soln MIE444 - midterm_2023

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School

University of Toronto *

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444

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Mechanical Engineering

Date

Feb 20, 2024

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pdf

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9

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University of Toronto Faculty of Applied Science and Engineering Department of Mechanical and Industrial Engineering Midterm Exam October 13, 2023 MIE 444 Mechatronics Principles Examiner: Sinisa Colic (This exam paper has 9 pages including this cover page) NAME: __________________________________ STUDENT NO:____________________________ Instructions to Candidate: GRADE: Duration: 90 minutes Type A exam 1 _____/9 No aid materials permitted 2 _____/6 Non-programmable calculators are permitted 3 _____/4 Maximum mid-term mark is 15% of final grade 4 _____/5 Answer questions in space provided 5_____ /6 Show steps leading to final answers TOTAL: solutions
Page 2-9 Q1) [9 Points] Assume that you have a 12 V NiMH battery that under normal operation has a voltage that varies from 9 V to 14 V, and a microcontroller that has an Analog to Digital converter that can measure inputs from 0 to 5 V. 1. Design a battery monitoring circuit to produce voltage measurements safe (i.e., maximum of 5 V) for the microcontroller by selecting two resistors, R1 and R2, of your choosing as shown in the diagram below (3 points) 2. For the selected resistors, what is the range of voltages entering the analog pin A1? (1 point) 1pt 1pt setup 1pt correct resister ratio 1pt
Page 3-9 3. Design and draw a circuit using comparators, your choice of resistors, and a dc power supply that will turn on 5 LEDs according to the battery voltage level. All LEDs should turn on when the battery voltage exceeds 13V and all LED should be off if the battery voltage is less than 9V. This question should be completed independently of the previous two parts. (5 points) 0.5pt correct ref voltage 9-14V 1pt five comparators 1pt computing resistor divider voltages to obtain correct comparator thresholds (0/1pt if using more than 1 voltage source instead) 1pt correct circuit and wiring 0.5pt LED protective resistors 0.5pt GND 0.5pt correct saturations
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Page 4-9 Q2) [6 Points] An analog signal is to be converted to digital form. The highest frequency component in the signal is 50 Hz. The system requirements also state that the quantization interval should be less than 0.2% of the peak to peak signal amplitude. 1. What is the required minimum sampling frequency to avoid aliasing? (1 point) 2. Determine the minimum number of bits required for the Analog to Digital Converter. (3 points) 3. The microcontroller used to perform the A/D conversion has 128 kbytes (1 byte = 8 bits) of memory for storage. Assuming the minimum sampling to avoid aliasing, how long can we record the signal? (2 points) Acceptable alternative solution 9 bits => 2 x 8-bit registers required to store data 1pt setting up 1pt correct answer 1pt correctly relating Q and ΔV 1pt correct answer 1pt - setup 1pt correct answer
Page 5-9 Q3) [4 Points] A 5-bit Successive Approximation A/D converter is used to convert an analog signal that varies between -2 V and 6 V. What is digital representation of the analog value 3.1 V? 1pt 8V full voltage range, with components added being 4V, 2V, 1V, 0.5V, 0.25V 2pt showing an iterative process for determining bits starting from MSB to LSB 1pt correct binary answer 10100 or 20 Part marks (max 2/4) if they use Q = ΔV/2 n , they need to show that they understand that successive approximation uses the iterative process
Page 6-9 Q4) [5 Points] A 5-bit resistor ladder network is used as a digital-to-analog converter. The supply voltage V s = 12 V. The resistance R = 12 kΩ and the feedback resistance of the operational amplifier R f is set initially to be equal to 6 kΩ (question 1 -3 below). Calculate the following: 1. The output voltage V out corresponding to the least significant bit. (1 point) 2. The maximum value of the output voltage. (1 point) 3. The output voltage corresponding to the binary input 10010. (1 point) 4. The required value of the operational amplifier feedback resistor R f so that the maximum analog output voltage, V out , will be -12 V. (2 points) 1pt 1pt 1pt 1pt 1pt
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Page 7-9 Q5) [6 Points] We would like to drive the motor, M , using the arrangement described in the diagram below. The control voltage, Va , is a square wave signal with 50% duty cycle ranging from 0 to 5 V. The battery, Vbatt , is 12V and the switch, S, is used to power the circuit on. ` a) Sketch the voltages Va , Vbatt , and Vt for two periods of operation in the space provided. You may assume the switch, S, is enabled. (4 points) b) You discover that the motor stops working shortly after running the above circuit. Despite switching the circuit on and off, the motor does not turn anymore. Why does the motor no longer operate? Modify the above circuit to correct the problem. (2 points) Answer (b): Answer (a): Va Vbatt Vt t t t The motor is like an inductor and when the transistor is no longer conducting the current drops rapidly causing a spike in voltage that could damage the transistor. 1pt 1pt 1pt 1pt 1pt drawing 1pt spike > 12V assumes transistor breakdown
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Page 9-9 Aid Sheet ------------------------------------------------------------------------------------------------------------------------------ Voltage Follower (Buffer) Inverting Amplifier Non-inverting Amplifier Summing Amplifier Difference Amplifier
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