Fractional Control of a Single-Link 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. Continuous and discrete approximate implementations of the fractional controller are simulated. Comparison of the responses to a step command of the manipulator controlled with the proposed 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. An interesting feature of this control scheme is that the overshoot is independent of the tip mass. This allows a constant safety zone to be delimited for any given placement task of the arm, independently of the load being carried, thereby making it easier to plan collision avoidance. Simulations also include comparison with standard PD controller, and verification of the assumption of dominant low-frequency vibration mode.