Observer-Based Prescribed-Performance Tracking and Vibration Suppression of a Fractional Viscoelastic Flexible Manipulator

Flexible manipulators combine low moving inertia with pronounced elastic vibration, and commonly used controllers often assume integer-order damping, direct velocity/full-state information, or plant-specific tuning without an explicit transient-error guarantee. This work considers a single-link manipulator with hereditary damping described by a physically parameterized fractional Kelvin–Voigt model. A model-assisted extended-state observer estimates the rigid-channel states and lumped uncertainty, while a modal differentiator reconstructs the flexible-mode velocity. The fractional nominal term is evaluated from measured modal history, and prescribed-performance tracking is combined with active modal damping under an explicit hub-torque constraint. A diffusive representation of the Caputo operator is used in the stability analysis, and the L1 discretization error is bounded explicitly. Under payload mismatch, external disturbances, and measurement noise, the controller achieves a tracking RMSE of 0.0059 rad, an RMS tip deflection of 2.29 mm, and Jv=7.85×10−5 m2s; the peak torque is 0.328 N m under a 0.50 N m limit. A conventional integer-order ADRC benchmark on the same plant gives 0.0518 rad and 5.23 mm, respectively. The prescribed tracking envelope is also maintained for an unloaded arm, a 300% payload increase, and an unmodeled second bending mode.