TEXAS A&M UNIVERSITY ENGR 111B: Foundations of Electrical & Computer Engineering Lab 6: Pulse Width Modulation Team Members: _________________________ _________________________ Section Number: __________ Team Number: __________ This Lab is due by the Beginning of the Next Lab Session. Written By: Hank Walker Lorne Liechty Written by Texas A&M University 1 Lab 6: Pulse Width Modulation Time Limit: 1 week OVERVIEW Using RC circuits we can not only time individual events, but we can also create repeating timers. This oscillatory timing is used in virtually every electronic device available. In this lab students will examine the use of a digitally oscillating signal to control DC motor speed. This approach contrasts with the simple resistor-based current limiting method you used previously. Topics covered in this lab include the following material: - Digitally Oscillating Signals - Pulse Width Modulation - Average Voltage, Current, and Power - How a PWM signal can be generated using a 555 timer - Diodes - PWM Signal Control of DC Motor BACKGROUND To assist students in completing the exercises required by this lab, the following background information has been provided. It is recommended that each student read all of the following information as a beneficial review of the topics required. DIGITAL OSCILLATIONS An oscillating signal is one which changes between two levels according to a regular pattern of intervals. AC (Alternating Current) voltages are included in the realm of oscillating voltages, but the term AC is reserved for signals which include both positive and negative voltages. A digital oscillation also switches between two levels according to defined intervals, and the ideal digital signal exists only at the specified levels and does not exist at the levels in between. The signals represented in Figures B1 are two different digitally oscillating signals. Figure B1: Digitally Oscillating Signals Written by Texas A&M University 2 Examining the signals in Figure B1, notice that the lower of the two voltages does not have to be set to zero volts, or ground; the lower voltage of a digital signal is defined to be a logical LOW or 0, but the value is not required to be zero. When a signal is not centered around zero the signal is said to have a DC offset that raises or lowers the signal to a new center voltage. Signals that do not have DC offsets fall into the realm of AC signals, since their voltages will fall below zero and therefore reverse the flow of current. Each time that the voltage of a digital signal rises to its HIGH state and then back to its LOW state, the signal is said to have pulsed. The amount of time that a digital signal remains in its HIGH state before returning to the LOW state is called the pulse width. The period of a digital signal is length of time before a signal repeats itself. Adding the HIGH pulse width and the LOW state time together is also equal to the period of the signal. The frequency of a digital signal is equal to the inverse of the period, and represents the number of times that a signal repeats itself in one second. All of the stated elements of a digitally oscillating signal are shown and labeled in Figure B2. Figure B2: Digital Signal with Labels PWM Signals Pulse Width Modulation (PWM) is a process which changes the pulse width of a signal, while keeping the frequency/period constant. The result is a signal that may be switched HIGH for a longer or shorter amount of time than it is switched LOW. When a PWM circuit alters the pulse width in this way, it is said to be changing the duty cycle of the signal, which is the ratio of the pulse width time over the total period. Duty Cycle is a dimensionless quantity that is stated as a percentage. Figure B3 shows two examples of pulse width modulated signals. Written by Texas A&M University 3 Figure B3: Pulse Width Modulated Signals Average Voltage / Current / Power Another property of a PWM signal is that the time average values of its voltage and current vary with its modulation. A digitally oscillating signal that is HIGH and LOW for equal amounts of time has a time average voltage or current equal to 50% of the difference between its HIGH and LOW voltage/current values. During the time that the signal is HIGH, the voltage and current are at their maximum values, but when the signal is LOW the voltage and current are at their minimum values. Power is equal to voltage multiplied by current, and therefore the average power is directly proportional to the square of the duty cycle, since both the average voltage and average current rise with duty cycle. Since pulse width