PID Optimization Tuning Using Lagrangian Mechanics

Authors

  • Ethan Kou Henry M. Gunn High School
  • Majid Moghadam University of California Santa Cruz

DOI:

https://doi.org/10.47611/jsrhs.v13i1.5956

Keywords:

Lagrangian Mechanics, PID

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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References or Bibliography

Visioli, A. (2006). Practical PID control. Springer Science & Business Media.

Rawlings, J. B. (2000). Tutorial overview of model predictive control. IEEE control systems magazine, 20(3), 38-52.

Samak, C. V., Samak, T. V., & Kandhasamy, S. (2021). Control strategies for autonomous vehicles. In Autonomous Driving and Advanced Driver-Assistance Systems (ADAS) (pp. 37-86). CRC Press.

Brizard, A. J. (2014). Introduction To Lagrangian Mechanics, An. World Scientific Publishing Company.

Bemporad, A., Morari, M., Dua, V., & Pistikopoulos, E. N. (2002). The explicit linear quadratic regulator for constrained systems. Automatica, 38(1), 3-20.

Published

02-28-2024

How to Cite

Kou, E., & Moghadam, M. (2024). PID Optimization Tuning Using Lagrangian Mechanics. Journal of Student Research, 13(1). https://doi.org/10.47611/jsrhs.v13i1.5956

Issue

Section

HS Research Articles