Experiment 8 : Pulse Width Modulation

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1 Name/NetID: Teammate/NetID: Experiment 8 : Pulse Width Modulation Laboratory Outline In experiment 5 we learned how to control the speed of a DC motor using a variable resistor. This week, we will learn an alternative method of driving the motor that requires the use of the transistor we learned about last week. Rather than adjust a constant voltage to the motors, we will change the average voltage applied to the motors using pulse width modulation (PWM). This method has some advantages over the constant voltage method. Analysis of Motor Efficiency Using the motor drive that we constructed earlier, we will implement a new method of motor speed control and compare it to the method used in Experiment #5. There are many parameters that can be used for this comparison and we will learn how to decide which parameters are relevant to us and which are not. Methods of Generating PWM Signals We will generate PWM signals using a new circuit. In the past, you used a simple oscillator circuit and a function generator. Neither of these methods provided a convenient way to control duty cycle if this were to be inserted into an autonomous vehicle. Today, we revisit the oscillator circuit and use the magic of diodes to alter its function in a way that we can understand. In the end, the bend of a flex sensor will become the controller of the PWM s duty cycle and enable the PWM generator to be used without the experimenter adjusting a knob!

2 Driving Motors with PWM Analyzing a PWM Signal A problem encountered with the previous techniques of speed control is strongly related to the stall current of the motor. A lower DC voltage will eventually stall the motor, drawing a large current that drains the battery while failing to turn the motor. Pulse-Width Modulation (PWM) is a method by where the peak voltage is high enough to overcome the stall point on the IV curve and, theoretically, no current will be drawn from the battery when the voltage falls back to zero. Less energy is wasted in the speed-control mechanism. By controlling the Duty Cycle of a square-wave signal rather than the level of a DC voltage, the wheel should move continuously at a slow speed without stalling. Configure the function generator to produce a 0 5 square-wave signal with a frequency of 500Hz and duty cycle of 80%. Configure the oscilloscope to measure the frequency and duty cycle produced by the function generator. Question 1: Use the oscilloscope s Quick Measure to measure the average voltage. = (experimental) Question 2: Use the cursors on the oscilloscope to measure and of your square wave and compute the duty cycle. Record your data and computations here.

3 Question 3: Mathematically compute the average voltage and determine if the oscope measurement agrees. = = (theoretical) (Remember that you don t need calculus to compute this!) Question 4: Compute the %error of the two previous average voltage measurements using a theoretical value of a perfect 80% duty cycle signal as the theoretical reference below.!"#\$! % =100 = #\$!

4 Driving a Motor The function generator cannot supply the higher current needed to drive the motor. Instead, we will employ the transistor circuit we studied earlier. If you haven t already, construct the motor drive circuit as shown and connect the function generator as the input. Figure 1: Circuit schematic of the motor drive circuit. Question 5: Use your oscilloscope to measure the voltage across the motor. Comment on what you see. Why do you think this signal might not look like a perfect square wave?

5 Question 6: Use your oscilloscope to measure the average voltage across the motor when driven by the full range of duty cycles (starting from 20% to 80% in appropriately-sized steps). Be sure to use increasing to find the duty cycle necessary for turn-on if you can. Note: As an alternative to collecting this data using the function generator, you may use the RedBoard to generate PWM signals (refer to earlier modules on using the Arduino, especially the one on PWM). Just be careful to record the PWM percentage produced by the board for each measurement. Duty Cycle (%) % &'( % ) &'( *+* Comments Table 1: I-V curve for motor with PWM signal while Increasing Duty Cycle. *While will be measured by the scope,, should be estimated from the motor IV data you collected last week.

6 Question 7: Decrease the duty cycle to find the stalling point if you can. Report the stalling duty cycle here. Generating PWM with a Circuit In previous experiments, we constructed an oscillator circuit using a resistor, capacitor and inverter as shown below. In this circuit, the frequency of oscillation is controlled by the time it takes for the capacitor to charge and discharge. Since the capacitor charges and discharges through the same resistor, the amount of time the oscillator spends at 5 V equals the amount of time it spends at 0 V, i.e. it has a 50% duty cycle. Figure 1: A simple oscillator circuit. Now let s make a couple of simple modifications to oscillator that allows us to control the duty cycle. Specifically, we ll modify the circuit so that the capacitor charges through one resistor and discharges through another. In addition, we ve added an extra inverter at the output of the circuit so that we can integrate this oscillator into other circuits without its behavior being affected. Construct the modified oscillator circuit shown below. (- = 100./, 0 1 = 10 2Ω, 0 4 = 22 2Ω)

7 Figure 6: Circuit schematic of an oscillator with a selectable duty cycle. Question 8: Measure the frequency and duty cycle of this oscillator. Question 9: 6-= :7 8 = Apply the following formula to estimate the duty cycle of this oscillator.

8 Question 10: Suppose we replace R2 with the flex sensor. What range of duty cycles do you expect this new circuit to produce? (You ll need to measure/recall the minimum and maximum resistance of the flex sensor.) Question 11: Replace 0 4 with the flex sensor and record the minimum and maximum duty cycle. Putting it together Connect your flex-sensor-controlled PWM circuit to the input of your motor drive circuit. If necessary, adjust the value of 0 1 so that the motor slows as much as possible without stalling. Question 12: Draw the circuit diagram for the full circuit and include the values of any and all resistors.

10 Lab Report Rubric The following rubric will be provided at the end of each lab procedure. As a final step in preparing your lab report, you will use this rubric to analyze your own performance. Section Criterion Comments: Experimental Setup and/or Design Description Measurements Computations Circuit Schematics are drawn neatly, accurately, and properly labeled. Decisions regarding experimental setup and design are clearly explained. Tables include units and proper precision. Any new device introduced should be characterized using measurements! Computations performed on raw data are explicitly described and follow rules for significant figures. Analysis Modeling Conclusion General Formatting Graphs have title, labels, units, scale, legend; Lines for curve-fitting appear in the graph when needed and parameters like the intercepts and the slope are labeled. A mathematical model for the curve-fit graph allows for more abstract references to the device s behavior. The expected behavior is explained in the context of the graph. Conclusions are drawn from your experimental results to support the reason(s) for completing the experiment. Closes the loop on the Introduction. Answers to questions clearly labeled. The overall appearance of the report is professional. Self-assessment This table has been thoughtfully completed.

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