A Comparative Analysis of Optimal LQR and Conventional PID Control Strategies for Trajectory Tracking in a 3-DOF Spherical Articulated Manipulator

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