# 全狀態回授

## 原理

${\displaystyle {\dot {\underline {x}}}=\mathbf {A} {\underline {x}}+\mathbf {B} {\underline {u}},}$

${\displaystyle {\underline {y}}=\mathbf {C} {\underline {x}}+\mathbf {D} {\underline {u}},}$

${\displaystyle \left|s{\textbf {I}}-{\textbf {A}}\right|=0.}$

${\displaystyle {\underline {u}}=-\mathbf {K} {\underline {x}}}$.

${\displaystyle {\dot {\underline {x}}}=(\mathbf {A} -\mathbf {B} \mathbf {K} ){\underline {x}};}$
${\displaystyle {\underline {y}}=(\mathbf {C} -\mathbf {D} \mathbf {K} ){\underline {x}}.}$

## 全狀態回授的例子

${\displaystyle {\dot {\underline {x}}}={\begin{bmatrix}0&1\\-2&-3\end{bmatrix}}{\underline {x}}+{\begin{bmatrix}0\\1\end{bmatrix}}{\underline {u}}}$

${\displaystyle \left|s\mathbf {I} -\left(\mathbf {A} -\mathbf {B} \mathbf {K} \right)\right|=\det {\begin{bmatrix}s&-1\\2+k_{1}&s+3+k_{2}\end{bmatrix}}=s^{2}+(3+k_{2})s+(2+k_{1})}$.

${\displaystyle \mathbf {K} ={\begin{bmatrix}3&3\end{bmatrix}}}$.

## 參考資料

1. ^ *Sontag, Eduardo. Mathematical Control Theory: Deterministic Finite Dimensional Systems. Second Edition. Springer. 1998. ISBN 0-387-98489-5.
2. ^ Design and Analysis of Full-state Feedback Controller for a Tractor Active Suspension. [2018-06-28]. （原始内容存档于2018-02-18）.
3. ^ Control Design Using Pole Placement. [2018-06-28]. （原始内容存档于2018-06-29）.