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arXiv · 2310.00016

PID Optimization Using Lagrangian Mechanics

Ethan Kou·Majid Moghadam
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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.

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BibTeXRIS

Ethan Kou, Majid Moghadam. 2023-09-25. PID Optimization Using Lagrangian Mechanics. https://doi.org/10.47611/jsrhs.v13i1.5956

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