An operational-amplifier circuit that may be used as a controller is shown inFigure Qla.-1(а)R4wwR2wwwwR3R1Figure QlaR1, R2, R3 and R4 are resistors and Cl and C2 are capacitors. Assume bothop-amps are ideal and their input/output voltages are ei, e and eo, as shown inthe Figure. Using the impedance approach:obtain the transfer function for each op-amp, i.e. E(s)/E:(s) andE(s)/E(s).(i)hence obtain the complete transfer function for the system, i.e.E(s)/Ei(s).(ii)(iii)Determine D(s) = E.(s)/E:(s) when R1 = R2 = R3 = R4 = 1 N andC1 =1 F, C2 2 F.(b)Consider the closed-loop control system shown in Figure Qlb.1ΣK.D(s)(s + 2)Figure QlbK is the gain and D(s) is the transfer function obtained in part (a)-iii.(i)Plot open loop zeros and poles for the above system in the s-plane. [".Determine whether the point (-1+j) is a closed loop pole for any valueof K, by considering the angle criterion at this point.(ii)(c)Briefly summarise the steps, which need to be taken to linearise a nonlinearsystem.

Figure Qla. R4 ww R2 R1 R3 e Figure Qla RI, R2, R3 and R4 are resistors and Cl and C2 are capacitors. Assume both op-amps are ideal and their input/output voltages are ei, e and eo, as shown in the Figure. Using the impedance approach: obtain the transfer function for each op-amp, i.e. E(s)/E:(s) and E(s)/E(s). (i) (ii) hence obtain the complete transfer function for the system, i.e. E(s)/Ei(s). (iii) Determine D(s) = E.(s)/E:(s) when RI = R2 = R3 R4 12 and Ci =1 F, C2 2 F. (b) Consider the closed-loop control system shown in Figure Qlb. Σ K.D(s) (s+2) Figure Qlb K is the gain and D(s) is the transfer function obtained in part (a)-iii. (i) Plot open loop zeros and poles for the above system in the s-plane. ". Determine whether the point (-1+j) is a closed loop pole for any value of K, by considering the angle criterion at this point. (ii)

Figure Qla. R4 ww R2 R1 R3 e Figure Qla RI, R2, R3 and R4 are resistors and Cl and C2 are capacitors. Assume both op-amps are ideal and their input/output voltages are ei, e and eo, as shown in the Figure. Using the impedance approach: obtain the transfer function for each op-amp, i.e. E(s)/E:(s) and E(s)/E(s). (i) (ii) hence obtain the complete transfer function for the system, i.e. E(s)/Ei(s). (iii) Determine D(s) = E.(s)/E:(s) when RI = R2 = R3 R4 12 and Ci =1 F, C2 2 F. (b) Consider the closed-loop control system shown in Figure Qlb. Σ K.D(s) (s+2) Figure Qlb K is the gain and D(s) is the transfer function obtained in part (a)-iii. (i) Plot open loop zeros and poles for the above system in the s-plane. ". Determine whether the point (-1+j) is a closed loop pole for any value of K, by considering the angle criterion at this point. (ii)

Delmar's Standard Textbook Of Electricity

7th Edition

ISBN:9781337900348

Author:Stephen L. Herman

Publisher:Stephen L. Herman

Chapter18: Resistive-inductive Parallel Circuits

Section: Chapter Questions

Problem 13PP: In an R-L parallel circuit, IT=1.25 amps, R=1.2k, and XL=1k. Find IR

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