hw10_sol

# hw10_sol - MEEN 364 Fall 2004 Homework Set 10 Due November...

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MEEN 364 Homework Set 10 Fall 2004 November 4, 2004 1 Homework Set 10 – Due November 11, 2004 @ 5:00 PM 1. G P H Transfer functions with the reference input, R: PGH PG R y Hy R PG y v R PG y Pu y + = = = = 1 ) ( ) ( PGH G R u R PGH PGH G u Hy R G u v R G u + = + = = = 1 ) 1 1 ( ) ( ) ( PGH PGH R v y PGH PG H v Hy v + = + = = 1 1 Transfer functions with the input disturbance , W: PGH P W y GHy W P y Gv W P y u W P y + = = = + = 1 ) ( ) ( ) ( PGH PGH W u W PGH P GH u GHy u Gv u + = + = = = 1 1 PGH HP W v W PGH P H v Hy v + = + = = 1 1 Transfer functions with the sensor noise , N: PGH PGH N y y N PGH y PGv y Pu y + = + = = = 1 ) ( PGH GH N u N PGH PGH GH u y N GH u Gv u + = + + = + = = 1 1 1 ) ( PGH H H v N PGH PGH H v y N H v + = + + = + = 1 1 1 ) (

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MEEN 364 Homework Set 10 Fall 2004 November 4, 2004 2 2. The Bode plot start with a slope of –1 indicating that the transfer function has a factor of s 1 . The starting value of G is 10 indicating that the gain of the TF is 10 The crossover frequency is ω =10 rad/s. Thus the TF is given by 10( 1) ( 10) 10 () s s Gs ss + + == The response to a unit step input is given by: ) ( ) ( ) ( s U s G s Y = 2 10 1 1 ) 10 ( ) ( s s s s s s Y + = + = Therefore, )] ( [ ) ( 1 s Y L t y = () 1 ()1 0 yy t t ⇒= ) 0 ( t 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 5 10 15 20 25 Time (s) y(t) Unit step response
MEEN 364 Homework Set 10 Fall 2004 November 4, 2004 3 3. 2 () 1( ) 1 A Gs A ss a Ts A s a s A + == = ++ + + + a) 2 22 [() ] ds a s A dA s as A ++− = A ( ] ( ) T A ) A d A sa sAsa sAA s ST s Td A A s a ssa A + =⋅ = = b) ] da s as A = A 2 ] ( ) T a ad a sA s A a s s a A = = c) In this case, β = + ) 2 2 ] (1 ( )) dG ββ = + s s 2 2 ) ] ) 1 G G G G G +−− ⋅= ⋅= 1 T A A ss A S A A + + +

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## This note was uploaded on 04/18/2010 for the course MEEN 364 taught by Professor Staff during the Spring '08 term at Texas A&M.

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hw10_sol - MEEN 364 Fall 2004 Homework Set 10 Due November...

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