hw11_sol - MEEN 364 Fall 2004 Homework Set 11 Due November...

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MEEN 364 Homework Set 10 Fall 2004 November 11, 2004 1 Homework Set 11 – Due November 22, 2004 @ 5:00 PM 1. a) We are required to find V(s) / W(s) , taking a zero reference input V c . The block diagram then becomes: This is a closed-loop unity feedback system. Its transfer function is: 3 2 12 31 3 () 1 m skm Vs m s kk m Ws s m ks m skm s + == ++ +⋅ + 2 b) If w is a unit ramp function, w(t) =t , its Laplace transform is W(s) = 1 / s 2 , and we can apply the final value theorem to find v ss : 22 00 2 1 1 1 lim lim ss ss m s vs s s m kk s →→ =⋅ =⋅ = 2 c) To find the system type respect to reference, first we must find the transfer function between V c and V , considering w = 0: 3 2 3 1 c m sm k s mk k m s m k k k s + + 2
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MEEN 364 Homework Set 10 Fall 2004 November 11, 2004 2 The error transfer function is: 2 3 12 22 31 2 () 11 cc sm k s mk k Es Vs V s V s s mk s mk k s mk s mk k + =− = ++ 2 Now we evaluate the steady state error for unit step, ramp, and velocity inputs: Unit step: 2 3 2 00 2 1 lim ( ) lim 0 ss c ss c k s es V s s s m ks m k k s →→ ⎛⎞ + =⋅ ⋅ =⋅ = ⎜⎟ ⎝⎠ Unit ramp: 2 33 2 1 1 lim ( ) lim ss c c k s k k k k + =⋅ ⋅ =⋅ = 2 Therefore, the system is Type 1, the velocity constant is: 3 1 v ss kk K ek == d) We have already gotten V(s) / W(s) , so the error transfer function is: ( ) 2 2 2 1 k k k m s Ws s m s m +− + = 2 Unit step: ( ) 2 2 2 2 1 2 1 1 lim ( ) lim 1 ss k k k
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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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hw11_sol - MEEN 364 Fall 2004 Homework Set 11 Due November...

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