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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?

share|improve this question
    
Consider using LaTeX for formatting. –  Epictetus Dec 4 '12 at 9:56
    
Yes, please, please learn some LaTeX for posting huge formulas like this. It was very difficult to read as it was. –  Simon Hayward Dec 4 '12 at 10:05
2  
Some MSE users tried to improve your post using TeX (for better readability). Please check whether these edits did not unintentionally change the meaning of your post. –  Julian Kuelshammer Dec 4 '12 at 10:10
    
Yes, that is the other problem! Cheers Julian. :) –  Simon Hayward Dec 4 '12 at 10:37
    
yes the edits done are correct what is latex I am hearing it first time the edits are correct –  Registered User Dec 4 '12 at 10:53

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