Residual vibration suppression of a flexible heavy-duty multi-joint robotic manipulator using linear quadratic regulator and optimal input shaper

Controlling end-effector vibrations in flexible heavy-duty robotic manipulators is challenging, particularly during acceleration and deceleration phases, due to variations in system parameters such as natural frequency and damping ratio. This paper proposes a method for residual vibration suppression that combines an Optimal Input Shaper (OIS) with a Linear Quadratic Regulator (LQR). By incorporating the distribution patterns of system parameters alongside the system’s vibration characteristics, a novel performance index function is developed. Using optimization theory, the OIS is designed based on frequency and damping error performance indices. A dynamic model of the flexible heavy-duty robotic manipulator is established using the Lagrange equation method. The proposed combination of the LQR controller and OIS is evaluated against a combination of the LQR controller and a Traditional Input Shaper (TIS) in terms of response time and vibration suppression effectiveness through MATLAB/Simulink simulations and experimental validation. The results demonstrate that both the TIS- and OIS-based LQR controllers effectively suppress residual vibrations at the manipulator’s end-effector, with the OIS offering superior vibration suppression and faster response times.