final08_mae143b

final08_mae143b - Final - MAE143B, Summer II 2008 September...

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Final - MAE143B, Summer II 2008 Name: Student #: September 5, 2008 3:00pm-6:00pm, Center 115 open-book and open-notes fnal exam use the available space to derive your results, attach extra paper i± necessary use o± any electronic equipment (calculator, phone, PDA) not allowed during exam 1 Consider the mechanical system depicted on the left with mass m =1 ,sp r ings t iFne s s k = 6, damping d = 5 and a position x ( t ). ±or this mechanical system we de²ne the input u ( t )asthe force applied to the mass and the output y ( t ) is de²ned as the acceleration of the mass: u ( t )= F ( t ) ,y ( t )=¨ x ( t ) m jj ± F ( t ) ± x ( t ) k d single mass mechanical system 1a Show that the proper (but not strictly proper) transfer function G ( s s 2 s 2 +5 s +6 (1) models the dynamics between input u ( s ) and output y ( s ) in the Laplace domain. [5pts] 1

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1b With G ( s ) given in (1), compute output y ( t ) due to unit step input signal u ( t ). [10pts] 1c Compute a state space model of the dynamic system based on the two-dimensional state vector [ x ( t x ( t )] T .[5p t s ] 2
2 To improve the speed of the response of the mechanical system, a proportional feedback controller u ( t )= K p [ r ( t ) y ( t )] , with K p > 0( 2 )

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This note was uploaded on 05/27/2010 for the course MAE MAT143B taught by Professor Linearcontrol during the Spring '10 term at UCSD.

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final08_mae143b - Final - MAE143B, Summer II 2008 September...

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