Spec:Controls

Controls -- Controls module specifications

S3

 * Differential model (R3) : The controllable form of $$\sum_{n=1}^N a_n dy^n/dt^n = b_0 u$$ is
 * $$\dot x = \begin{bmatrix}

0 & 1 & 0 & \cdots & 0 \\ \vdots & 0 & 1 & 0 & 0 \\ \vdots & \vdots & 0 & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \\ -a_1/a_n & -a_2/a_n & \cdots & -a_{n-2}/a_n & -a_{n-1}/a_n \end{bmatrix} x + \begin{bmatrix} 0 \\ \vdots \\ \vdots \\ 0 \\ b_0/a_n \end{bmatrix}u$$

y = \begin{bmatrix}1 & 0 & \cdots & 0 \end{bmatrix} x + 0 u $$
 * The observable form is