Robust fractional order differentiators using generalized modulating functions method

Discretization Schemes for Fractional-Order Differentiators and Integrators

For fractional-order differentiator where is a real number, its discretization is a key step in digital implementation. Two discretization methods are presented. The first scheme is a direct recursive discretization of the Tustin operator. The second one is a direct discretization method using the Al-Alaoui operator via continued fraction expansion (CFE). The approximate discretization is minim...

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of comp...

Pole-zero Approximations of Digital Fractional-order Integrators and Differentiators Using Signal Modeling Techniques

A novel strategy to the development of digital pole-zero approximations to fractional-order integrators and differentiators is presented here. The scheme is based in the signal modeling techniques applied to deterministic signals, namely the Padé, the Prony and the Shanks methods. It is shown that the illustrated algorithms yield good results both in the time and the frequency domains. Moreover...

A Numerical Integration Method by Using Generalized Series of Functions

Robust Fractional Order Control of Under-actuated Electromechanical System

This paper presents a robust fractional order controller for flexible-joint electrically driven robots under imperfect transformation of control space. The proposed approach is free from manipulator dynamics, thus free from problems associated with torque control strategy in the design and implementation. As a result, the proposed controller is simple, fast response and superior to the torque c...