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How do we obtain a state-space realization and a block diagram of a given transfer function?

Consider the transfer function

$$\frac{C(s)}{R(s)}=\frac{5s}{3s^{2}+3s+1}$$

Steps 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 Stack Exchange, but what I want to understand is:

How is the graph of this equation plotted?

  • 0
    Consider using LaTeX for formatting.2012-12-04
  • 0
    Yes, please, please learn some LaTeX for posting huge formulas like this. It was very difficult to read as it was.2012-12-04
  • 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.2012-12-04
  • 0
    Yes, that is the other problem! Cheers Julian. :)2012-12-04
  • 0
    yes the edits done are correct what is latex I am hearing it first time the edits are correct2012-12-04

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