Fractional calculus approach to modeling and control of (bio)mechanical systems

Abstract

Recently, an increasing attention has been paid to fractional calculus (FC) and its application in control and modeling of fractional order (bio)mechanical system. Fractional derivatives and integrals may have a wide application in describing complex properties of materials including long-term memory, non-locality of power law type and fractality [1]. In this presentation we applied the concept of fractional order for biomehanical modeling of human arm dynamics as well as soft tissues, specially human skin as well as human blood. Besides, it is also presented the connection between fractional order differintegral operators and behavior of the memsystems which can be used for modeling dynamics of (bio)mechanical systems. Further, we present robust feedback-(feedforward) loop fractional-order iterative learning control [2] for regular and singular fractional order system. Particularly, a feedback-(feedforward) PDalpfa / PIbetaDalpfa type iterative learning control (ILC) of fractional order system- (regular and degenerate type) which includes time delay are considered [3]. Sufficient conditions for the convergence of a proposed PD alpha type of learning control algorithm for a class of fractional state space time delay system are given in time domain. Finally, a simulation results show the feasibility and effectiveness of the suggested approach.