Editorial
A Comparative Analysis of Optimal LQR and Conventional PID Control Strategies for Trajectory Tracking in a 3-DOF Spherical Articulated Manipulator
@ARTICLE{10.4108/eetsmre.11147, author={Chau Nhan Phuc Pham and Minh Tan Tram and Quan-Truong Vuong}, title={A Comparative Analysis of Optimal LQR and Conventional PID Control Strategies for Trajectory Tracking in a 3-DOF Spherical Articulated Manipulator}, journal={EAI Endorsed Transactions on Sustainable Manufacturing and Renewable Energy}, volume={2}, number={4}, publisher={EAI}, journal_a={SUMARE}, year={2026}, month={1}, keywords={3 DoF spherical articulated robotic arm, Linear Quadratic Regulator (LQR),, Proportional-Integral-Derivative (PID).}, doi={10.4108/eetsmre.11147} }- Chau Nhan Phuc Pham
Minh Tan Tram
Quan-Truong Vuong
Year: 2026
A Comparative Analysis of Optimal LQR and Conventional PID Control Strategies for Trajectory Tracking in a 3-DOF Spherical Articulated Manipulator
SUMARE
EAI
DOI: 10.4108/eetsmre.11147
Abstract
The demand for high-precision, energy-efficient control in industrial robotics necessitates a rigorous comparison between conventional and optimal control methods. This paper presents a detailed comparative analysis of the ubiquitous PID (Proportional-Integral-Derivative) controller and the modern LQR (Linear Quadratic Regulator) optimal controller, applied to the highly non-linear dynamics of a 3-DOF spherical articulated manipulator. The study extends beyond ideal tracking to evaluate performance under realistic industrial constraints, including external disturbances, model uncertainty, and the novel scenario of actuator saturation. Through comprehensive MATLAB/Simulink simulations, we quantify performance using Root Mean Square Error (RMSE) and Integrated Control Effort (∫τ2dt). The results demonstrate that while PID is simple, LQR provides superior stability, higher resistance to parameter uncertainty, and optimal energy consumption across dynamic trajectories. This work offers quantitative guidance for selecting the appropriate controller based on specific industrial requirements, highlighting the trade-offs between implementation complexity and optimal system performance
Copyright © 2026 Pham-Chau-Nhan Phuc et al., licensed to EAI. This is an open access article distributed under the terms of the CC BY-NC-SA 4.0, which permits copying, redistributing, remixing, transformation, and building upon the material in any medium so long as the original work is properly cited.
