Fractional-order control of a flexible manipulator

A new method to control single-link lightweight flexible manipulators in the presence of changes in the load is proposed in this paper. The overall control scheme consists of three nested control loops. Once the friction and other nonlinear effects have been compensated, the inner loop is designed to give a fast motor response. The middle loop decouples the dynamics of the system, and reduces its transfer function to a double integrator. A fractional-derivative controller is used to shape the outer loop into the form of a fractional-order integrator. The result is a constant-phase system with, in the time domain, step responses exhibiting constant overshoot, independently of variations in the load (tip mass). In simulation, comparison of the responses to a step command of the manipulator controlled with the controller implemented by different approximations and with the ideal fractional controller showed that the latter could be accurately approximated by standard continuous and discrete controllers of high order preserving the robustness. Simulations also include comparison with standard PD controller, and verification of the assumption of dominant low-frequency vibration mode.