Adaptive tackling of the swinging problem for a 2 DOF crane – payload system

The control of a crane carrying its payload by an elastic string corresponds to a task in which precise, indirect control of a subsystem dynamically coupled to a directly controllable subsystem is needed. This task is interesting since the coupled degree of freedom has little damping and it is apt to keep swinging accordingly. The traditional approaches apply the input shaping technology to assist the human operator responsible for the manipulation task. In the present paper a novel adaptive approach applying fixed point transformations based iterations having local basin of attraction is proposed to simultaneously tackle the problems originating from the imprecise dynamic model available for the system to be controlled and the swinging problem, too. The most important phenomenological properties of this approach are also discussed. The control considers the 4th time-derivative of the trajectory of the payload. The operation of the proposed control is illustrated via simulation results.

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.