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# quiz1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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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

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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 (11:05–11:55am) A DC motor is connected to an op–amp circuit in cascade as shown in Figure 1. The op–amp circuit subsystem is shown in Figure 2; the input to the op–amp 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 op–amp’s output v s ( t ), the output is the angular velocity ω ( 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 op–amp circuit subsystem. We will analyze the behavior of each subsystem independently, and that of the overall cascaded system. Figure 1: Cascade of an op–amp circuit subsystem and a DC motor subsystem. Figure 2: The op–amp circuit subsystem. Figure 3: The DC motor subsystem. Additional data for the op–amp circuit subsystem are: the resistors R 1 = 100Ω, R 2 = 100Ω and R 3 = 100 kΩ, and the capacitor C 4 = 1 µF . 2
Additional data for the DC motor subsystem are: motor resistance R = 1Ω; the torque constant K m = 1 N m / A and back–emf constant K v = 1 V sec / rad; the load 2 · · shaft inertia J = 1 kg m and viscous friction coeﬃcient b = 1 N m sec / rad. The · · · motor’s own inertia and inductance are negligible.

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quiz1 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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