# ps02 - Problem Set#1 that have been posted on Stellar The...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Problem Set #2 Posted: Friday, Sept. 14, ’07 Due: Friday, Sept. 21, ’07 1. In class, we showed in two diﬀerent ways that the torque constant of a DC motor equals the back–EMF constant, K m = K v . Verify from the deﬁnitions of these constants, K m i = T and K v ω = v e , respectively, that the units associated with these constants are consistent as well. 2. Rework Problem 2 of Problem Set #1 (the motor–shaft system of Lecture 2 with non–zero initial condition) by using the Laplace transform. You should arrive at the same step response as you did in Problem Set #1. 3. Obtain the inverse Laplace transform of the following frequency–domain expres- sions: a) F 1 ( s ) = (4 s 10) ; s ( s + 2)( s + 5) 4 b) F 2 ( s ) = ; s 2 s 2 + 4 ± c) F 3 ( s ) = s 3 3 s 2 + s + 2 H ( s ), where H ( s ) is a well–behaved function of s , s whose inverse Laplace transform is h ( t ). 4. Obtain the transfer function of problem 4.a in the Problem Set #1 by Laplace transforming the equations of motion that you derived previously. (If you don’t have copy of your solution, you can ﬁnd the equations on motions in the solutions to

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Unformatted text preview: Problem Set #1 that have been posted on Stellar. ) The input to the system is the force f ( t ) and the output the rotation angle θ ( t ). 5. On the next page is a diagram of a DC motor connected in parallel to a current source i s . The torque and back–EMF constants of the motor are K m , K v , re-spectively, the motor resistance is R , also modeled as connected in parallel, the motor inertia is J m (not shown), and the motor inductance is negligible. The motor load is an inertia J with compliance K and viscous friction coeﬃcient b , and it is attached to the motor via a gear pair with gear ratio N 1 /N 2 . The system 1 input is the current is and the output is the rotation angle 8 of the inertia. Derive the transfer function of this system....
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## This note was uploaded on 02/23/2012 for the course MECHANICAL 2.004 taught by Professor Derekrowell during the Fall '08 term at MIT.

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ps02 - Problem Set#1 that have been posted on Stellar The...

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