This paper addresses formulation of stabilizability and motion tracking conditions for mechanical 
    systems from the point of view of constraints put on them. We present a new classification of constraints, 
    which includes nonholonomic constraints that arise in both mechanics and control. Based on our 
    classification we develop kinematic and dynamic control models of systems subjected to these constraints. 
    We demonstrate that a property of being a &#8220;hard-to-control&#8221; nonholonomic system may 
    not be related to the nature of the constraints. It may result from the formulation of control 
    objectives for a 
    system. We examine two control objectives which are stabilization to the target equilibrium by a 
    continuous static state feedback control and motion tracking. Theory is illustrated with examples 
    of control objective 
    formulations for systems with constraints of various types.

El&#380;bieta  Jarz&#281;bowska

Stabilizability and Motion Tracking Conditions for  Mechanical Nonholonomic Control Systems

In the computation of turbulent flows via turbulence modeling, the treatment of the convective 
            terms is a key issue. In the present work, we present a numerical technique for simulating 
            two-dimensional incompressible turbulent flows. In particular, the performance of the high 
            Reynolds <mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>κ</mml:mi></mml:math>-<mml:math id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ɛ</mml:mi></mml:math> model and a new high-order upwind scheme 
            (adaptative QUICKEST by Kaibara et al. (2005)) is assessed for 2D confined and free-surface 
            incompressible turbulent flows. The model equations are solved with the fractional-step 
            projection method in primitive variables. 
Solutions are obtained by using an adaptation of the front tracking GENSMAC 
(Tomé and McKee (1994)) methodology for calculating fluid flows at high Reynolds numbers. 
The calculations are performed by using the 2D version of the 
<i>Freeflow</i> simulation system (Castello et al. (2000)). A specific way of implementing 
wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid 
flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over 
a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. 
The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent 
fluid from an entry port beneath the free surface.

V. G. Ferreira

A. C. Brandi

F. A. Kurokawa

P. Seleghim Jr.

A. Castelo

J. A. Cuminato

Incompressible Turbulent Flow Simulation Using the 
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t-44.5 92.5q0 46 38 78t95 45v2q-35 10 -54.5 33t-19.5 52q0 55 53 88.5t122 33.5q67 0 98.5 -23.5t31.5 -49.5z"/></g></svg> Model and Upwind Schemes

Long-term mission identification and model validation for in-flight manipulator
     control system in almost zero gravity with hostile space environment are extremely
      important for robotic applications. In this paper, a robot joint mathematical model is 
      developed where several nonlinearities have been taken into account. In order
       to identify all the required system parameters, an integrated identification strategy 
       is derived. This strategy makes use of a robust version of 
least-squares procedure (LS) for getting the initial conditions and a general nonlinear 
optimization method (MCS&#8212;multilevel coordinate search&#8212;algorithm) to estimate the 
nonlinear parameters. The approach is applied to the intelligent robot joint (IRJ) 
experiment that was developed at DLR for utilization opportunity on the International
 Space Station (ISS). The results using real and simulated measurements have shown 
 that the developed algorithm and strategy have remarkable features in identifying all the 
 parameters with good accuracy.

Adenilson R. da Silva

Luiz C. Gadelha de Souza

Bernd  Sch&#228;fer

Joint Dynamics Modeling and Parameter Identification for  Space Robot Applications

A statistical approach for the treatment of turbulence data generated
by computer simulations is presented. A model for compressible flows
at large Reynolds numbers and low Mach numbers is used for
simulating a backward-facing step airflow. A scaling analysis has
justified the commonly used assumption that the internal energy
transport due to turbulent velocity fluctuations and the work done
by the pressure field are the only relevant mechanisms needed to
model subgrid-scale flows. From the numerical simulations, the
temporal series of velocities are collected for ten different
positions in the flow domain, and are statistically treated. The
statistical approach is based on probability averages of the flow
quantities evaluated over several realizations of the simulated
flow. We look at how long of a time average is necessary to obtain
well-converged statistical results. For this end, we evaluate the
mean-square difference between the time average and an ensemble
average as the measure of convergence. This is an interesting
question since the validity of the ergodic hypothesis is implicitly
assumed in every turbulent flow simulation and its analysis.  The
ergodicity deviations from the numerical simulations are compared
with theoretical predictions given by scaling arguments. A very good
agreement is observed. Results for velocity fluctuations, normalized
autocorrelation functions, power spectra, probability density
distributions, as well as skewness and flatness coefficients are
also presented.

T. F. Oliveira

R. B. Miserda

F. R. Cunha

Dynamical Simulation and Statistical Analysis of Velocity Fluctuations of a Turbulent Flow behind a Cube

A direct version of the boundary element method (BEM) is developed to 
        model the stationary dynamic response of reinforced plate structures, such as 
        reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary 
        fundamental solutions of thin plates and plane stress state are used to transform
         the governing partial differential equations into boundary integral equations (BIEs). 
         Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state 
         (membrane) and for the out-of-plane state (bending). These uncoupled systems 
         are joined to form a macro-element, in which membrane and bending effects are 
         present. The association of these macro-elements is able to simulate thin-walled 
         structures, including reinforced plate structures. In the present formulation, the BIE 
         is discretized by continuous and/or discontinuous linear elements. Four 
         displacement integral equations are written for every boundary node. Modal data, 
         that is, natural frequencies and the corresponding mode shapes of reinforced plates, 
         are obtained from information contained in the frequency response functions (FRFs). 
         A specific example is presented to illustrate the versatility of the proposed 
         methodology. Different configurations of the reinforcements are used to simulate 
         simply supported and clamped boundary conditions for the plate structures. 
         The procedure is validated by comparison with results determined by the finite 
         element method (FEM).

