Inverted Pendulum - Control Systems

I am writing a simple to understand series on controlling real physical systems. You may access it here.

Inverted Pendulum only System

python free_fall_pendulum.py

Freefall Inverted Pendulum System

Inverted Pendulum and Cart System

python free_fall_cart_and_pendulum.py

Forced Inverted Pendulum and Cart System

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

Control Inverted Pendulum and Cart System

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)