110年 - 110 國立臺灣大學_碩士班招生考試_電機工程研究所甲組:控制系統(C)(含電路系統分析)#101161

1. Figure 1 shows a non-ideal operational amplifier with negative feedback. Show the configuration of this circuit connection is unstable. (15%)

(a) What values of ω_n and ξ correspond to the shaded regions? (6%)

(b)Let K_a = a = 2. Find values for K_land K, so that the poles of the closed-loop system lie within the shaded regions. (6%)

(c) Demonstrate that no matter what the value of K_A and A are, the controller provides enough flexibility to place the poles anywhere in the letft-half plane. (8%)

3. Modify the Routh criteria so that it can apply to the case in which all the poles are to be to the left of a when a ＞ 0 to the polynomial: s³ + (6 + K)s²+ (5 + 6K) + 5K = 0, with the assume value of c-1.(15%)

(a) Draw the block diagram for the plant with the condition that one integrator for each state variable. (4%)

(b)Find the transfer function. (4%)

(c)Find the closed-loop characteristic equation if the "state feedback" is u = -[K₁K₂]x;(6%)

(d)Find the closed-loop characteristic equation if the "output feedback" is u = -K•y . (6%)

(a) Write the state equation for the circuit. The input u(t) is current, and the output y is voltage. Let X₁ =i_L and x₂ = v_c . (5%)

(b) What condition on R, L, and C will guarantee that the system is "controllable"? (5%)

(c What condition on R, L, and C will guarantee that the system is "observerable"? (5%)

6. Assume the closed-loop system of Fig. 4 has a feedforward transfer function given by Design a lag compensator D(s) so that the dominant poles of the closed-loop system are located at s = -1 ± j and the steady-state error to a unit ramp input is less than 0.2. (15%)

110年 - 110 國立臺灣大學_碩士班招生考試_電機工程研究所甲組:控制系統(C)(含電路系統分析)#101161

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