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pset4 - voltage Assume the following numerical values for...

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ME3015 PROBLEM SET #4 (25 points). Document as outlined in the course admin letter. Due: The beginning of Lesson 13 (October 5 th ). 1. (8 points) Derive the transfer function of the electrical system ) ( / ) ( s E s E i O shown below. Draw a schematic diagram of an analogous mechanical system. 2. (8 points) Obtain an electrical system analogous to the mechanical system shown below where f (t) is the force input to the mass 1. The displacements x 1 and x 2 are measured from their static equilibrium points. 3. (9 points) Obtain the transfer function ) ( / ) ( 2 s E s a of the electromechanical system with a DC servomotor where ) ( ) ( 2 2 t s L (load shaft position) and ) ( ) ( t e s E a a L (input voltage). Assume the following numerical values for the constants.
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Unformatted text preview: voltage). Assume the following numerical values for the constants. (see back page for the figure) R a : Armature resistance = 0.2 L a : Armature inductance = negligible K b : Back-EMF constant = 5.5 x 10-2 V-s/rad K : Motor-torque constant = 6 x 10-5 N-m/A b L : Viscous coefficient between output shaft and bearing = 4 x 10-2 N-m-s/rad b r : Viscous coefficient between armature and bearing = negligible J r : Moment of inertia of motor = 1 x 10-5 kg-m 2 J L : Moment of inertia of the load = 4.4 x 10-3 kg-m 2 n : Gear ratio = N 1 / N 2 = 0.1 e i ( t ) e o ( t ) R 1 R 2 C 1 C 2 k 1 x 1 b f(t) x 2 m 1 m 2 k 2 k 3...
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