(b) (15%) Find a PROPER controller C such that the following conditions both hold: (i) the closed-loop is STABLE; and (ii) the response of the closed-loop system to any step input always has ZERO steady state error.

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.

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(b) (15%) Find a PROPER controller C such that the following conditions both hold: (i) the closed-loop is STABLE; and (ii) the response of the closed-loop system to any step input always has ZERO steady state error.

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