HOMEWORK/ASSIGNMENT No. 2 Weightage-7.5. ALL QUESTIONS ARE COMPULSORY. APPROACHES TO YOUR ANSWER ALSO CARY GOOD MARKS Date of release-10th May 2023. Date of hardcopy submission: 24th May 2023. Total Marks: 50 Q1 A process is described by the transfer function 4(1-5s) (s) = (25s + 1)(4s + 1)(2s + 1) which also includes actuator, sensor and filter dynamics. The process engineering group has the option of redesigning the process to eliminate the right-half plane (RHP) zero. They need to determine whether this modification will yield a substantially faster controlled process. a. For a proportional-only controller, find the stability bounds for Kc for the existing process! b. Repeat part (a) for the case where the RHP zero has been eliminated! C. By analysing the results from (a) and (b), what can you conclude about the potential speed of response of this controlled process if the zero can be eliminated! Q2 Total marks on QI =25 Fig. 1 shows the block diagram of a control structure which employs the P-only controller. The transfer functions in Fig. 1 are given as follows. s+2 Process: G ; (4s + 1)(10s +1) 2 Internal Model: G = Sensor: G -; P-controller: G = K 10s +1 Based on the transfer functions given above, find the following: a) The overall closed-loop transfer functions for: i. The disturbance change (Y/D) ii. Setpoint change (Y/R) b) Find the range for the controller gain (K) over which the closed-loop system shown in Fig. 1 is stable. = 1 s+1

HOMEWORK/ASSIGNMENT No. 2 Weightage-7.5. ALL QUESTIONS ARE COMPULSORY, APPROACHES TO YOUR ANSWER ALSO CARY GOOD MARKS Total Marks: 50 Q1 A process is described by the transfer function (s)=(25s+1)(4s+1)(2s+1)4(15s) which also includes actuator, sensor and filter dynamics. The process engineering group has the option of redesigning the process to eliminate the right-half plane (RHP) zero. They need to determine whether this modification will yield a substantially faster controlled process. a. For a proportional-only controller, find the stability bounds for Kc for the existing process! b. Repeat part (a) for the case where the RHP zero has been eliminated! c. By analysing the results from (a) and (b), what can you conclude about the potential speed of response of this controlled process if the zero can be eliminated! Total marks on QI=25 Q2 Fig. 1 shows the block diagram of a control structure which employs the P-only controller. The transfer functions in Fig. 1 are given as follows. Process: Gp=(4s+1)(10s+1)s+2; Sensor: Gm=s+11 Internal Model: Gn=10s+12; P-controller: Ge=K Based on the transfer functions given above, find the following: a) The overall closed-loop transfer functions for: i. The disturbance change (Y/D) ii. Setpoint change (Y/R) b) Find the range for the controller gain (K) over which the closed-loop system shown in Fig. 1 is stable