The input v(t) and output \omega(t) of a DC motor are related by the differential equation
0.005\frac{d^2\omega}{dt^2} + 0.06\frac{d\omega}{dt} + 0.1064\omega(t)= v(t).
A valid state for the system is
\mathbf{x}(t) = \begin{bmatrix} \omega(t)\\frac{d\omega}{dt}\end{bmatrix}.
Which of the following is the state space model corresponding to this choice of state?

Question

The input   v(t)  and output   \omega(t)  of a DC motor are related by the differential equation 
  0.005\frac{d^2\omega}{dt^2} + 0.06\frac{d\omega}{dt} + 0.1064\omega(t)= v(t). 
 A valid state for the system is  
  \mathbf{x}(t) = \begin{bmatrix} \omega(t)\\frac{d\omega}{dt}\end{bmatrix}. 
 Which of the following is the state space model corresponding to this choice of state?

Accepted Answer

\frac{d\mathbf{x}(t)}{dt} = \begin{bmatrix} 0 & 1\-21.28 & -12\end{bmatrix} \mathbf{x}(t) + \begin{bmatrix} 0\200\end{bmatrix} v(t),\qquad\omega(t) = \begin{bmatrix} 1 & 0\end{bmatrix}\mathbf{x}(t)

Answer

\frac{d\mathbf{x}(t)}{dt}=\begin{bmatrix}0 & 1\21.28 & 12\end{bmatrix}\mathbf{x}(t)+\begin{bmatrix}0\200\end{bmatrix}v(t),\qquad\omega(t)=\begin{bmatrix}1 &0\end{bmatrix}\mathbf{x}(t)

Answer

\frac{d\mathbf{x}(t)}{dt} =\begin{bmatrix} 0 & 1\-21.28 & -12\end{bmatrix} \mathbf{x}(t) + \begin{bmatrix} 200\0\end{bmatrix} v(t),\qquad\omega(t) = \begin{bmatrix} 1 & 0\end{bmatrix}\mathbf{x}(t)

Answer

\frac{d\mathbf{x}(t)}{dt} =\begin{bmatrix} 0 & 1\-21.28 & -12\end{bmatrix} \mathbf{x}(t) + \begin{bmatrix} 0\1\end{bmatrix} v(t),\qquad\omega(t) = \begin{bmatrix} 1 & 0\end{bmatrix}\mathbf{x}(t)

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The input v(t) and output \omega(t) of a DC motor are related by the diffe...

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