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Inverted Pendulum Control

For my senior thesis project I developed and built an inverted pendulum, as well as, simulations in Matlab where I implemented linear such as PID, LQG and swing-up non-linear controllers. These are the highlights of this project.

 

Download the full document of this work below, it is only available in portuguese.

Hardware Design

This Project was designed using Solidworks CAD tool. The Pendulum has two degrees of freedom and it is controlled by a Raspberry Pi 3B along with Odrive board for the BLDC motor and two optical encoders. 

pendulo_solid.png
inverted_pendulum.jpeg

Mathematical Model

In order to simulate the pendulum a mathematical model based on Lagrange method was analyzed. For the linear controllers the equations were linearized  and converted to state-space form. Then, the state-space system is discretized using zero order hold technique.

pendulo_draw.png
pendulo_eq1.png
pendulo_eq2.png

Experiments

Swing-up Controller

Linear Quadratic Gaussian (LQG)  Controller

Proportional Derivative Integrative(PID) Controller

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