PID Optimization Using Lagrangian Mechanics

TL;DR

This paper uses Lagrangian mechanics to simulate an inverted pendulum system and proposes optimizing PID controller gains through an objective function to improve balancing performance.

Contribution

It introduces a novel approach combining Lagrangian mechanics with PID gain optimization for inverted pendulum control.

Findings

Lagrangian mechanics effectively simulates the inverted pendulum system.

Optimized PID gains improve balancing accuracy.

The method enhances control tuning without physical experiments.

Abstract

Creating a simulation of a system enables the tuning of control systems without the need for a physical system. In this paper, we employ Lagrangian Mechanics to derive a set of equations to simulate an inverted pendulum on a cart. The system consists of a freely-rotating rod attached to a cart, with the rod's balance achieved through applying the correct forces to the cart. We manually tune the proportional, integral, and derivative gain coefficients of a Proportional Integral Derivative controller (PID) to balance a rod. To further improve PID performance, we can optimize an objective function to find better gain coefficients.