modulation varies the duty cycle of a signal, it also varies the average voltage and current levels in the circuit. If the frequency is high enough, this average voltage or current can be interpreted as a virtual DC value. An analogy is that a video is a collection of still pictures, but it looks like smooth motion to our eyes, since the pictures change faster than the eye can respond. Similarly, a PWM signal fed into a motor will act as a smooth voltage if the PWM frequency is high compared to the rate at which the motor can respond. Pulse width modulation is much more complicated than using a circuit with resistors to divide the voltage or current. However, since resistors dissipate all of their power as heat, they perform little useful work with the power they are given. Because a PWM signal can change the apparent DC values of a circuit without the use of resistors, they waste very little power. This is a useful property in situations where power is not unlimited. Written by Texas A&M University 4 HOW THE 555 TIMER GENERATES A PWM SIGNAL The 555 timer is an integrated circuit that has been used for decades in electronics for pulse generation, time delay generation, and pulse width modulation. As shown in Figure B4, a 555 timer consists of two comparators and a Flip-Flop which is a device used in digital logic similar to an SR Latch. Flip-Flops are not covered in this series of labs, but they are extensions of latches that also hold their outputs stable until they have been changed by a differing digital input. The comparator inputs are fed by an RC time constant provided by the user, An animated schematic of the 555 as an oscillator is available online at http://www.williamson-labs.com/pu-aa-555-timer_med.htm to help you understand its function. Many other 555 timer resources are available on the Web. See http://www.uoguelph.ca/~antoon/gadgets/555/555.html for a tutorial. Figure B4: NE555 functional block diagram Diodes As shown in Figure B5, a diode is made by combining two portions of p-type and n-type semi-conducting material. Written by Texas A&M University 5 Figure B5: Diagram of a PN Junction Diode A diode is an electrical device which regulates the flow of current through a circuit. Depending on the polarity of the voltage applied across it, a diode will be either turned on or off. Figure B6 shows the two possible states of an ideal diode and how the current in the circuit is affected by the diode’s state. Figure B6: States of Diode As you can see, if the diode voltage is forward biased then the current will flow freely in the circuit. However, if the diode voltage is reversed biased current cannot flow in the opposite direction through the diode. It is also important to note that when in the forward biased state an actual diode will have an associated voltage drop across it, which is usual equal to approximately 0.7 volts for a silicon diode. The PWM Generation Circuit Figure B7, contains a schematic of one method for using a 555 timer to create a fixed frequency PWM signal. Written by Texas A&M University 6 Figure B8: Schematic for a PWM Generator Using a 555 Timer In the schematic, C1, R1, R2, and the potentiometer are all used to vary the timing of the circuit. The reason that the pulse width of the signal is variable in this configuration is that diode D2 creates a path for current to bypass the resistance between the tap of the potentiometer and D1 to charge capacitor C1. Further, as the capacitor discharges, D2 prohibits the flow of current directly to ground and forces the capacitor to discharge through D1 and the previously avoided resistance. During the charging cycle a voltage drop is induced across D2; as such diode D1 is necessary to repeat that same voltage drop during the discharge cycle so that the operating frequency of the signal is maintained. The equations which govern the Duty Cycle and frequency of this configuration are given as: t1 ( HIGH ) 0.67 * R A * C1 t2 ( LOW ) 0.67 * RB * C1 1 Period T t1 t 2 Frequency f T where RA is equal to the total resistance of R2 plus the resistance between R2 and the tap of the potentiometer (between 100 and 10.1k ohms), and RB is equal to the resistance between the tap and R1 plus the resistance of R1 (between 100 and 10.1k ohms). The duty cycle varies from approximately 1% to 99%. DC Motor Control If you swap the power connections of the motor (e.g. swap the black and white wires on the cable driving the motor), the motor will change directions. NOTE: Be careful not to swap the black (ground) and white (positive battery voltage) wires running from the Lego brick outputs. This will put reverse