所屬科目：中山◆電機◆控制系統
Question 1.(20%、5% for each sketch)The pole/zero plots of four transfer functions G1(s) to G4(s) are shown in Figure 1. Sketch the step response of each transfer function. On your sketches, you should show important details of the responses. such as the overshoot, undershoot, steady state, etc. if any. Missing any important detail will result in mark deduction.
(b) (10%) For the equilibrium (uq, uq, iq) = (0.5, 0.5, 0.4), linearize the governing equations and derive a transfer function model to relate the Laplace transform △U(s) of δu(t) = ข(t) -ขq (as an output) and the Laplace transform △u(s) of δu(t) = u(t) - uq (as an input). Is the transfer function stable?
Question 3(10%) Consider a standard negative feedback system shown in Figure 3, where. Determine how many seconds loop delay τ> 0 can be tolerated if a phasc margin of more than 45* is required in the presence of such delay.
Question 4(15%) Consider a standard negative feedback system shown in Figure 4, where the plantand the compensator . Find the positive compensator parameter values K > 0, such S+4 that the following conditions both hold: (i) the closed-loop is STABLE; and (ii) the closed-loop impulsc response has a mode that decays SLOWER than.
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The pole/zero plots of four transfer functions G1(s) to G4(s) are shown in Figure 1. Sketch the step
response of each transfer function. On your sketches, you should show important details of the responses.
such as the overshoot, undershoot, steady state, etc. if any. Missing any important detail will result in
mark deduction.
Consider a standard negative feedback system shown in Figure 3, where
. Determine how many seconds loop delay τ> 0 can be tolerated if a phasc margin of more than 45* is required in the presence of such delay. 
Consider a standard negative feedback system shown in Figure 4, where the plant
and the compensator 
. Find the positive compensator parameter values K > 0, such S+4 that the following conditions both hold: (i) the closed-loop is STABLE; and (ii) the closed-loop impulsc response has a mode that decays SLOWER than
.