6.081, Spring Semester, 2007—Assignment for Week 8 1MASSACHVSETTS INSTITVTE OF TECHNOLOGYDepartment of Electrical Engineering and Computer Science6.099—Introduction to EECS ISpring Semester, 2007Assignment for Week 8This handout contains• Software Lab for April 3rd• Prelab exercises due Thursday April 5th before lab• Thursday lab using the Robot head.• Post-lab write-up due Tuesday April 10th in Lecture.Getting a head with circuitsIn all the previous labs, we have mostly abstracted away the electrical nature of the signals beingprocessed and generated by the robot. In this laboratory you will design and build an electricalfeedback system which controls a robot “head”. In subsequent labs, you will put “eyes” on thehead to help your robot “see”. As with the previous labs, you will start by building a pythontool to help you analyze circuits, and then you will use that tool to help you design an improvedrobot head controller. So this week you will be extending the constraint resolver, analyzing anelectromechanical system, and designing a circuit. Whew!The summary of tasks for this week are:• Post-lecture software lab on adding op-amps to the constraint resolver• Pre-lab tutor exercises to practice on circuits with op-amps.• Robot head lab on modifying the robot head controller to use on supply.• Post-lab writeup.Tuesday’s Software Lab: Adding an Op-amp to the Constraint Re-solverYou will be extending the constraint resolver program for analyzing circuits by adding an op-ampmodel to the program. You can then use your augmented constraint resolver to help you design acircuit to control the motor.Download and test the constraint systemThe procedures for this lab is at the 6.099 web site on the calendar for this week. Downloadresolver.tar (or resolver.zip, if you prefer) again and unzip it. Make sure you can run one of theexample files.6.081, Spring Semester, 2007—Assignment for Week 8 2Add an op-amp model to the constraint resolverIn class we discussed the following operational amplifier circuit, referred to as an inverting amplifier.+_Opamp+_inRfRoutVV+V-+15-15VoIn order to simplify the analysis of the op-amp circuit, we assumed that V+− V−≈ 0 and that nocurrent enters the op-amp inputs. Using those assumptions, we determined that the relationshipbetween Vinand VoutwasVout= −RfRinVin.The main reason we could assume that V+− V−≈ 0 was that the op-amp was connected in afeedback configuration and the gain of the op-amp was very large. You will now investigate theaccuracy of that approximation using the constraint resolver.The abstract model we used for the op-amp was a voltage-controlled voltage source model, andusing that model in the inverting amplifier yields a somewhat different looking schematic6.081, Spring Semester, 2007—Assignment for Week 8 3+_+_Opamp Model+_ioutwhere the gain of the voltage-controlled voltage source, K, is a very large number. Please addthis voltage-controlled voltage source model to the constraint solver, allowing K to be a parameterlike resistance is for resistors. Keep in mind that this model has four terminals, but there is onlyone nonzero current, iout. Therefore, your constraint should involve four voltages and one current.Please carefully consider what to do with iout, the current generated at the output terminals of theop-amp. Note that this output current is not used in the op-amp constitutive relations (recall thatthe same situation occurs with a voltage source element). What constraint will involve the op-ampcurrent?Test your implementation by analyzing the inverting amplifier above using Rin= 10, 000, Rf=100, 000, and the op-amp gain equal to K = 1000.Finally, roughly determine the smallest value of op-amp gain, K, for whichVoutVin= −RfRinis accurate to within ten percent.To Hand InYou will need your op-amp extension for Thursday’s lab, please be sure to save a copy where youcan access it later. You can hand in a description of your op-amp constraint on Tuesday April 10thas part of Thursday’s lab write-up.6.081, Spring Semester, 2007—Assignment for Week 8 4Exercises with the online tutorUse the online tutor to complete the tutor problems.Thursday’s Robot Head Lab – Using Op-amp CircuitsThe robot head is in four parts: the base (a big flat grey Lego plate), the circuit protoboardwhich is attached to the plate, the “head” which has a protoboard mounted on a rotating Legoplatform, and a the motor driver which is connected to the rotating head. In addition, there isa potentiometer (little blue thingy) on the bottom of the rotating head. The potentiometer shaftis connected to the head so that the shaft rotates with the head, and it is wired to the platecircuit board. The potentiometer is used to measure the head position. Note that one end of thepotentiometer is connected to the positive supply and one end is connected to the negative supply.When so-connected, the potentiometer acts as adjustable voltage divider, with the divider outputbeing the center connection to the potentiometer as shown in the following figure.+15-15VAs the above figure indicates, the voltage at the potentiometer center connection (when measuredwith respect to ground) will be zero when the potentiometer is in its center position, and will beeither plus or minus fifteen volts when the potentiometer is turned all the way clockwise or all theway counterclockwise. The voltage at the center connection of the potentiometer is then related tohead angle θ, see below, and so the voltage produced will be proportional to the head angle.6.081, Spring Semester, 2007—Assignment for Week 8 5+15-15VAbove is a diagram of the robot head system that we will use. The mechanical portion of the systemincludes the rotating head, motor, and potentiometer. The head is connected to the shaft of themotor and is directly connected to a potentiometer, so that the head, motor, and potentiometerall rotate in unison. The outer pins of the potentiometer are connected to -15 and +15 volts,respectively. Hence, as the head swings from one end of its range to the other, the voltage atthe potentiometer’s wiper (middle pin) swings from -15 to +15 volts. This voltage should beproportional to the angular position of the head θ. This head-position voltage, Vp, is fed back tothe controller. The input to the system is Vref, a voltage generated by another potentiometer. Thevoltage Vrefcan be used to select a desired head position. The system is
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