Showing papers in "Mathematical Problems in Engineering in 2007"

Homotopy Perturbation Method for Solving Fourth-Order Boundary Value Problems

Abstract: We apply the homotopy perturbation method for solving the fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the method. Homotopy method can be considered an alternative method to Adomian decomposition method and its variant forms.

Patrol Mobile Robots and Chaotic Trajectories

Abstract: This paper presents a study of special trajectories attainment for mobile robots based on the dynamical features of chaotic systems This method of trajectories construction is envisaged for missions for terrain exploration, with the specific purpose of search or patrol, where fast scanning of the robot workspace is required We propose the imparting of chaotic motion behavior to the mobile robot by means of a planner of goal positions sequence based on an area-preserving chaotic map As a consequence, the robot trajectories seem highly opportunistic and unpredictable for external observers, and the trajectories's characteristics ensure the quick scanning of the patrolling space The kinematic modeling and the closed-loop control of the robot are described The results and discussion of numerical simulations close the paper

Analysis of Convective Straight and Radial Fins with Temperature-Dependent Thermal Conductivity Using Variational Iteration Method with Comparison with Respect to Finite Element Analysis

Abstract: In order to enhance heat transfer between primary surface and the environment, radiating extended surfaces are commonly utilized. Especially in the case of large temperature differences, variable thermal conductivity has a strong effect on performance of such a surface. In this paper, variational iteration method is used to analyze convective straight and radial fins with temperature-dependent thermal conductivity. In order to show the efficiency of variational iteration method (VIM), the results obtained from VIM analysis are compared with previously obtained results using Adomian decomposition method (ADM) and the results from finite element analysis. VIM produces analytical expressions for the solution of nonlinear differential equations. However, these expressions obtained from VIM must be tested with respect to the results obtained from a reliable numerical method or analytical solution. This work assures that VIM is a promising method for the analysis of convective straight and radial fin problems.

Quality Evaluation in Flexible Manufacturing Systems: A Markovian Approach

Abstract: The flexible manufacturing system (FMS) has attracted substantial amount of research effort during the last twenty years. Most of the studies address the issues of flexibility, productivity, cost, and so forth. The impact of flexible lines on product quality is less studied. This paper intends to address this issue by applying a Markov model to evaluate quality performance of a flexible manufacturing system. Closed expressions to calculate good part probability are derived and discussions to maintain high product quality are carried out. An example of flexible fixture in machining system is provided to illustrate the applicability of the method. The results of this study suggest a possible approach to investigate the impact of flexibility on product quality and, finally, with extensions and enrichment of the model, may lead to provide production engineers and managers a better understanding of the quality implications and to summarize some general guidelines of operation management in flexible manufacturing systems.

A Network Model for Parallel Line Balancing Problem

Abstract: Gokcen et al. (2006) have proposed several procedures and a mathematical model on single-model (product) assembly line balancing (ALB) problem with parallel lines. In parallel ALB problem, the goal is to balance more than one assembly line together. In this paper, a network model for parallel ALB problem has been proposed and illustrated on a numerical example. This model is a new approach for parallel ALB and it provides a different point of view for interested researchers.

Inductorless Chua's Circuit: Experimental Time Series Analysis

Abstract: 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 R as the control parameter and varying from 1300 Ω to 2000 Ω. Experimental time series at fixed R were used to reconstruct attractors by the delay vector technique. The flow attractors and their Poincare 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.

A Note on Variable Viscosity and Chemical Reaction Effects on Mixed Convection Heat and Mass Transfer Along a Semi-Infinite Vertical Plate

Abstract: In the present study, an analysis is carried out to study the variable viscosity and chemical reaction effects on the flow, heat, and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the shooting method. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. In addition, tabulated results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented and discussed.

