P = and P2 = and there are no disturbances. S+0.05 s+10 i. Consider the control system in figure 3, Assume the controllers, PID1 and PID2 is Proportional – Integral (PI), get the close loop transfer function for the system. TF = ii. By using Routh's stability criterion, please get the value of Kp that makes the system marginally stable. The critical gain Kcr is equal to Kp. Kcr = iii. By apply a Ziegler-Nichols tuning rule (method 2), determination of the values of parameters for Kp, Ti and Td. iv. Obtain a unit-step response curve for the system (Y1(s)). V. Obtain a unit-step response curve for secondary controller, (Y2())