Topic: Control Systems
From the figure, obtain state equation
- A. $[\dot{X}]=\begin{bmatrix} 0 & -3 \\ -2 & 4 \end{bmatrix}[X]+\begin{bmatrix} 0 \\ 1 \end{bmatrix}u$
- B. $[\dot{X}]=\begin{bmatrix} -2 & 4 \\ 0 & -3 \end{bmatrix}[X]+\begin{bmatrix} 0 \\ 1 \end{bmatrix}u$
- C. $[\dot{X}]=\begin{bmatrix} 0 & -3 \\ -2 & 4 \end{bmatrix}[X]+\begin{bmatrix} 1 \\ 0 \end{bmatrix}u$
- D. $[\dot{X}]=\begin{bmatrix} -2 & 4 \\ 0 & -3 \end{bmatrix}[X]+\begin{bmatrix} 1 \\ 0 \end{bmatrix}u$
Answer: B. $[\dot{X}]=\begin{bmatrix} -2 & 4 \\ 0 & -3 \end{bmatrix}[X]+\begin{bmatrix} 0 \\ 1 \end{bmatrix}u$
Explanation: From the signal flow graph: $\dot{x}_1=-2x_1+4x_2$ and $\dot{x}_2=-3x_2+u$. Hence, $[\dot{X}]=\begin{bmatrix} -2 & 4 \\ 0 & -3 \end{bmatrix}[X]+\begin{bmatrix} 0 \\ 1 \end{bmatrix}u$.