How to find the state-variable equations, i.e, the state equation & the output equation for the system described by the signal flow graph below?

# Electronic – How to find the state-variable equations from the signal flow graph of the system

control system

## Best Answer

Between each point you have to define a state-variable and it will give you this equations:

$$ \begin{align} & X_1 = U \\ & X_2 = -X_1 \\ & X_1(point)=X_2 \\ & X_2 = -X_1 \\ & X_2(point) = X_3 \\ & X_3 = -X_2 \\ & X_3(point) = -X_3 \\ & Y = X_3 \\ \end{align} $$

$$ X(point) = \begin{bmatrix}0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & -1\end{bmatrix}*X \\ Y= \begin{bmatrix}0 & 0 & 1\end{bmatrix}X $$ For example you have \$ X_3 (t) = C_0 \cdot ^{(-t)} \$ (if you solve this equation).