KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec28

KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec28

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1 Chapter 11 Proportional Control and Disturbance Changes From Fig. 11.16 and Eq. 11-29 the closed-loop transfer function for disturbance changes with proportional control is ( 29 ( 29 ( 29 ( 29 1 1 (11-53) 1 1 p OL K s H s Q s K s + = + + Rearranging gives ( 29 ( 29 2 1 1 (11-54) τ 1 H s K Q s s O = + where is defined in (11-39) and K 2 is given by 1 τ 2 (11-55) 1 p OL K K K = +
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Chapter 11 A comparison of (11-54) and (11-37) indicates that both closed- loop transfer functions are first-order and have the same time constant. • However, the steady-state gains, K 1 and K 2 , are different. From Eq. 11-54 it follows that the closed-loop response to a step change in disturbance of magnitude M is given by ( 29 ( 29 1 2 1 (11-56) t h t K M e - = - The offset can be determined from Eq. 11-56. Now since we are considering disturbance changes and for a step change of magnitude M . Thus,
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KING FAHD UNIVERSITY CHEMICAL ENGINEERING COURSE NOTES (Process Control)-Lec28

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