A Stochastic Model for the HIV/AIDS Dynamic Evolution

Abstract: This paper analyses the HIV/AIDS dynamic evolution as defined by CD4 levels, from a macroscopic point of view, by means of homogeneous semi-Markov stochastic processes. A large number of results have been obtained including the following conditional probabilities: an infected patient will be in state j after a time t given that she/he entered at time 0 (starting time) in state i; that she/he will survive up to a time t, given the starting state; that she/he will continue to remain in the starting state up to time t; that she/he reach stage j of the disease in the next transition, if the previous state was i and no state change occurred up to time t. The immunological states considered are based on CD4 counts and our data refer to patients selected from a series of 766 HIV-positive intravenous drug users.

On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW

Abstract: This paper considers the solution to a class of the second-order Sylvester matrix equation EVF2−AVF−CV=BW. Under the controllability of the matrix triple (E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrix F in a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the second-order Sylvester matrix equation, and can perform important functions in many analysis and design problems in control systems theory. As a demonstration, an illustrative example is given to show the effectiveness of the proposed solution.

Fault Detection and Control of Process Systems

Abstract: 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

Stabilization and Observability of a Rotating Timoshenko Beam Model

Abstract: A control system describing the dynamics of a rotating Timoshenko beam is considered. We assume that the beam is driven by a control torque at one of its ends, and the other end carries a rigid body as a load. The model considered takes into account the longitudinal, vertical, and shear motions of the beam. For this distributed parameter system, we construct a family of Galerkin approximations based on solutions of the homogeneous Timoshenko beam equation. We derive sufficient conditions for stabilizability of such finite dimensional system. In addition, the equilibrium of the Galerkin approximation considered is proved to be stabilizable by an observer-based feedback law, and an explicit control design is proposed.

Design of Optimal Hybrid Position/Force Controller for a Robot Manipulator Using Neural Networks

Abstract: The application of quadratic optimization and sliding-mode approach is considered for hybrid position and force control of a robot manipulator. The dynamic model of the manipulator is transformed into a state-space model to contain two sets of state variables, where one describes the constrained motion and the other describes the unconstrained motion. The optimal feedback control law is derived solving matrix differential Riccati equation, which is obtained using Hamilton Jacobi Bellman optimization. The optimal feedback control law is shown to be globally exponentially stable using Lyapunov function approach. The dynamic model uncertainties are compensated with a feedforward neural network. The neural network requires no preliminary offline training and is trained with online weight tuning algorithms that guarantee small errors and bounded control signals. The application of the derived control law is demonstrated through simulation with a 4-DOF robot manipulator to track an elliptical planar constrained surface while applying the desired force on the surface.

On bumps and reduction of switching transients in multicontroller systems

Abstract: This paper is concerned with the realization and implementation of multicontroller systems, consisting of several linear controllers, subject to the bump phenomenon which occurs when switching between one controller acting in closed loop and another controller in the set of “offline” controllers waiting to take over the control loop. Based on a deep characterization of the bump phenomenon, the paper gives a novel and simple parameterization of such set of linear controllers, possibly having different state dimensions, to cope with bumps and their undesirable transients in switched-mode systems. The proposed technique is based on a non minimal state-space representation allowing a common memory and a unique dynamics shared by all controllers in that set. It also makes each initially open-loop unstable controller run in a stable way regardless of whether that controller is connected to the controlled process.

Conjugate Heat Transfer of Mixed Convection for Viscoelastic Fluid Past a Stretching Sheet

Abstract: A conjugate heat transfer problem of a second-grade viscoelastic fluid past a stretching sheet has been studied. Governing equations include heat conduction equation of a stretching sheet, continuity equation, momentum equation, and energy equation of a second-grade fluid, analyzed by a combination of a series expansion method, the similarity transformation, and a second-order accurate finite-difference method. These solutions are used to iterate with the heat conduction equation of the stretching sheet to obtain distributions of the local convective heat transfer coefficient and the stretching sheet temperature. Ranges of dimensionless parameters, the Prandtl number Pr, the elastic number E and the conduction-convection coefficient Ncc are from 0.001 to 10, 0.0001 to 0.01, and 0.5 to 2.0, respectively. A parameter G, which is used to represent the dominance of the buoyant effect, is present in governing equations. Results indicated that elastic effect in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a stretching sheet. In addition, same as the results from Newtonian fluid flow and conduction analysis of a stretching sheet, a better heat transfer is obtained with a larger Ncc, G, and E.

