141_1_MidtermSolutions

141_1_MidtermSolutions - EE 141 – Midterm 11/05/08...

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Unformatted text preview: EE 141 – Midterm 11/05/08 Duration: 1 hour and 40 minutes The midterm is closed book and closed lecture notes. No calculators. You can use a single page of handwritten notes. Please carefully justify all your answers. R L v e + +-- i Figure 1: Circuit for Problem 1. Problem 1: Consider the electric circuit used to drive a DC motor, represented in Figure 1. 1. Write the differential equation governing the voltage on the circuit knowing that the voltage drop across the DC motor is given by e = K e dθ dt where θ is angular position of the motor’s axle. Summing all the voltages we obtain: v = Ri + L di dt + K e dθ dt 2. Write the differential equation governing θ knowing that: the motor has moment of inertia J , there is a friction torque proportional to the angular velocity with constant of proportionality b , the circuit’s current i induces a torque given by K t i . 1 J d 2 θ dt 2 =- b dθ dt + K t i 3. Compute the transfer function from input voltage to the motor’s angular position.3....
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This note was uploaded on 05/10/2010 for the course EE EE141 taught by Professor Tabuada during the Spring '09 term at UCLA.

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141_1_MidtermSolutions - EE 141 – Midterm 11/05/08...

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