- #1

Matt atkinson

- 116

- 1

I was given the state space model of a circuit and asked to determine the system elements. So basically, I think I have to find a suitable circuit which describes the state space equation. I am not really sure how to approach this question and every time I attempt it, it becomes really complicated.

Here's the task:

The system is to be implemented by a passive electrical circuit whose elements comprise of resistors R, capacitors X and/or inductors L. The input is a voltage source ##v_i(t)## and the output [itex]v_o(t)[/itex]. Given, the system state variables are chosen as the voltages across capacitors and the currents through inductors, determine a model structure and the system elements, whether a R,C or L component which produces the given state model. Hence determine the matrix terms [itex]a_{ij}, b_{i}[/itex] and [itex]c_{i}[/itex] in terms of R, L and C.

Here's the state space model:

##

\begin{pmatrix}

\dot{x_1}\\

\dot{x_2}\\

\dot{x_3}\\

\dot{x_4}\\

\end{pmatrix}

=

\begin{pmatrix}

a_{11} & a_{12} & a_{13} & a_{14}

\\ a_{21} & a_{22} & 0 & a_{24}

\\ a_{31} & 0 & a_{33} & 0

\\ a_{41} & a_{42} & 0 & 0

\end{pmatrix}

\begin{pmatrix}

x_1(t)\\x_2(t)\\x_3(t)\\x_4(t)

\end{pmatrix} +

\begin{pmatrix}

b_1\\0\\0\\0

\end{pmatrix}

v_i(t)

##

##

v_o(t)=

\begin{pmatrix}

0& c_2 & 0& 0

\end{pmatrix}

\begin{pmatrix}

x_1(t)\\x_2(t)\\x_3(t)\\x_4(t)

\end{pmatrix}

##

So far, I have tried to make ##x_1## an inductor current and then I get stuck. Could anyone point me in the right direction?