Positioning and Trajectory Tracking with Deflection Suppression in Flexible Link Robotic Manipulator Using PID-LQR Controller

Abstract

This study aims to enhance the dynamic response of a flexible link robot manipulator (FLRM) to achieve faster positioning, improved trajectory tracking, and effective suppression of link deflection. A dynamic model of the FLRM was developed, and a hybrid control strategy integrating a proportional–integral–derivative (PID) controller with a linear quadratic regulator (LQR) was designed and implemented within the closed-loop system architecture. The complete system was modeled and simulated using MATLAB/Simulink. Initial simulations assessed the performance of the PID and LQR controllers independently. The PID controller yielded a rise time of 0.2617 s, peak time of 0.9434 s, settling time of 3.2394 s, and overshoot of 11.9676%. In contrast, the LQR controller demonstrated superior dynamic characteristics, with a rise time of 0.2505 s, peak time of 0.3489 s, settling time of 0.4769 s, and minimal overshoot of 0.0048%. To further enhance system performance and reduce trajectory tracking error, a hybrid PID–LQR controller was developed, incorporating refined PID parameters. Simulation results showed that the hybrid controller achieved a rise time of 0.1444 s, peak time of 0.2706 s, settling time of 0.2637 s, and overshoot of 0.5119%. These outcomes demonstrate that the PID–LQR hybrid controller significantly outperforms the individual PID and LQR approaches by achieving near-zero overshoot, faster response, and reduced stabilization time.