Further Analysis: In this lab we took our controller design one step further from lab 6 in that we analytically determined controller gains based on a desired natural frequency of 5 and damping coefficient of 0.8. Through polynomial coefficient matching, we found the found the proportional gains to be -3.2839 -0.2771 -9.09 and -3.9995 for the balls velocity, platform angular velocity, the balls position, and the angular position of the platform. All except for the gains associated with the balls position and velocity were changed by less than 5% . We increased our balls position gain by 300% and decreased our balls velocity gain by the same amount.
More information about the analysis can be found at https://bitbucket.org/rmmcmull/cpe-mech-team/src/master/LAB_0X06/

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