6.01, Spring Semester, 2008—Assignment 8 Revised, Issued: Thursday, April 3 1MASSACHVSETTS INSTITVTE OF TECHNOLOGYDepartment of Electrical Engineering and Computer Science6.01—Introduction to EECS ISpring Semester, 2008Assignment 8 Revised, Issued: Thursday, April 3Revised Design Lab: Replaces only the design lab sectionof the original handout. There are post-lab homeworkproblems in the original handout that you need to do.Design LabThe goal of today’s design lab is to build a circuit to control the position of a motor. In later labs,we will use this motor to turn the “head” of our robot.At a high level, we can think of our motor controller as follows:+KmotorθdθV−We wish to command a desired angle θdthat is the input to a feedback loop that compares thedesired angle to the measured angle θ. The difference is multiplied by a gain K to generate anoutput voltage V that will cause the motor to turn in a direction to make the measured and desiredangles equal.We cannot conveniently manipulate angles, so we will use potentiometers to convert the angle oftheir input shaft to a voltage. A potentiometer is a three terminal device. The resistance betweenthe middle and bottom terminals increases in proportion to the angle of the input shaft (θ) and theresistance between the middle and top terminals decreases, so that the sum of the top and bottomresistors is constant (here it is 5KΩ). By connecting a potentiometer as shown below we can createa device that converts θ into a voltage Vo(measured relative to GND).+12 V−12 VVo1KΩ5KΩ1KΩpotθVoModel6.01, Spring Semester, 2008—Assignment 8 Revised, Issued: Thursday, April 3 2Question 11: Construct the circuit shown above (be sure to adjust the power supplies to ±12Vbefore connecting the circuit.) Mathematically determine the range of V0that the device cangenerate. Measure the range (relative to GND) and compare the measured and calculatedranges.Question 12: Use the potentiometer from the previous question to drive the voltage input tothe motor. Use a Lego motor with adaptor cable and breadboard adapter (6 pins). Themotor is connected between pins 5 and 6 of the adaptor. Connect pin 5 to the output of thepotentiometer and connect pin 6 to GND. How fast can you get the motor to turn? Explain.Question 13: Use an op amp to buffer the output of the potentiometer (this is similar to whatwe did last week when we used an op amp as a buffer between two voltage dividers). Useone of the two op amps in the KA-334 package (see schematic below). Let Vcc= +12 V(pin 2) and Vss= −12 V (pin 4). Compare the behavior of the motor now to its behaviorin the previous circuit. Can you make it go in both directions?Checkpoint: 30 minutes• Show the potentiometer controlling your motor. Be sure it can go in both directions.When we use the motor to position the robot “head,” we will only have access to a +12 V supply(the robot does not have a −12 V supply). One way to get bidirectional turning from a single+12 V supply is by generating a “virtual ground” that is midway between 0 V and +12 V.Question 14: Reconnect power to the op amp so that it uses a single +12 V supply, i.e., connectVcc= +12 V (pin 2) and Vss= GND (pin 4). Use a second op amp to generate a “virtualground” signal. Modify your previous op amp circuit so that it uses the virtual ground toallow the motor to turn in both directions.Be careful about the following:• Your ’virtual ground’ should be halfway between the power supply rails. (So thatthe power supply rails become ±6 with respect to the virtual ground.)• Henceforth, think of this as ground, think of what was formerly +12 as +6 (it is6 volts higher than ground), and think of what was formerly 0 as -6 (it is 6 voltslower than ground). Remember that what matters is the relative voltages.6.01, Spring Semester, 2008—Assignment 8 Revised, Issued: Thursday, April 3 3Checkpoint: 60 minutes• Show the potentiometer controlling your motor, with a +6 and -6 supply. Be sure itcan go in both directions.For the remainder of today’s lab, you will need a “head assembly,” which you can obtain from thestaff. These head assemblies have circuitry that is pre-built on the “bottom board.” The “topboard,” which is mounted so that it can be swiveled by a Lego gear motor, has no circuitry on itright now. Examine and familiarize yourself with the circuitry on the bottom board (shown below).You will note that there are two KA334 op-amps, wired for power but not for input or output.The photograph of the bottom board (above) shows the following:1. Potentiometer 1: This ’pot’ is connected between the power supply and ground rails by two 1kresistors. The potentiometer has a total resistance of 5kΩ, just like the example you startedthis lab with.2. Potentiometer 2: When you get the head assembly, this potentiometer will be connected tothe bottom of the Lego motor. It is connected to the power and ground rails directly (notthrough resistors).6.01, Spring Semester, 2008—Assignment 8 Revised, Issued: Thursday, April 3 43. Two KA334 op-amps. As you can see, they are both connected to the power and groundrails. Two of the input pins (numbered 5 and 8) are connected by short red wires to rows ofholes beyond the ends of the op-amps. This is just for your convenience in wiring. The othertwo input pins are unconnected. The two op-amp outputs (pins 1 and 3) are also connectedto outboard rows of pins. Note that pin 1 of one of the op-amps is connected to two 47 ohmresistors in parallel. You should use that connection to the motor when it comes time toconnect to the motor. DO NOT DO THIS YET.4. There are two connectors from pins to cables. One of these is an RJ-11 like the one you havealready used to connect to the motor. As you already know, pins five and six are the motorconnections. The other cable connection accepts the RJ-45 cable that is on the robot, and iswired so that this board will get power and ground connections from the robot battery. Forthe moment you can ignore this connector and derive +12V and 0V from the same powersupply you have been using.5. Note that, on some but not all protoboards, the left and right power rails must be connectedby jumpers. The jumpers for the bottom two power rails are shown in the photograph asVCC, VSSJumpers. There must be similar jumpers for the top two power rails. The upperjumpers cannot be seen in the photograph because they are beneath the RJ-11 Motor Jack.Please make
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