HW4Solution - ARO322AerospaceFeedbackControlSystems...

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ARO 322 Aerospace Feedback Control Systems Homework #4 Due 10/26/2007 1. For the following system, find the closed-loop transfer function and response of the closed-loop system for a unit step input. Find the final value and verify the result using MATLAB or Simulink. Y(s) R(s) E(s) U(s) + - B(s) Solution We have, [ ] 3 ( ) ( ) ( ) 1 ( ) ( ) 1 1 10 ( ) ( ) 5 Thus, 1 ( ) ( ) ( ) 1 And 1 1 10 ( ) ( ) ( ) 1 5 ( 5) ( ) ( ) ( ) 10 1 ( ) ( 1)( 5) 10 ( ) 10( 1) ( ) ( ) 10( 1) ( ) 6 5 10 10( ( ) ( ) E s R s B s B s Y s s Y s E s s s E s R s Y s s Y s R s Y s s s s s s Y s Y s R s s Y s s s s Y s s R s Y s s R s s s s s Y s R s = - = + = + = - + = - + + + + = + + + + = + + = + + + + = 3 2 1) 6 5 10 s s s + + + 1 s 1 1 + s 5 10 + s
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3 3 0 0 For unit step input, 1 10( 1) ( ) 6 5 10 Using final value theorem, 1 10( 1) ( ) lim ( ) lim ( ) lim 1 6 5 10 final t s s s Y s s s s s s y t y t sY s s s s s s s + = + + + + = = = = + + + The unit step response of the above closed loop transfer function can found using
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HW4Solution - ARO322AerospaceFeedbackControlSystems...

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