Fixed-time observer-based adaptive control for flexible manipulators with system uncertainties

A neural network sliding mode control strategy (NNSMC-FTO) based on a fixed-time observer is proposed to address insufficient trajectory tracking accuracy and vibration suppression difficulties in flexible joint manipulators arms (FJSM) under payload, nonlinear friction, and model uncertainties. The proposed strategy comprises three principal components: First, a state-space representation of the sliding surface and position error vector is introduced. This formulation reduces the number of virtual controllers required in traditional backstepping by 30%, significantly decreasing computational complexity. Second, the fixed-time observer is enhanced through adaptive adjustment of power function parameters in response to disturbances, enabling precise estimation of payload and friction. Concurrently, the observer is extended to estimate and compensate for Radial Basis Function Neural Network (RBFNN) approximation errors. Finally, an RBFNN approximation model is incorporated to online approximate unmodeled system dynamics, ensuring virtual controller stability while suppressing the effects of model parameter deviations. Simulation results demonstrate that compared with baseline methods, the proposed strategy reduces the mean absolute error of joint position tracking to 13.76% and decreases end-effector vibration amplitude by 33.96%, validating its high-precision tracking capability and strong robustness in scenarios with model uncertainties and significant disturbances.