6.01, Spring Semester, 2008—Exploration 10: Due: Thursday, May 1 1MASSACHVSETTS INSTITVTE OF TECHNOLOGYDepartment of Electrical Engineering and Computer Science6.01—Introduction to EECS ISpring Semester, 2008Exploration 10: Due: Thursday, May 1Exploration 10: designing b etter headsIn design lab 9 (question 15) we studied the effects of gain on the stability of a head orientationcontroller. In that lab, we modified the gain by changing the gain of a circuit. In design lab 10we studied the effect of delays on stability when head orientation was controlled by the computer.There is still one other aspect of the design that will have an important impact on the systemstability: the physical design of the head itself. The way that you position the two photo-resistorson the head, how they are oriented, and the shape of the nose that you build may have veryimportant implications for how the final system will behave. For example, for some designs, theoutput of the photoresistors varies smoothly with head rotation, while in others, it is not evenmonotonic. Nonlinearities can be problematic, especially when they effect the error signals thatare generated when the head angle is close to the target. In the previous labs, design choices thataffect these non-linearities were made arbitrarily. In this exploration we will study the effect ofthose choices.This exploration is divided into three parts. In the first part, we will build the basic infrastructurefor testing and calibrating the sensors. In the second part, we will explore several head designs andwe will see how they affect the function relating the output of the photo-resistors with the angle ofthe head. In the third part, you can study the effect of your design choices on the stability of theangle controller. Can you propose an optimal head design?Question 1: Write a Python program to sweep the head back and forth. The head should firstrotate so that it is “looking” directly forward (θ = 0). It should then sweep uniformly to theleft. When it reaches θ = −π/3 (not quite full left, which would be π/2), it should reversedirection and sweep uniformly to the right till it reaches θ = π/3. It should then returnuniformly to θ = 0. This whole sequence should take approximately 5 seconds.Question 2: To build an optimal feedback controller for light tracking, we must quantify theperformance of the photosensors. Measure and plot how the computer’s representation ofthe left and right photosensor depend on the angle of the head when the light (which isstationary) is coming from a point that is 1 foot directly in front of the head.6.01, Spring Semester, 2008—Exploration 10: Due: Thursday, May 1 2Question 3: Change the distance between the two photo-resistors and remeasure the relationsbetween the photosensor outputs and head angle. Compare results for the two differentdistances and explain any differences.Question 4: Change the length of the nose (or remove the nose entirely) and remeasure therelations between the photosensor outputs and head angle. Compare results before andafter the change and explain any differences.Question 5: Suggest some other change to the physical layout of the head that will affect therelation between photosensor outputs and head angle. Compare results before and after thechange and explain any differences.Question 6: Describe features of the relations that were measured in the last three questionsthat are desirable and undesirable. Design a physical layout of the head that is “optimized”in the sense that the desirable features are maximized and the undesirable features areminimized. Describe the resulting layout.Question 7: Test your “optimized” design from the last part for two different locations of thelamp: one at one foot (as before) and one at four feet. Describe the effect of changing thelamp distance.Question 8: Generally, we expect better performance if the “error” signal that we generatefrom the photoresistors varies linearly with head angle and does not depend on distance tothe lamp. Optimize your head design and the way you compute the error signal from thephotoresistor voltages. Measure and plot the resulting error signal as a function of headangle and lamp distance.Question 9: Test the effects of your optimizations on the stability of the system for light track-ing. Determine the highest stable gain for the optimized system and for your original system.In what ways (if any) has the system been improved.
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