Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

α-Mellin Transform and One of Its Applications

MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45

Simulation by discrete mass modeling of offshore wind turbine system with DC link

This paper presents an integrated model for an offshore wind turbine taking into consideration a contribution for the marine wave and wind speed with perturbations influences on the power quality of current injected into the electric grid. The paper deals with the simulation of one floating offshore wind turbine equipped with a permanent magnet synchronous generator, and a two-level converter connected to an onshore electric grid. The use of discrete mass modeling is accessed in order to reveal by computing the total harmonic distortion on how the perturbations of the captured energy are attenuated at the electric grid injection point. Two torque actions are considered for the three-mass modeling, the aerodynamic on the flexible part and on the rigid part of the blades. Also, a torque due to the influence of marine waves in deep water is considered. Proportional integral fractional-order control supports the control strategy. A comparison between the drive train models is presented.

Offshore Wind Energy System with DC Transmission Discrete Mass: Modeling and Simulation

This paper presents an integrated model for an offshore wind energy system taking into consideration a contribution for the marine wave and wind speed with perturbations influences on the power quality of current injected into the electric grid. The paper deals with the simulation of one floating offshore wind turbine equipped with a PMSG and a two-level converter connected to an onshore electric grid. The use of discrete mass modeling is accessed in order to reveal by computing the THD on how the perturbations of the captured energy are attenuated at the electric grid injection point. Two torque actions are considered for the three-mass modeling, the aerodynamic on the flexible part and on the rigid part of the blades. Also, a torque due to the influence of marine waves in deep water is considered. PI fractional-order control supports the control strategy. A comparison between the drive train models is presented.

Blade pitch control malfunction simulation in a wind energy conversion system with MPC five-level converter

This paper is on a wind energy conversion system simulation of a transient analysis due to a blade pitch control malfunction. The aim of the transient analysis is the study of the behavior of a back-to-back multiple point clamped five-level full-power converter implemented in a wind energy conversion system equipped with a permanent magnet synchronous generator. An alternate current link connects the system to the grid. The drive train is modeled by a three-mass model in order to simulate the dynamic effect of the wind on the tower. The control strategy is based on fractional-order control. Unbalance voltages in the DC-link capacitors are lessen due to the control strategy, balancing the capacitor banks voltages by a selection of the output voltage vectors. Simulation studies are carried out to evaluate not only the system behavior, but also the quality of the energy injected into the electric grid.

A DC-DC Step-Up mu-Power Converter for Energy Harvesting Applications, Using Maximum Power PointTracking, Based on Fractional Open Circuit Voltage

A DC-DC step-up micro power converter for solar energy harvesting applications is presented. The circuit is based on a switched-capacitorvoltage tripler architecture with MOSFET capacitors, which results in an, area approximately eight times smaller than using MiM capacitors for the 0.131mu m CMOS technology. In order to compensate for the loss of efficiency, due to the larger parasitic capacitances, a charge reutilization scheme is employed. The circuit is self-clocked, using a phase controller designed specifically to work with an amorphous silicon solar cell, in order to obtain themaximum available power from the cell. This will be done by tracking its maximum power point (MPPT) using the fractional open circuit voltage method. Electrical simulations of the circuit, together with an equivalent electrical model of an amorphous silicon solar cell, show that the circuit can deliver apower of 1132 mu W to the load, corresponding to a maximum efficiency of 66.81%.

Fractional generalization of memristor and higher order elements

Fractional calculus generalizes integer order derivatives and integrals. Memristor systems generalize the notion of electrical elements. Both concepts were shown to model important classes of phenomena. This paper goes a step further by embedding both tools in a generalization considering complex-order objects. Two complex operators leading to real-valued results are proposed. The proposed class of models generate a broad universe of elements. Several combinations of values are tested and the corresponding dynamical behavior is analyzed.

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?

Hamilton’s Principle with Variable Order Fractional Derivatives

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.

Robust model predictive controller with output feedback and target tracking

A model predictive controller (MPC) is proposed, which is robustly stable for some classes of model uncertainty and to unknown disturbances. It is considered as the case of open-loop stable systems, where only the inputs and controlled outputs are measured. It is assumed that the controller will work in a scenario where target tracking is also required. Here, it is extended to the nominal infinite horizon MPC with output feedback. The method considers an extended cost function that can be made globally convergent for any finite input horizon considered for the uncertain system. The method is based on the explicit inclusion of cost contracting constraints in the control problem. The controller considers the output feedback case through a non-minimal state-space model that is built using past output measurements and past input increments. The application of the robust output feedback MPC is illustrated through the simulation of a low-order multivariable system.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

A Sensorless PMDC Motor Speed Controller with a Logical Overcurrent Protection

A method to control the speed or the torque of a permanent-magnet direct current motor is presented. The rotor speed and the external torque estimation are simultaneously provided by appropriate observers. The sensorless control scheme is based on current measurement and switching states of power devices. The observer’s performances are dependent on the accurate machine parameters knowledge. Sliding mode control approach was adopted for drive control, providing the suitable switching states to the chopper power devices. Despite the predictable chattering, a convenient first order switching function was considered enough to define the sliding surface and to correspond with the desired control specifications and drive performance. The experimental implementation was supported on a single dsPIC and the controller includes a logic overcurrent protection.

Observability of nonlinear fractional dynamical systems

We study the observability of linear and nonlinear fractional differential systems of order 0 < α < 1 by using the Mittag-Leffler matrix function and the application of Banach’s contraction mapping theorem. Several examples illustrate the concepts.

On a generalized Laguerre operational matrix of fractional integration

A new operationalmatrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived.The fractional integration is described in the Riemann-Liouville sense.This operational matrix is applied together with generalized Laguerre tau method for solving general linearmultitermfractional differential equations (FDEs).Themethod has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposedmethod is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.