Chaos Synchronization Criteria and Costs of Sinusoidally Coupled Horizontal Platform Systems

Abstract: 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.

Incompressible Turbulent Flow Simulation Using the κ-ɛ Model and Upwind Schemes

Abstract: 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 κ-ɛ 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 (Tome and McKee (1994)) methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of the Freeflow 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.

A Finite Circular Arch Element Based on Trigonometric Shape Functions

Abstract: The curved-beam finite element formulation by trigonometric function for curvature is presented. Instead of displacement function, trigonometric function is introduced for curvature to avoid the shear and membrane locking phenomena. Element formulation is carried out in polar coordinates. The element with three nodal parameters is chosen on curvature. Then, curvature field in the element is interpolated as the conventional trigonometric functions. Shape functions are obtained as usual by matrix operations. To consider the boundary conditions, a transformation matrix between nodal curvature and nodal displacement vectors is introduced. The equilibrium equation is written by minimizing the total potential energy in terms of the displacement components. In such equilibrium equation, the locking phenomenon is eliminated. The interesting point in this method is that for most problems, it is sufficient to use only one element to obtain the solution. Four examples are presented in order to verify the element formulation and to show the accuracy and efficiency of the method. The results are compared with those of other concepts.

Rational Probabilistic Deciders—Part I: Individual Behavior

Abstract: This paper is intended to model a decision maker as a rational probabilistic decider (RPD) and to investigate its behavior in stationary and symmetric Markov switch environments. RPDs take their decisions based on penalty functions defined by the environment. The quality of decision making depends on a parameter referred to as level of rationality. The dynamic behavior of RPDs is described by an ergodic Markov chain. Two classes of RPDs are considered—local and global. The former take their decisions based on the penalty in the current state while the latter consider all states. It is shown that asymptotically (in time and in the level of rationality) both classes behave quite similarly. However, the second largest eigenvalue of Markov transition matrices for global RPDs is smaller than that for local ones, indicating faster convergence to the optimal state. As an illustration, the behavior of a chief executive officer, modeled as a global RPD, is considered, and it is shown that the company performance may or may not be optimized—depending on the pay structure employed. While the current paper investigates individual RPDs, a companion paper will address collective behavior.

An Approximate Solution for Flow between Two Disks Rotating about Distinct Axes at Different Speeds

Abstract: The flow of a linearly viscous fluid between two disks rotating about two distinct vertical axes is studied. An approximate analytical solution is obtained by taking into account the case of rotation with a small angular velocity difference. It is shown how the velocity components depend on the position, the Reynolds number, the eccentricity, the ratio of angular speeds of the disks, and the parameters satisfying the conditions u=0 and ν=0 in midplane.

Limit Cycle for the Brusselator by He's Variational Method

Abstract: He's variational method for finding limit cycles is applied to the Brusselator. The technique developed in this paper is similar to Kantorovitch's method in variational theory. The present theory can be applied not only to weakly nonlinear equations, but also to strongly ones, and the obtained results are valid for the whole solution domain.

A Mixture Theory for Micropolar Thermoelastic Solids

Abstract: We derive a nonlinear theory of heat-conducting micropolar mixtures in Lagrangian description. The kinematics, balance laws, and constitutive equations are examined and utilized to develop a nonlinear theory for binary mixtures of micropolar thermoelastic solids. The initial boundary value problem is formulated. Then, the theory is linearized and a uniqueness result is established.

Joint Dynamics Modeling and Parameter Identification for Space Robot Applications

Abstract: 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—multilevel coordinate search—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.