voltage on your circuits, and may destroy chips such as the LM393 and NE555. The motor reverses directions Written by Texas A&M University 7 when the connections are swapped because the current flowing through the motor has changed directions. When current moves through the windings of a motor, it produces an associated electromagnetic field. The magnetic field produced by the wires attached to the armature (rotating core) of your DC motor reacts with the inherent magnetic field of small permanent magnets attached to the sides of the stator (fixed shell). This reaction either attracts or repels the windings of wire attached to the axle and causes it to turn. Figure B9 is a basic diagram of a DC motor and its components to assist in understanding its operation. Figure B9: Diagram of Basic DC Motor Conveniently enough, if a magnetic field is produced by flowing current in one direction, the opposite magnetic field is produced by flowing current in the opposite direction and therefore causes the motor to turn in the other direction. This is what causes the motor to change directions when the motor power wires are switched. DC MOTOR SPEED CONTROL The DC motors on your robot are capable of varying their speed based upon the current that is drawn through them. The driving force of the motor is caused by the interaction of the magnetic field produced by the current though the windings on the armature and the permanent magnets attached to the stator. The magnitude of the force caused by this interaction varies as the current through the windings varies, thus regulating the speed of the motor. Speed Control Using a PWM signal In Lab 4, you controlled the speed of your motors by limiting the current through it with a potentiometer. A PWM signal can also be used to vary the motor speed. As mentioned previously, the average voltage and current of a PWM signal can be adjusted by modifying the duty cycle of the signal. When the current through the motor is varied using a PWM signal, the end result is the same as when the current is modified using a resistor; causing the motor to slow down. A PWM signal has two advantages when controlling motor speed. First, since it turns the motor on or off, it does not waste as much power as using a resistor to control Written by Texas A&M University 8 the speed. Second, unloaded motors usually have a linear speed-voltage relationship. The relationship for the NXT motor is shown in Figure B10. Figure B10: Unloaded NXT speed vs. voltage (from www.philohome.com). However, in Lab 4, you discovered that the speed is superlinear in voltage when the motor is under load. The NXT characteristics are shown in this table from http://www.philohome.com: Rotation Mechanical Electrical Torque Current Efficiency speed power power NXT 4.5 V 16.7 N.cm 33 rpm 0.6 A 0.58 W 2.7 W 21.4 % 7V 16.7 N.cm 82 rpm 0.55 A 1.44 W 3.85 W 37.3 % 9V 16.7 N.cm 117 rpm 0.55 A 2.03 W 4.95 W 41 % 12 V 16.7 N.cm 177 rpm 0.58 A 3.10 W 6.96 W 44.5 % As can be seen, doubling the voltage from 4.5V to 9V increases motor speed by 3.5x. In a PWM signal, since the motor is either all the way on (full voltage) or all the way off, the speed is simply proportional to the full power speed times the duty cycle. So a 50% duty cycle signal will run the motor at half its full speed for that voltage and torque. (Torque is the twisting force on the motor, e.g. the force that the wheel exerts when resisting turning against the floor). Written by Texas A&M University 9 LAB EXERCISES BEFORE YOU COME TO LAB: As in Lab 4, you will drive the robot in a circle with a radius of 2 feet. In order to do this, you must first calculate what speeds you will need each motor to operate at, so that the robot will follow the circular path. Use Figure L1 and the equation below to determine the wheel speeds necessary to navigate this path. Speed1 Radius1 2 feet Speed 2 Radius2 2 feet w R1 R2 w = width of robot Figure L1: Circular Path of Robot The width of the robot from wheel center to wheel center is 11.3 cm, and the tires are 5.7 cm in diameter. The ratio should produce a circular path which places the outside edge of the robot on the 4 foot diameter circle. Enter the values for the speeds of the right and left wheels in Table L2. As in Lab 4, the outer wheel will run at full speed, and you will reduce the speed of the inner wheel using PWM. CIRCULAR PATH WHEEL SPEEDS Right Wheel Left Wheel Speed (ft/s) Table L1 You will use the 555 timer to produce a PWM signal which will control the speed of the inner wheel. First, you will need to construct the circuit given in Figure L2. Figure L2: PWM Speed Control Written