I am writing a simple to understand series on controlling real physical systems. You may access it here.
python free_fall_pendulum.py
Freefall Inverted Pendulum System
python free_fall_cart_and_pendulum.py
In this example, the motors on the cart are actuated at fixed time. Thus, they deliver an external force on the system at pre-determined time.
python forced_cart_and_pendulum.py
In this example, the motors are actuated such that the lineared system
becomes stable. The linearization point is pendulum up (or [0,0,-pi/2,0]).
See also anaysis_linearization.py for analysis of linearized system and its
stability.
For this we have made used of the python package control for
the functions pole_place and lqr. In the future will try and
understand how these work and implement these.
There were a few subtle things that need to be mathematically correct for
this to work. Look at the code to know the exact details.
python controlled_cart_and_pendulum.py
Here is the system stabilized using Eigenvalues as a result of LQR (Linear Quadratic Regular)
