HW1-Fall-2009 (modcon) - below assuming that the engine...

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1 Modeling and Control Fall 2009 HW#1 PROBLEM #1 For each of the following Transfer Functions write the corresponding differential equation a). 7 2 1 ) ( ) ( 2 s s s F s X b) ) 8 )( 7 ( 10 ) ( ) ( s s s F s X c) 15 9 8 2 ) ( ) ( 2 3 s s s s s F s X PROBLEM #2 Solve the following differential equation using Laplace transforms. Assume all initial conditions to be zero. ) ( 10 25 8 2 2 t u x dt dx dt x d u(t): step function PROBLEM #3 Find the partial fraction expansion of the following polynomial ) 10 6 ( 10 2 2 s s s PROBLEM #4 Find the output response c(t) for each of the systems below. Also find the time constant c , rise time T r , and settling time T s s 1 C(s) 5 (s+5)
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3 PROBLEM #7 PROBLEM #8 a) Write the equations of motion for the speed and forward motion of the car shown
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Unformatted text preview: below assuming that the engine imparts a force u as shown in the figure. Assume that the rotational inertia of the wheels is negligible. u (force developed by the engine) Assume that there is friction retarding the speed is proportional to the speed with a coefficient b. Assume m is mass of the car Write the equation in terms of velocity (v) b) Take the Laplace transform of the differential equation c) What is the transfer function between the input u and output velocity v d) Use MATLAB to find response of the velocity of the car for a step input of u=500N, if m=1000 kg, and b= 50N.sec/m...
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This note was uploaded on 04/11/2010 for the course MANE 4050 taught by Professor Li during the Fall '08 term at Rensselaer Polytechnic Institute.

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HW1-Fall-2009 (modcon) - below assuming that the engine...

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