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che446_10_hw8

# che446_10_hw8 - Homework#8 ChE 446 Fall 2010 Problem 1...

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Homework #8 ChE 446 Fall 2010 Problem 1. Consider the following transfer function model, Y ( s ) = G p ( s ) U ( s ) + G L 1 ( s ) L 1 ( s ) + G p ( s ) G L 2 ( s ) L 2 ( s ) where G L 2 = K L 2 and: G p ( s ) = K p ( τ 1 s + 1)( τ 2 s + 1) K p , τ 1 , τ 2 > 0 1. Consider a standard feedback control system with G c = K c . Express the transfer function Y ( s ) L 2 ( s ) as a general second-order transfer function ( i.e. find K , τ , and ξ ). Determine the values of K c that yield a stable closed-loop system. Calculate the offset as a function of K c . 2. Consider a cascade control system with G c 1 = K c 1 and G c 2 = K c 2 . Find the transfer function Y ( s ) L 2 ( s ) . Determine the values of K c 1 and K c 2 that yield a stable closed-loop system. Calculate the offset as a function of K c 1 and K c 2 . 3. Consider a feedforward/feedback control system with G c = K c and G f = K f . Express the transfer function Y ( s ) L 2 ( s ) as a general second-order transfer function. Determine the values of K c and K f that yield a stable closed-loop system. Calculate the offset as a function of K c and K f .

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che446_10_hw8 - Homework#8 ChE 446 Fall 2010 Problem 1...

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