W09 314 HW02 all - EECS 314 Winter 2009 Homework set 2...

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EECS 314 Winter 2009 Homework set 2 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2009 Alexander Ganago Page 1 of 2 Scores for the HW set: Problem 1 2 3 4 5 6 7 Total Score Problem 1 Potentiometer as an angular position sensor The circuit shown on this diagram shows a potentiometer used as a sensor for the angular position (angle α ) of a robotic arm. At α = 0, the potentiometer’s tap is in its middle position so that R X = R 0 = R P /2 At an arbitrary, non-zero angle α (in degrees) the resistance equals R X = R P /2 + K α where K is constant measured in k Ω /degrees. Part 1 (10 points) Assume R P = 240 k Ω , K = 0.8 k Ω /degree. Calculate in degrees: α MIN , α MAX, and the Range of angles ( α MAX - α MIN ) . Write your answers: α MIN = _____, α MAX = _____, Range = _____ As shown in lectures, the output voltage is a linear function of the angle: V OUT = a + b α , where a and b depend on V S and the potentiometer. Assume V S = 30 V Calculate a in volts and b in volts/degree. Wirte your answers: a = ______________ volts b = _______________ volts/degree Continued on the next page. Part 1 2 3 4 Total
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EECS 314 Winter 2009 Homework set 2 Student’s name ___________________________ Discussion section # _______ (Last, First, write legibly, use ink) (use ink) Instructor is not responsible for grading and entering scores for HW papers lacking clear information in the required fields above © 2009 Alexander Ganago Page 2 of 2 Problem 1, continued Part 2 (10 points) Make a computer-generated plot of V OUT vs. the angle α over the interval from – 150 degrees to +150 degrees; attach your computer code or show your work in hand-written form. Part 3 (10 points) Calculate the angles in degrees: α 4 corresponding to V OUT = 4 V and α 7 corresponding to V OUT = 7 V α 4 = ____________˚ α 7 = ____________˚ Assume that the error of readout of V OUT is 10 mV and calculate the error Δα of readout of the angle α . Δα = ____________˚ Briefly discuss how to reduce the error of readout of the angle α : increase/decrease R P ; increase/decrease K; increase/decrease V S , etc. (when you vary one parameter, keep others unchanged) Part 4 (10 points) Suppose you have to monitor the angular position of a robotic arm from negative 120˚ to positive 120˚, with a readout device that accepts voltages from 0 to +5 V, with +2.5 V readout at the middle position of the potentiometer’s tap. Can you use the device discussed above (Parts 1 – 3)?
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W09 314 HW02 all - EECS 314 Winter 2009 Homework set 2...

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