- #1
phys_student1
- 106
- 0
Let:
$$x_1=A\sin{\omega t}$$ $$x_2=\dot{x}_1=A\omega \cos{\omega t}$$ $$y=A\omega$$
We want to represent this system in a state space model. The state transition matrix read:
$$A=\begin{bmatrix} 0 & 1 &\\ -\omega^2 & 0 \\ \end{bmatrix}$$ I am not sure what the output matrix will be like. Can we say
$$y=A\omega=\frac{-x_2}{\cos{\omega t}}$$
So that:
$$C=\begin{bmatrix} 0 & \frac{-1}{\cos{\omega t}} \end{bmatrix}$$
$$x_1=A\sin{\omega t}$$ $$x_2=\dot{x}_1=A\omega \cos{\omega t}$$ $$y=A\omega$$
We want to represent this system in a state space model. The state transition matrix read:
$$A=\begin{bmatrix} 0 & 1 &\\ -\omega^2 & 0 \\ \end{bmatrix}$$ I am not sure what the output matrix will be like. Can we say
$$y=A\omega=\frac{-x_2}{\cos{\omega t}}$$
So that:
$$C=\begin{bmatrix} 0 & \frac{-1}{\cos{\omega t}} \end{bmatrix}$$