141_1_Midterm

# 141_1_Midterm - 4 Assuming that all the coeﬃcients...

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EE 141 – Midterm Fall 2008 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 dt where θ is angular position of the motor’s axle. 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 . 3. Compute the transfer function from input voltage to the motor’s angular position.

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Unformatted text preview: 4. Assuming that all the coeﬃcients appearing in the transfer function have value 1, that is K t = K e = J = L = R = b = 1, what is the impulse response of this system? 1 2 +-A B C +-r y E D + + + Figure 2: Block diagram for Problem 2. Problem 2: Consider the system represented in Figure 2 with input r and output y . 1. Compute the transfer function from r to y . 2. Consider the system described by the transfer function: 2 s + 5 s 3 + ( k + 20) s 2 + 10 s + 20 For which values of k is this system stable? 3 4 Problem 3: 1. Draw a sketch of the root locus for a plant with transfer function: s + 1 ( s-1)( s + 2) 2 in a unit-feedback conﬁguration. 2. Where can you place the slowest pole by choosing diﬀerent values of K ? 5 6...
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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_Midterm - 4 Assuming that all the coeﬃcients...

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