by Texas A&M University 10 The pinouts of the Texas Instruments NE555P timer are shown in Figure L3. VERY IMPORTANT: Unlike most chips, pin 1 is ground, rather than pin 4 as in the LM393. Due to its ancient age, the 555 violates the normal pin-out convention. Figure L3: Texas Instruments NE555P pinout As discussed above, the two 100 resistors limit the PWM duty cycle range from about 1% to about 99%. The diodes permit the duty cycle to be >50% (high). The output drives a 1k resistor to the base of a 2N3704 NPN transistor to power the motor, since the 555 output cannot quite provide the current required of the motor. As a reminder, the 2N3704 has a non-standard pinout, shown in Figure L4. Figure L4: Packaging Diagram of 2N3704 NPN Transistor. It is housed in a TO-92 package. With the flat side up, the emitter is on the left, collector in the middle, and base on the right. (Most transistors have the base in the middle and collector on the right). When determining which capacitor is which, the following website for capacitor codes may be useful: http://xtronics.com/kits/ccode.htm. The diodes have a line on the end that corresponds to the line in the schematic. That is, current flows out of the end with the line. EXPERIMENTAL PROCEDURE 1. The first test will be to run the robot in a straight line. Attach your PWM circuit to the faster motor. Calculate the duty cycle needed to have faster motor run at the same speed as the slower motor. Remember that in Lab 4, you computed the difference in resistance between the two motors, and put a potentiometer on the lower-resistance (faster) motor to slow it down. In this case you will adjust the Written by Texas A&M University 11 duty cycle of the PWM circuit to slow the faster motor down by a corresponding amount. For example, suppose the left motor is 50 ohms and the right motor is 55 ohms, for a 7.2V battery, the left motor draws the left motor draws 144 mA and the right motor draws 131 mA. To reduce the left motor current to 131 mA, the effective left motor voltage must be reduced to 6.55V (131 mA * 50 ohms). This is 91% of the battery voltage (6.55V/7.2V). So the PWM circuit should be set to 91% duty cycle. 2. Calculate the values of RA and RB above to achieve the appropriate duty cycle and adjust the potentiometer accordingly. Recall that RA is the value of Ra plus the value between the Ra connection and the tap on the pot in Figure L2. Similarly for RB. 3. We can use an oscilloscope to measure the duty cycle directly, but an alternative is to measure the voltage from the 555 with your voltmeter. Your voltmeter responds more slowly than the 555 frequency, so will measure the average value. 4. Run your robot with the calculated duty cycle. Tweak the potentiometer until the robot runs in a straight line. Afterwards, measure the resistance of each side of the potentiometer and calculate the duty cycle actually used. Use your voltmeter to measure the average voltage out of the PWM circuit. Note that you should measure it directly at pin 3, since the voltage at the base of the transistor will be at most 0.8V. Record all values in Table R1. 5. Using the process above, calculate the potentiometer resistance which would cause the robot to follow a circular track with a radius of 2 ft. Use the speeds that were calculated before the lab in Table L1. Record the calculated value of RA in Table R2. 6. Test your calculated values by running the robot in a circle. If your values are not satisfactory, adjust them so that the robot successfully navigates a 4-ft diameter circle. Record your corrected value of RA, along with their associated percent error from the calculated values in Table R2. Written by Texas A&M University 12 RESULTS: to be uploaded onto WebCT Straight Line Values Speed (ft/s) Calculated RA (kΩ) Calculated Duty Cycle (%) Measured PWM Output Voltage (V) Tweaked RA (kΩ) Calculated Tweaked Duty Cycle (%) Measured MWP Tweaked Output Voltage (V) Table R1 CIRCLE RUN Calculated RA Corrected RA Resistance Resistance % Error Inside Inside Wheel Wheel Table R2 Written by Texas A&M University 13 REPORT: to be uploaded onto WebCT REPORT REQUIRMENTS Answer the following questions: - What are the pros and cons of the current limiting (via resistor) motor speed control method used in Lab 4? - What are the pros and cons of the PWM motor speed control method? - What would be your recommendation and why, for which system to use if: o Your robot needed cheap and effective speed control. o Your robot was going to be used by NASA to explore Mars. Written by Texas A&M University 14
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