Wyjaśnienie:
Opis:
[tex]$F=M\ddot x+B\ddot x+kx$[/tex]
[tex]u=\left[\begin{array}{c}F\end{array}\right][/tex]
[tex]y=\left[\begin{array}{c}x&\dot x&\ddot x& F_k&F_B\end{array}\right][/tex]
Przyjmujemy zmienne stanu:
[tex]x=x_1\\\dot x=x_2[/tex]
Wyznaczamy równania stanu:
[tex]\dot x=\dot x_1=x_2[/tex]
[tex]$\ddot x=\dot x_2=\frac{1}{M}\bigg[F-B\dot x-kx\bigg]=\frac{1}{M}\bigg[F-Bx_2-kx_1\bigg] $[/tex]
Równania wyjść:
[tex]x=x_1\\\dot x=x_2\\\ddot x=\frac{1}{M} [F-Bx_2-kx]\\F_k=kx_1\\F_B=bx_2[/tex]
Równania stanu i wyjść:
[tex]\left[\begin{array}{c}\dot x_1&\dot x_2\end{array}\right] =\left[\begin{array}{cc}0&1\\-\frac{k}{M} &-\frac{B}{M} \end{array}\right] \left[\begin{array}{c}x_1&x_2\end{array}\right] +\left[\begin{array}{c}0&\frac{1}{M} \end{array}\right] F[/tex]
[tex]y=\left[\begin{array}{c}x&\dot x&\ddot x& F_k&F_B\end{array}\right]=\left[\begin{array}{cc}1&0\\0&1\\-\frac{k}{M} &-\frac{B}{M}\\k&0\\0&B\end{array}\right] \left[\begin{array}{c}x_1&x_2&\end{array}\right] +\left[\begin{array}{c}0&0&\frac{1}{M}&0&0 \end{array}\right] F[/tex]
