Fractional modeling of flexural behavior of toenail plates: First step for clinical purposes.

This work presents an identification procedure of flexural behavior of toenail plates in twenty subjects with no history of feet or nail injury as of in-vivo measurements. In particular, four different mechanical models are considered to describe such properties, ranging from the pure elastic to viscoelastic behavior, the latter from the classical and fractional points of view. The quality of the adjustment of each model is examined by a group of performance indices. Experimental data show that the best identification is achieved by the fractional order viscoelastic model for all subjects. These novel results in modeling flexural behavior of toenails are consistent with the published literature suggesting that viscoelastic materials may be successfully modeled with derivatives of fractional order. This could contribute, together with additional variables, to help health professionals, and more especially podiatrists, to have reliable and quantitative measures of the nail flexural behavior which can be susceptible of treatment or for prevention.

Stable force control and contact transition of a single link flexible robot using a fractional-order controller.

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.