Symbolic Verification by MATLAB

I verified my hand-derived equations from Devlog 1 using MATLAB, calculating the linearization using both the Jacobian method and a multivariable Taylor series expansion. Applying the multivariable Taylor expansion in code was a great way to put my recent calculus studying into practice, and it felt rewarding when MATLAB output the exact same a and b constants I calculated by hand. After confirming the symbols, I substituted in estimated physical constants to build the transfer function and run a system analysis. The resulting pole-zero map clearly displays the unstable pole sitting in the right-half plane, showing the open-loop is NOT stable.

Timelapse for Session 2: https://lapse.hackclub.com/timelapse/z6mQ9aBNONhu

The MATLAB script can be found on the project’s GitHub repo.