A feedback control system is depicted in Figure Q4a, where K is the gain of a proportional controller and G(s) is the tr

[answerhappygod]

A Feedback Control System Is Depicted In Figure Q4a Where K Is The Gain Of A Proportional Controller And G S Is The Tr 1 (109.21 KiB) Viewed 20 times

A feedback control system is depicted in Figure Q4a, where K is the gain of a proportional controller and G(s) is the transfer function of a mechatronic system. R(S) Y(s) K G(S) S +1 s(s2 + 5s + 6) Figure Q4a. Feedback control system using proportional control. (a) Determine the fastest possible settling time (Ts) of the system in Figure Q4a. (marks 3) (b) The settling time Ts that was found in sub-question Q4a is deemed to be long. A lead compensator is now introduced into the system in order to reduce Ts. The extended block diagram including the pole-zero compensator is depicted in Figure 24b. The lead- compensated system that has been depicted in Figure Q4b must have a settling time Ts = 0.5 (sec) and maximum percent overshoot of 4.33%. R(S) + Y(S) S + Zc KC s + PC G(S) = S + 1 s(s2 + 5s + 6) Figure Q4b. Feedback control system based upon a lead-compensator. (i) Determine the location of the two dominant closed-loop poles that correspond to the system requirements (Ts = 0.5 (sec) and maximum percent overshoot of 4.33%). (marks 4) (ii) Determine the s-plane location of the compensator pole if the compensator zero is chosen to be located at s = -9 in the s-plane. (marks 5) Based on your findings in Q4b{ii), determine the compensator gain Kc that corresponds to the system requirements. (marks 4) (c) Design the operational amplifier circuit to implement this compensator. Assume you have the capacitor with 10 mF. Determine the resistance values of the circuit. (marks 4)
A feedback control system is depicted in Figure Q4a, where K is the gain of a proportional controller and G(s) is the transfer function of a mechatronic system. R(S) Y(s) K G(S) S +1 s(s2 + 5s + 6) Figure Q4a. Feedback control system using proportional control. (a) Determine the fastest possible settling time (Ts) of the system in Figure Q4a. (marks 3) (b) The settling time Ts that was found in sub-question Q4a is deemed to be long. A lead compensator is now introduced into the system in order to reduce Ts. The extended block diagram including the pole-zero compensator is depicted in Figure 24b. The lead- compensated system that has been depicted in Figure Q4b must have a settling time Ts = 0.5 (sec) and maximum percent overshoot of 4.33%. R(S) + Y(S) S + Zc KC s + PC G(S) = S + 1 s(s2 + 5s + 6) Figure Q4b. Feedback control system based upon a lead-compensator. (i) Determine the location of the two dominant closed-loop poles that correspond to the system requirements (Ts = 0.5 (sec) and maximum percent overshoot of 4.33%). (marks 4) (ii) Determine the s-plane location of the compensator pole if the compensator zero is chosen to be located at s = -9 in the s-plane. (marks 5) Based on your findings in Q4b{ii), determine the compensator gain Kc that corresponds to the system requirements. (marks 4) (c) Design the operational amplifier circuit to implement this compensator. Assume you have the capacitor with 10 mF. Determine the resistance values of the circuit. (marks 4)