Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control

A new method for approximating fractional derivatives: application in non-linear control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.N/

Numerical calculation of fractional derivatives of non-smooth data

This paper addresses the calculation of fractional derivatives of fractional order for non-smooth data. The noise is avoided by adopting an optimization formulation using genetic algorithms (GA). Given the flexibility of the evolutionary schemes it is established a hierarchical GA composed by a series of two GAs, each one with having a distinct fitness function.N/

Analysis of Fractional-Order Discrete Controllers in the Presence of Nonlinearities

Presently, the development of fractional-order controllers is one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. In this paper we consider the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order controllers in the presence of several nonlinearities is discussed. Some results are provided that assesses the superior robustness of such algorithms.N/

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms

Approximating fractional derivatives through the generalized mean

This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm

Statistical modelling of dual-arm robotic systems

The article presents a new approach to the analysis and design of two-arm robotic systems. Usually, system descriptions are based on a set of differential equations which require laborious computations. This motivates the need of alternative models based on other mathematical concepts. The proposed statistical method gives clear guidelines towards the robotic systems analysis and development.N/

Fractional control of two arms working in cooperation

This paper analyzes the performance of two cooperative robot manipulators. It is studied the implementation of fractional-order algorithms in the position/force control of two robots holding an object. The experiments reveal that fractional algorithms lead to performances superior to classical integer-order controllers.N/

Fractional-order position/force robot control

In this paper it is studied the implementation of fractional-order algorithms in position/force control of two cooperating robotic manipulaotrs. The performance and system robustness are analyzed in the time and frequency domains. The effect of backlash and flexibility at the robot joints is also investigated.N/