I've began to study dynamical system control and decided to explore case of cartpole - an inverted pendulum attached to a moving cart.
This topic has few new cool ideas which wanted to share, so video is quite long.
Chapters:
0:00 Intro/Lecture Plan
3:15 Solving system of ODEs via eigenstuff
8:08 Representation of a dynamical system
14:00 Linearization/ Taylor series
21:00 Example with pendulum
25:00 Stability condition for continuous system
30:00 Stability condition for discrete system
33:33 Control/Controllability/Closed loop system
39:00 Pole placement example
43:50 Cartpole Lagrangian
51:00 Cartpole Equations of Motion
58:00 Side note about deriving B
1:04:50 Cartpole Linearization
1:09:00 Cartpole pole placement
1:12:30 Visualization
1:13:05 Comments on nonlinearity
1:18:37 Recap
1:21:45 Old man yelling on cloud
1:23:00 GL!
References:
Aleksandar Haber's lecture on pendulum linearization.
th-cam.com/video/SfbRknFoSZ0/w-d-xo.html
Brunton's "control bootcamp"
th-cam.com/play/PLMrJAkhIeNNR20Mz-VpzgfQs5zrYi085m.html
Matlab's video on pole placement
se.mathworks.com/videos/state-space-part-2-pole-placement-1547198830727.html