Fuzzy super twisting mode control of a rigid-flexible robotic arm based on approximate inertial manifold dimensionality reduction

INTRODUCTION: The control of infinite-dimensional rigid-flexible robotic arms presents significant challenges, with direct truncation of first-order modal models resulting in poor control quality and second-order models leading to complex hardware implementations. METHODS: To address these issues, we propose a fuzzy super twisting mode control method based on approximate inertial manifold dimensionality reduction for the robotic arm. This innovative approach features an adjustable exponential non-singular sliding surface and a stable continuous super twisting algorithm. A novel fuzzy strategy dynamically optimizes the sliding surface coefficient in real-time, simplifying the control mechanism. RESULTS: Our findings, supported by various simulations and experiments, indicate that the proposed method outperforms directly truncated first-order and second-order modal models. It demonstrates effective tracking performance under bounded external disturbances and robustness to system variability. DISCUSSION: The method's finite-time convergence, facilitated by the modification of the nonlinear homogeneous sliding surface, along with the system's stability, confirmed via Lyapunov theory, marks a significant improvement in control quality and simplification of hardware implementation for rigid-flexible robotic arms.