Finite Element-Informed Tunable Control for Robust Vibration Mitigation in Flexible 3D of Robotic Arm

Abstract

This study presents the dynamic modeling and control of a clamped-free beam system using Proportional–Integral–Derivative (PID) control strategies, with a focus on comparing the performance of a Standard PID controller and an optimally Tuned PID controller. Flexible beam structures are widely used in robotic and precision engineering applications, where vibration suppression and accurate positioning are critical challenges due to inherent structural dynamics. A simulation-based approach was adopted to evaluate the effectiveness of both controllers using key performance metrics, including displacement response, velocity response, settling time, overshoot, Integral of Absolute Error (IAE), Steady-State Error (SSE), and Root Mean Square (RMS) control effort. The results demonstrate that the Standard PID controller exhibits significant oscillations, slower convergence, and higher accumulated tracking error due to insufficient damping of flexible modes. In contrast, the Tuned PID controller achieves superior performance by significantly reducing oscillations, minimizing steady-state error, and improving transient response characteristics. Quantitative analysis shows that the Tuned PID consistently yields lower IAE and SSE values across all joints, indicating enhanced tracking accuracy and improved overall system efficiency. However, this improved performance comes at the cost of increased control effort, highlighting a fundamental trade-off between control accuracy and actuator energy consumption. The findings confirm that proper tuning of PID parameters is essential for effective control of flexible systems. The study provides valuable insights into the design of efficient control strategies for vibration suppression in robotic manipulators and similar engineering applications.