Trajectory Tracking of a 3-DOF Parallel Manipulator Using Optimally Tuned LQR-PID Controller

This paper presents a comparative analysis of trajectory tracking control for a three-degree-of-freedom (3-DOF) parallel manipulator utilizing an optimally configured Linear Quadratic Regulator-Proportional Integral Derivative (LQR-PID) controller. The inherent nonlinearity and coupled dynamics of parallel manipulators present significant challenges in controller parameter selection. To identify suitable controller parameters, three optimization approaches—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO)—are implemented. The LQR weighting parameters and PID gains are concurrently optimized through minimization of a composite objective function incorporating Sum Squared Error (SSE), Integral Squared Error (ISE), and Integral Absolute Error (IAE). The optimized controllers undergo evaluation across multiple reference trajectories of the manipulator. Comparative simulation findings indicate that all three optimization techniques enhance tracking performance; notably, GWO delivers the most precise and consistent trajectory tracking among the examined approaches. The GWO-optimized controller demonstrates reduced tracking error, diminished integral error, and superior control-torque characteristics relative to GA- and PSO-optimized controllers. These findings validate the efficacy of GWO for optimal configuration of LQR-PID controllers in precision trajectory tracking applications for parallel robotic manipulators.