How do we obtain the state space diagram and state space model for transfer function for example the question is given
How to draw state variable diagram for the given transfer function
$\frac{C(s)}{R(s)}=\frac{5s}{3s^{2}+3s+1}$
Steps are for solution are
$$\frac{C(s)}{R(s)}=\frac{5s}{3s^{2}+3s+1}\frac{Q(s)}{Q(s)}\\$$
$$C(s)=5(s^{-1})Q(s)\\$$ $$\Rightarrow R(s)=(3+3s^{-1}+s^{-2})Q(s)$$ $$\Rightarrow R(s)=3Q(s)+3(s^{-1})Q(s)+s^{-2}Q(s)$$ $$\Rightarrow 3Q(s)=R(s)-3(s^{-1})Q(s)-s^{-2}Q(s)$$
$$\Rightarrow Q(s)=\frac13R(s)-s^{-1}Q(s)-\frac13s^{-2}Q(s)$$
$$\Rightarrow Q(s)=\frac13R(s)-Q(s)\left[s^{-1}+\frac13s^{-2}\right]$$
the graph which is plotted in the book is of last equation of above solution.
I do not know how to post the graph here on stackexchange, but what I want to understand is:
How is the graph of this equation plotted?
