MASSACHVSETTS INSTITVTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6 099 Introduction to EECS I Spring Semester 2007 Assignment for Week 8 This 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 circuits In all the previous labs we have mostly abstracted away the electrical nature of the signals being processed and generated by the robot In this laboratory you will design and build an electrical feedback system which controls a robot head In subsequent labs you will put eyes on the head to help your robot see As with the previous labs you will start by building a python tool to help you analyze circuits and then you will use that tool to help you design an improved robot head controller So this week you will be extending the constraint resolver analyzing an electromechanical 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 Resolver You will be extending the constraint resolver program for analyzing circuits by adding an op amp model to the program You can then use your augmented constraint resolver to help you design a circuit to control the motor Download and test the constraint system The procedures for this lab is at the 6 099 web site on the calendar for this week Download resolver tar or resolver zip if you prefer again and unzip it Make sure you can run one of the example files Add an op amp model to the constraint resolver In class we discussed the following operational amplifier circuit referred to as an inverting amplifier 15 V Vo Rin V 15 Vout Opamp Rf In order to simplify the analysis of the op amp circuit we assumed that V V 0 and that no current enters the op amp inputs Using those assumptions we determined that the relationship between Vin and Vout was Rf Vin Vout Rin The main reason we could assume that V V 0 was that the op amp was connected in a feedback configuration and the gain of the op amp was very large You will now investigate the accuracy of that approximation using the constraint resolver The abstract model we used for the op amp was a voltage controlled voltage source model and using that model in the inverting amplifier yields a somewhat different looking schematic iout Opamp Model where the gain of the voltage controlled voltage source K is a very large number Please add this voltage controlled voltage source model to the constraint solver allowing K to be a parameter like resistance is for resistors Keep in mind that this model has four terminals but there is only one nonzero current iout Therefore your constraint should involve four voltages and one current Please carefully consider what to do with i out the current generated at the output terminals of the op amp Note that this output current is not used in the op amp constitutive relations recall that the same situation occurs with a voltage source element What constraint will involve the op amp current Test your implementation by analyzing the inverting amplifier above using R in 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 which Vout Rf Vin Rin is accurate to within ten percent To Hand In You will need your op amp extension for Thursday s lab please be sure to save a copy where you can access it later You can hand in a description of your op amp constraint on Tuesday April 10th as part of Thursday s lab write up Exercises with the online tutor Use the online tutor to complete the tutor problems Thursday s Robot Head Lab Using Op amp Circuits The robot head is in four parts the base a big flat grey Lego plate the circuit protoboard which is attached to the plate the head which has a protoboard mounted on a rotating Lego platform and a the motor driver which is connected to the rotating head In addition there is a potentiometer little blue thingy on the bottom of the rotating head The potentiometer shaft is connected to the head so that the shaft rotates with the head and it is wired to the plate circuit board The potentiometer is used to measure the head position Note that one end of the potentiometer 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 output being the center connection to the potentiometer as shown in the following figure 15 V 15 As the above figure indicates the voltage at the potentiometer center connection when measured with respect to ground will be zero when the potentiometer is in its center position and will be either plus or minus fifteen volts when the potentiometer is turned all the way clockwise or all the way counterclockwise The voltage at the center connection of the potentiometer is then related to head angle see below and so the voltage produced will be proportional to the head angle 15 V 15 Above is a diagram of the robot head system that we will use The mechanical portion of the system includes the rotating head motor and potentiometer The head is connected to the shaft of the motor and is directly connected to a potentiometer so that the head motor and potentiometer all 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 at the potentiometer s wiper middle pin swings from 15 to 15 volts This voltage should be proportional to the angular position of the head This head position voltage V p is fed back to the controller The input to the system is V ref a voltage generated by another potentiometer The voltage Vref can be used to select a desired head position The system is designed so that V p tracks Vref Thus the user controls the position of the arm by changing V ref To see how this system works suppose that initially V p and Vref are equal and then Vref is increased rapidly Just after the increase V ref will be greater than Vp and so the error signal Ve will increase Because Ve has increased the controller output voltage V a increases which increases the current to the motor
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