quiz1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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Unformatted text preview: MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Quiz 1 Friday, October 5, 2007 PLEASE DO NOT TURN OVER UNTIL EXAM STARTS TOTAL PAGES: 3 i V ( ) s s V ( ) s ( ) s G 1 ( ) s G 2 ( ) s op-amp circuit DC motor MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering 2.004 Dynamics and Control II Fall 2007 Quiz 1 Friday, October 5, 2007 Duration: 50min (11:0511:55am) A DC motor is connected to an opamp circuit in cascade as shown in Figure 1. The opamp circuit subsystem is shown in Figure 2; the input to the opamp is a voltage source (battery) v i ( t ), the output is the voltage v s ( t ), and the transfer function of this subsystem is G 1 ( s ). The DC motor subsystem is shown in Figure 3; the input to the DC motor is the opamps output v s ( t ), the output is the angular velocity ( t ) of a shaft connected to the motor, and the transfer function of this subsystem is G 2 ( s ). The DC motor subsystem is not loading the opamp circuit subsystem. We will analyze the behavior of each subsystem independently, and that of the overall cascaded system. Figure 1: Cascade of an opamp circuit subsystem and a DC motor subsystem. Figure 2: The opamp circuit subsystem. Figure 3: The DC motor subsystem. Additional data for the opamp circuit subsystem are: the resistors R 1 = 100, R 2 = 100 and R 3 = 100 k, and the capacitor C 4 = 1 F . 2 Additional data for the DC motor subsystem are: motor resistance R = 1; the torque constant K m = 1 N m / A and backemf constant K v = 1 V sec / rad; the load 2 shaft inertia J = 1 kg m and viscous friction coecient b = 1 N m sec / rad. The motors own inertia...
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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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quiz1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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