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首頁 > 中山◆電機◆控制系統 > 102年 - 102 國立中山大學_碩士班招生考試_電機系(乙組)：控制系統#110070 >

題組內容

PROBLEM 2 (30%) An LCR circuit is shown in Fig. 1, with its control input to be u, and output y = x₂ .

(a) (10%) Derive a state-space representation of this LCR circuit.

其他申論題

(a) (10%) Find the transfer function of the system.

(b) (10%) Find the zero-input response y(t).

(c) (10%) Choose, among the following types of control, ones that are likely to stabilize the system (One or more answers may be correct. Answers without supporting explanation are not acceptable) : (i) P control (ii) I control (iii) D control (iv) PID control (v) PD control (vi) PI control

(d) (10%) Choose, among the following types of control, ones that are likely to regulate the system output to a constant level 0.5 with zero steady state error (One or more answers may be correct. Answers without supporting explanation are not acceptable): (1) P control (ii) I control (iii) D control (iv) PID control (v) PD control (vi) PI control

(b) (10%) Suppose L =C=R=1 and x1(0)=x2(0)=1. What is the output y in steady state if u =sin(t)?

(c) (10%) Following 2(b), let the control be u(t)=-k1x1(t)-k2x2(t). Choose the gains k1 and k2 such that the closed loop poles are -2 and -3.

(a) (10%) Use Laplace transform to derive the transfer function from e(t) to e(t-D).

(b) (10%) Estimate the maximum allowable delay for the system to maintain at least 20 dB of gain margin, by using the approximation , when |ω|<<1.

PROBLEM 4 (10%) After dozing off in the Monday morning class, your classmate asked you: "Integral control adds negative phase, thus decreasing the phase margin. Why would we ever want to use integral control?" Explain how you would answer him. system.

(a) Calculate the voltage induced in the rotating loop () and the current flowing through the resistor. (10%)

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