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104年 - 104 國立中山大學_碩士班招生考試_電機系(乙組):控制系統#110054
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Question 5(25%)
Consider the feedback system shown in Figure 4 again. Suppose now the plant has the transfer function
(a) (10%) Explain why a lag compensator (e.g., a PI controller) can
NEVER
stabilize G.
相關申論題
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.
#471448
(a) (10%) Determine all triples (uq, uq, iq) that are consistent with an equilibrium inductor current iq = 0.3, where uqand uq denote equilibrium values for the source voltage and the capacitor voltage.
#471449
(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?
#471450
(c) (10%) For the transfer function identified in (b), calculate the response of the transfer function when δu(t) =sin(t).
#471451
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.
#471452
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.
#471453
(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.
#471455
Question 4(10%) 請問「相位落後」補償器(phase-lagcompensator)可否用來提升系統之相位邊界(phase margin);也就是說,加了 phase-lag補償器後的系統,其相位界可否較未補償前的系統之相位邊界為大?必要時,請輔以適當的波德圖(Bodeplot)來說明你的理由。
#473290
(b)(15%)針對上述系統G,請重新設計一控制器,確保閉迴路系統之步階響應之穩態誤差小於 0.1%ㆍ
#473289
(a)(5%)令G的轉移函數為 ,C為一為比例控制器(這裡我們僅考慮正增益位)。當輸入為單位步階訊號時,請間系統輸出之穩態誤差之極小值(infimum)為何?
#473288
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