A#22 - “PI controller” “plant” X s s K K I P 1 25 s...

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Assignment #22 – p.1 ECSE-2410 Signals & Systems - Spring 2009 Due Tue 04/21/09 1(20). Find the closed loop system transfer function, ) ( ) ( s X s Y , expressed in terms of transfer functions . ) ( ), ( ), ( ), ( s D s C s B s A 2(45). In each case, sketch the root locus plots ( K > 0 ) for the following open loop transfer functions for unity feedback systems. Find the following, if they exist. Breakaway points and points of re-entry. Direction of travel of the roots as K varies from 0 to infinity. All asymptotes, asymptote angles and asymptote locations (centroids). Any j ω -axis crossings. (a) 2 1 ) ( s s s G + = (b) ) 1 ( 1 ) ( 2 + + = s s s s G (c) 3 2 ) 1 ( ) ( s s s G + = 3(15). The proportional-plus-integtral (PI) controller shown is used to improve the steady-state error
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Unformatted text preview: “PI controller” “plant” X ( s ) s K K I P + 1 25 . + s Y ( s ) of the feedback system shown by integrating out any residual error signal. Suppose 1 . = P I K K . (a) Sketch the root locus for varying K P . (b) Find the value of K P needed to place a pole of the closed loop at s=-5. (c) What is the steady-state error for the value of K P in (b) when the input is x ( t )= tu ( t )? 4(20). On next page. + - --+ +-+ A ( s ) B ( s ) C ( s ) D ( s ) X ( s ) Y ( s ) Assignment #22 - p.2 ECSE-2410 Signals & Systems - Spring 2009 Due Tue 04/21/09...
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This note was uploaded on 05/03/2009 for the course ECSE 2410 taught by Professor Wozny during the Spring '07 term at Rensselaer Polytechnic Institute.

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A#22 - “PI controller” “plant” X s s K K I P 1 25 s...

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