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Unformatted text preview: Homework #5 ChE 446 Fall 2010 Problem 1. Consider a standard feedback control system with process transfer function G ( s ) and controller transfer function G c ( s ). The process transfer function is, G ( s ) = K ( τ 1 s + 1)( τ 2 s + 1) where τ 1 > 0 and τ 2 > 0. The controller operates on the error E ( s ) = ˜ R ( s )- Y ( s ), where ˜ R ( s ) = G R ( s ) R ( s ). The transfer function G R ( s ) is stable. 1. Assume that G c ( s ) is a PI controller. Determine the values of K c and τ I that yield a stable closed-loop system in terms of the parameters of G ( s ). 2. Let G R ( s ) = 1 and G c ( s ) = K c . Find the closed-loop transfer function Y ( s ) R ( s ) and determine the values of K c that yield a stable closed-loop system. 3. Let K = 2, τ 1 = τ 2 = 1, and K c = 0 . 5. Derive the closed-loop response y ( t ) for a unit step change in r ( t ). Determine the offset. Problem 2. Consider a feedback control system described by the following equations: Y ( s ) = G p ( s ) U (...
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- Spring '09