Singular Perturbation-Based Composite Adaptive Fuzzy–LQR Control for Flexible Manipulators

In this paper, a composite control strategy combining adaptive fuzzy backstepping control and linear quadratic regulator control is proposed to address the trajectory tracking and vibration suppression challenges of a dual-link flexible manipulator subject to external disturbances. The dynamic model of the dual-link flexible manipulator is established using the assumed mode method. Due to the strong coupling between the rigid and flexible modes, the system exhibits increased control complexity, reduced tracking accuracy, and a higher susceptibility to high frequency vibration excitation, which adversely affects both stability and control performance. To mitigate these issues, the singular perturbation method is utilized to decompose the coupled system into slow and fast subsystems based on time scale separation. Within the proposed framework, an LQR controller is designed to suppress fast subsystem flexible vibrations, while an adaptive fuzzy backstepping controller ensures accurate trajectory tracking of the slow subsystem. The coordinated control of the two subsystems allows the manipulator to maintain robust performance in the presence of external disturbances. System stability is rigorously proven via Lyapunov based analysis. Compared with conventional PD control, the proposed controller reduced the ITAE of tracking error by 6.90% and 3.37% on link1 and link2 respectively; the RMSE of end-effector vibration displacement decreased by 47.06% and 56.47% on link1 and link2 respectively. The proposed composite control method demonstrates superior performance in tracking accuracy, vibration suppression, and robustness.