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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec17

# KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec17

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1 More General Transfer Function Models Chapter 6 Poles and Zeros: The dynamic behavior of a transfer function model can be characterized by the numerical value of its poles and zeros. General Representation of ATF: There are two equivalent representations: ( 29 0 0 (4-40) m i i i n i i i b s G s a s = = =

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2 Chapter 6 where { z i } are the “zeros” and { p i } are the “poles”. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 2 1 2 (6-7) m m n n b s z s z s z G s a s p s p s p - - - = - - - K K We will assume that there are no “pole-zero” calculations. That is, that no pole has the same numerical value as a zero. Review: in order to have a physically realizable system. n m i
3 Chapter 6 Example 6.2 For the case of a single zero in an overdamped second-order transfer function, ( 29 ( 29 ( 29 ( 29 1 2 τ 1 (6-14) τ 1 τ 1 a K s G s s s + = + + calculate the response to the step input of magnitude M and plot the results qualitatively. Solution

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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec17

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