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A new method to control single-link lightweight flexible manipulators in the presence of payload changes is proposed. Undoubtedly, the control of this kind of structures is nowadays one of the most challenging and attractive research areas, being remarkable its application to the aerospace industry, among others. One of the interesting features of the design method presented here is that the overshoot of the controlled system is independent of the tip mass. This allows a constant safety zone to be delimited for any given placement task of the arm, independent of the load being carried, thereby making it easier to plan collision avoidance. Other considerations about noise and motor saturation issues are also presented. To satisfy this performance, the overall control scheme proposed 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 simplifies 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, independent of variations in the load, and robust, in a stability sense, to spillover effects. Experimental results are shown, when controlling the flexible manipulator with this fractional order derivator, that prove the good performance of the system.