The control of robots that interact with the environment is an open area of research. Two applications that benefit from this study are: the control of the force exerted by a robot on an object, which allows the robot to perform complex tasks like assembly operations, and the control of collisions, which allows the robot safely collaborate with humans. Robot control is difficult in these cases because: (1) bouncing between free and constrained motion appears that may cause instability, (2) switching between free motion (position) controller and constrained motion (force) controller is required being the switching instants difficult to know and (3) robot control must be robust since the mechanical impedance of the environment is unknown. Robots with flexible links may alleviate these drawbacks. Previous research on flexible robots proved stability of a PD controller that fed back the motor position when contacting an unknown environment, but force control was not achieved. This paper proposes a control system that combines a fractional-order D tip position controller with a feedforward force control. It attains higher stability robustness and higher phase margin than a PD controller, which is the integer-order controller of similar complexity. This controller outperforms previous controllers: (1) it achieves force control with nearly zero steady state error, (2) this control is robust to uncertainties in the environment and motor friction, (3) it guarantees stability (like others) but it also guarantees a higher value of the phase margin, i.e., a higher damping, and a more efficient vibration cancellation, and (4) it effectively removes bouncing. Experimental results prove the effectiveness of this new controller.@en