11.單迴路控制系統如【圖11】所示，則其狀態微分方程式為？ (A) x = bmatrix 0 & 1 & 0 \ 0 & 0 & 1 \ -6 & -16 & -8 bmatrix x + bmatrix 0 \ 0 \ 1 bmatrix u(t) (B) x = bmatrix 0 & 1 & 0 \ 0 & 0 & 1 \ -7 & -15 & -8 bmatrix x + bmatrix 0 \ 0 \ 1 bmatrix u(t) (C) x = bmatrix 0 & 1 & 0 \ 0 & 0 & 1 \ -5 & -10 & -6 bmatrix x + bmatrix 0 \ 0 \ 1 bmatrix u(t) (D) x = bmatrix 0 & 1 & 0 \ 0 & 0 & 1 \ -9 & -18 & -10 bmatrix x + bmatrix 0 \ 0 \ 1 bmatrix u(t)

20. 則下列何者為可控制典型式(Controllable Canonical Form)？ (A) \( \dot{X}(t) = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -\beta_1 & -\beta_2 & -\beta_3 \end{bmatrix} X(t) + \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} U(t) \)，\( Y(t) = \begin{bmatrix} \alpha_1 & \alpha_2 & \alpha_3 \end{bmatrix} X(t) \) (B) \( \dot{X}(t) = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ \beta_3 & \beta_2 & \beta_1 \end{bmatrix} X(t) + \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} U(t) \)，\( Y(t) = \begin{bmatrix} \alpha_3 & \alpha_2 & \alpha_1 \end{bmatrix} X(t) \) (C) \( \dot{X}(t) = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -\beta_1 & -\beta_2 & -\beta_3 \end{bmatrix} X(t) + \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} U(t) \)，\( Y(t) = \begin{bmatrix} \alpha_3 & \alpha_2 & \alpha_1 \end{bmatrix} X(t) \) (D) \( \dot{X}(t) = \begin{bmatrix} 0 & 0 & -\beta_1 \\ 1 & 0 & -\beta_2 \\ 0 & 1 & -\beta_3 \end{bmatrix} X(t) + \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} U(t) \)，\( Y(t) = \begin{bmatrix} \alpha_1 & \alpha_2 & \alpha_3 \end{bmatrix} X(t) \)

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