Luiz Carlos Facundo Sanches

Euclides Mesquita

Renato Pavanello

Leandro Palermo Jr.

Dynamic Stationary Response of Reinforced Plates by  the Boundary Element Method

The purpose of this work is to study the processing and transmission of clock
signals in networks of geographically distributed nodes, in order to derive conditions for
frequency and phase synchronization between the nodes. The focus is 
on the master-slave architecture, which presents a priority scheme of clock 
distribution. One-way master-slave (OWMS ) and two-way master-slave 
(TWMS) chains are studied, considering that the slave nodes are third-order 
phase-locked loops (PLLs). Third-order PLLs are chosen to improve the transient 
response but, if their parameters are not well adjusted, stability problems and chaotic 
behaviors appear, restricting the lock-in range of the network.
Lock-in range for third-order PLLs with Sallen-Key filter is determined and it is
verified whether this range is reduced when the PLLs are connected to a network.
Numerical experiments show how chain size changes the lock-in ranges and the
acquisition times.

José Roberto Castilho Piqueira

Marcela de Carvalho Freschi

Models for Master-Slave Clock Distribution Networks with Third-Order Phase-Locked Loops

We consider the obtention of modes and frequencies of segmented 
            Euler-Bernoulli beams with internal damping and external viscous damping at the
discontinuities of the sections. This is done by following a Newtonian approach
in terms of a fundamental response of stationary beams subject to both types of
damping. The use of a basis generated by the fundamental solution of a differential
equation of fourth-order allows to formulate the eigenvalue problem and to write
the modes shapes in a compact manner. For this, we consider a block matrix that
carries the boundary conditions and intermediate conditions at the beams
and values of the fundamental matrix at the ends and intermediate points of the beam. For
each segment, the elements of the basis have the same shape since they are chosen as a
convenient translation of the elements of the basis for the first segment. Our method
avoids the use of the first-order state formulation also to rely on the Euler basis of
a differential equation of fourth-order and it allows to envision how conditions will
influence a chosen basis.

Rosemaira Dalcin Copetti

Julio C. R. Claeyssen

Teresa  Tsukazan

Modal Formulation of Segmented Euler-Bernoulli Beams

Some algebraic sufficient criteria for synchronizing two horizontal 
    platform systems coupled by sinusoidal state error feedback control are 
    derived by the Lyapunov stability theorem for linear time-varying system and 
    Sylvester's criterion. The state variables are restricted in a subregion in 
    order to obtain easily verified criteria. The validity of these algebraic criteria is 
    illustrated with some numerical examples. A new concept, synchronization cost, 
    is introduced based on a measure of the magnitude of the feedback control. The 
    minimal synchronization cost as well as optimal coupling strength is calculated 
    numerically. The results are meaningful in engineering application.

Jianping Cai

Xiaofeng Wu

Shuhui Chen

Chaos Synchronization Criteria and Costs of Sinusoidally Coupled Horizontal Platform Systems

This paper develops a stochastic hybrid model-based control 
                system that can determine online the optimal control actions, detect faults 
                quickly in the control process, and reconfigure the controller accordingly using 
                interacting multiple-model (IMM) estimator and generalized predictive control 
                (GPC) algorithm. A fault detection and control system consists of two main 
                parts: the first is the fault detector and the second is the controller 
                reconfiguration. This work deals with three main challenging issues: design of 
                fault model set, estimation of stochastic hybrid multiple models, and stochastic 
                model predictive control of hybrid multiple models. For the first issue, we propose 
                a simple scheme for designing faults for discrete and continuous random 
                variables. For the second issue, we consider and select a fast and reliable fault 
                detection system applied to the stochastic hybrid system. Finally, we develop a 
                stochastic GPC algorithm for hybrid multiple-models controller reconfiguration 
                with soft switching signals based on weighted probabilities. Simulations for the 
                proposed system are illustrated and analyzed.

Vu Trieu Minh

Nitin Afzulpurkar

W. M. Wan Muhamad

Fault Detection and Control of Process Systems

We have implemented an operational amplifier inductorless realization of the Chua's circuit. We have registered time series from its dynamical variables with the resistor <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math> as the control parameter and varying from 1300 <mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Ω</mml:mi></mml:math> to 2000 <mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Ω</mml:mi></mml:math>. Experimental time series at fixed <mml:math id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>R</mml:mi></mml:math> were used to reconstruct attractors by the delay vector 
technique. The flow attractors and their Poincaré maps considering 
parameters such as the Lyapunov spectrum, its subproduct the Kaplan-Yorke 
dimension, and the information dimension are also analyzed here. The results for 
a typical double scroll attractor indicate a chaotic behavior characterized by a positive
 Lyapunov exponent and with a Kaplan-Yorke dimension of 2.14. The occurrence of 
 chaos was also investigated through numerical simulations of the Chua's circuit 
 set of differential equations.

R. M. Rubinger

A. W. M. Nascimento

L. F. Mello

C. P. L. Rubinger

N. Manzanares Filho

H. A. Albuquerque

Inductorless Chua's Circuit: Experimental Time Series Analysis

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<p><em>Mathematical Problems in Engineering</em> is a broad-based journal publishing&nbsp;results of rigorous engineering research across all disciplines, carried out using mathematical tools.</p>


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<p>Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.</p>


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Mathematical Problems in Engineering

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Mathematical Problems in Engineering

Dynamics and Control in Sciences and Engineering

Dynamics and Control in Sciences and Engineering

Articles

Stabilizability and Motion Tracking Conditions for Mechanical Nonholonomic Control Systems

Incompressible Turbulent Flow Simulation Using the - Model and Upwind Schemes

Joint Dynamics Modeling and Parameter Identification for Space Robot Applications