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107年 - 107 國立中山大學_碩士班招生考試_電機系(乙組):控制系統#110506
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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。
相關申論題
(2.1) (10%) Find the corresponding response y(t).
#473291
(2.2) (3%) Calculate the peak value and the steady state value of y(t).
#473292
(3.2) Similar to the sub-question (3.1), please find out all possible relationships of T associated with the subspaces in the set{R(A), R(AT), N(A), N(AT)}. Give detailed arguments for your answers. (6%)
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(3.3) Now let (λ,v) be an eigenpair of matrix A withλ≠0. Then from the definition of A, it can be shown that y lies in certain subspace of Rn and λ is an eigenvalue of another matrix, denoted by with m=rank(A).Please (i) (2%) indicate the subspace of Rn where the eigenvector v lies, and (ii)(6%) use vectors x, ly, and z to describe the matrix B.
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(4.1) Find the set of such that matix A becomes singular. (5%)
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(4.2) Let's define an inner product for P2 by <p(x),q(x),for arbitrary and γ≠I an undecided parameter. Find the orthonormal basis, denoted by F := [f1, f2], of P2, generated from basis E given above to satisfy the subspace equality constraints Span(f1)=Span(I) and Span(f1,f2)=Span(1,x). (8%)
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(4.3) Let B denote the matrix representation of transformation L with respect to the ordered bases F computed in (4.2) and F'=for P2 and R2 , respectively. Find the matrix B. (6%)
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(4.4) Now suppose a = and β =0. Find all possible values of γ such that the set ofeigenvalues of B is.(6%)
#473299
(a)(7%)Let f(2) be a complex function defined by where denotes the complex conjugate of the complex variable z. Does the function f(z) satisfy the Cauchy-Riemann equations? Give your reason (no credit will be given if there is no explanation).
#473300
(b)(8%) Does the derivative of f(z) at z =0 ,i.e., f'(0), exist? Give your reason (no credit will be given if there is no explanation).
#473301
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