Application of fractional algorithms in the control of a robotic bird

In this paper, it is studied the dynamics of the robotic bird in terms of time response and robustness. It is analyzed the wing angle of attack and the velocity of the bird, the tail influence, the gliding flight and the flapping flight. The results are positive for the construction of flying robots. The development of computational simulation based on the dynamic of the robotic bird should allow testing strategies and different algorithms of control such as integer and fractional controllers.

Fractional central differences and derivatives

Journal of Vibration and Control, Vol. 14, Nº 9-10

Robotic manipulators with vibrations: short time fourier transform of fractional spectra

This paper analyzes the signals captured during impacts and vibrations of a mechanical manipulator. In order to acquire and study the signals an experimental setup is implemented. The signals are treated through signal processing tools such as the fast Fourier transform and the short time Fourier transform. The results show that the Fourier spectrum of several signals presents a non integer behavior. The experimental study provides valuable results that can assist in the design of a control system to deal with the unwanted effects of vibrations.

Pseudo-fractional ARMA modelling using a double Levinson recursion

IET Control Theory & Applications, Vol. 1, Nº 1

Fractional dynamics in the trajectory control of redundant manipulators

Under the pseudoinverse control, robots with kinematical redundancy exhibit an undesirable chaotic joint motion which leads to an erratic behavior. This paper studies the complexity of fractional dynamics of the chaotic response. Fourier and wavelet analysis provides a deeper insight, helpful to know better the lack of repeatability problem of redundant manipulators. This perspective for the study of the chaotic phenomena will permit the development of superior trajectory control algorithms.

Fractional central differences and derivatives

Journal of Vibration and Control, 14(9–10): 1255–1266, 2008

Application of Continuous Wavelet Transform to the Analysis of the Modulus of the Fractional Fourier Transform Bands for Resolving Two Component Mixture

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

Fractional Dynamics and Control of Distributed Parameter Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of some distributed parameter systems.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Visualizing control systems performance: A fractional perspective

This article presents a novel method for visualizing the control systems behavior. The proposed scheme uses the tools of fractional calculus and computes the signals propagating within the system structure as a time/frequency-space wave. Linear and nonlinear closed-loop control systems are analyzed, for both the time and frequency responses, under the action of a reference step input signal. Several nonlinearities, namely, Coulomb friction and backlash, are also tested. The numerical experiments demonstrate the feasibility of the proposed methodology as a visualization tool and motivate its extension for other systems and classes of nonlinearities.

An examination of the effects on learning seen in children afforded the opportunity to control the order of repetitions for three novel spatiotemporal sequences

Children were afforded the opportunity to control the order of repetitions for three novel spatiotemporal sequences. The following was predicted: a) children and adults in the self-regulated (SELF) groups would produce faster movement (MT) and reaction times (R T) and greater recall success (RS) during retention compared to the age-matched yoked (YOKE) groups; b) children would choose to switch sequences less often than adults; c) adults would produce faster MT and RT and greater RS than the children during acquisition and retention, independent of experimental group. During acquisition, no effects were seen for RS, however for MT and RT there was a main effect for age as well as block. During retention a main effect for practice condition was seen for RS and failed to reach statistical significance for MT and RT, thus partially supporting our first and second hypotheses. The third hypothesis was not supported.

Double sampling (x)over-bar control chart for a first-order autoregressive moving average process model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Double sampling X̄ control chart for a first order autoregressive process

In this paper we propose the Double Sampling X̄ control chart for monitoring processes in which the observations follow a first order autoregressive model. We consider sampling intervals that are sufficiently long to meet the rational subgroup concept. The Double Sampling X̄ chart is substantially more efficient than the Shewhart chart and the Variable Sample Size chart. To study the properties of these charts we derived closed-form expressions for the average run length (ARL) taking into account the within-subgroup correlation. Numerical results show that this correlation has a significant impact on the chart properties.

Multiple independent origins of mitochondrial control region duplications in the order Psittaciformes

mitochondrial genomes are generally thought to be under selection for compactness, due to their small size, consistent gene content, and a lack of introns or intergenic spacers. As more animal mitochondrial genomes are fully sequenced, rearrangements and partial duplications are being identified with increasing frequency, particularly in birds (Class Ayes). In this study, we investigate the evolutionary history of mitochondrial control region states within the avian order Psittaciformes (parrots and cockatoos). To this aim, we reconstructed a comprehensive multi-locus phylogeny of parrots, used PCR of three diagnostic fragments to classify the mitochondrial control region state as single or duplicated, and mapped these states onto the phylogeny. We further sequenced 44 selected species to validate these inferences of control region state. Ancestral state reconstruction using a range of weighting schemes identified six independent origins of mitochondrial control region duplications within Psittaciformes. Analysis of sequence data showed that varying levels of mitochondrial gene and tRNA homology and degradation were present within a given clade exhibiting duplications. Levels of divergence between control regions within an individual varied from 0-10.9% with the differences occurring mainly between 51 and 225 nucleotides 3' of the goose hairpin in domain I. Further investigations into the fates of duplicated mitochondrial genes, the potential costs and benefits of having a second control region, and the complex relationship between evolutionary rates, selection, and time since duplication are needed to fully explain these patterns in the mitochondrial genome. (C) 2012 Elsevier Inc. All rights reserved.