In this video, we introduce an example system to control: an inverted pendulum on a cart. We describe the state-space, find the fixed points, and simulate the system in Matlab. Because the linearized system is controllable, we will be able to arbitrarily place the eigenvalues of the closed-loop system through feedback in the next two videos.
Code available at: http://faculty.washington.edu/sbrunton/control_bootcamp_code.zip
These lectures follow Chapters 1 & 3 from:
Machine learning control, by Duriez, Brunton, & Noack
Chapters available at: http://faculty.washington.edu/sbrunton/mlcbook/