141_1_MidtermSolutions (2) 14-00-23

141_1_MidtermSolutions (2) 14-00-23 - EE 141 Midterm...

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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 d dt where is angular position of the motors axle. Summing all the voltages we obtain: v = Ri + L di dt + K e d dt 2. Write the differential equation governing 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 circuits current i induces a torque given by K t i . 1 J d 2 dt 2 =- b d dt + K t i 3. Compute the transfer function from input voltage to the motors angular position.3....
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141_1_MidtermSolutions (2) 14-00-23 - EE 141 Midterm...

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