Numerical and Analytical Study of Optimal Low-Thrust Limited-Power Transfers between Close Circular Coplanar Orbits

Abstract: A numerical and analytical study of optimal low-thrust limited-power trajectories for simple transfer (no rendezvous) between close circular coplanar orbits in an inverse-square force field is presented. The numerical study is carried out by means of an indirect approach of the optimization problem in which the two-point boundary value problem, obtained from the set of necessary conditions describing the optimal solutions, is solved through a neighboring extremal algorithm based on the solution of the linearized two-point boundary value problem through Riccati transformation. The analytical study is provided by a linear theory which is expressed in terms of nonsingular elements and is determined through the canonical transformation theory. The fuel consumption is taken as the performance criterion and the analysis is carried out considering various radius ratios and transfer durations. The results are compared to the ones provided by a numerical method based on gradient techniques.

Suboptimal RED Feedback Control for Buffered TCP Flow Dynamics in Computer Network

Abstract: We present an improved dynamic system that simulates the behavior of TCP flows and active queue management (AQM) system. This system can be modeled by a set of stochastic differential equations driven by a doubly stochastic point process with intensities being the controls. The feedback laws proposed monitor the status of buffers and multiplexor of the router, detect incipient congestion by sending warning signals to the sources. The simulation results show that the optimal feedback control law from the class of linear as well as quadratic polynomials can improve the system performance significantly in terms of maximizing the link utilization, minimizing congestion, packet losses, as well as global synchronization. The optimization process used is based on random recursive search technique known as RRS.

Rational Probabilistic Deciders—Part II: Collective Behavior

Abstract: This paper explores the behavior of rational probabilistic deciders (RPDs) in three types of collectives: zero sum matrix games, fractional interactions, and Edgeworth exchange economies. The properties of steady states and transients are analyzed as a function of the level of rationality, N, and, in some cases, the size of the collective, M. It is shown that collectives of RPDs, may or may not behave rationally, depending, for instance, on the relationship between N and M (under fractional interactions) or N and the minimum amount of product exchange (in Edgeworth economies). The results obtained can be useful for designing rational reconfigurable systems that can autonomously adapt to changing environments.

Multiobjective Output Feedback Control of a Class of Stochastic Hybrid Systems with State-Dependent Noise

Abstract: This paper deals with dynamic output feedback control of continuous-time active fault tolerant control systems with Markovian parameters (AFTCSMP) and state-dependent noise. The main contribution is to formulate conditions for multiperformance design, related to this class of stochastic hybrid systems, that take into account the problematic resulting from the fact that the controller only depends on the fault detection and isolation (FDI) process. The specifications and objectives under consideration include stochastic stability, ℋ2 and ℋ∞ (or more generally, stochastic integral quadratic constraints) performances. Results are formulated as matrix inequalities. The theoretical results are illustrated using a classical example from literature.

Nonlinear Equations with a Retarded Argument in Discrete-Continuous Systems

Abstract: The paper deals with dynamic problems of discrete-continuous systems with local nonlinearities, the analysis of which is reduced to solving nonlinear differential equations with a retarded argument. This concerns the discrete-continuous systems subject to torsional, longitudinal, or shear deformations, where the equations of motion for elastic elements are classical wave equations. It is assumed that the characteristics of local nonlinearities are of a soft-type and in the paper they are described by four nonlinear functions. After a short general description of the approach used, the detailed considerations and numerical results are presented for a multimass discrete-continuous system with a local nonlinearity having the characteristics of a soft-type subject to shear deformations.

Retailer's EOQ Model with Limited Storage Space Under Partially Permissible Delay in Payments

Abstract: The main purpose of this paper wants to investigate the optimal retailer's lot-sizing policy with two warehouses under partially permissible delay in payments within the economic order quantity (EOQ) framework. In this paper, we want to extend that fully permissible delay in payments to the supplier would offer the retailer partially permissible delay in payments. That is, the retailer must make a partial payment to the supplier when the order is received. Then the retailer must pay off the remaining balance at the end of the permissible delay period. In addition, we want to add the assumption that the retailer's storage space is limited. That is, the retailer will rent the warehouse to store these exceeding items when the order quantity is larger than retailer's storage space. Under these conditions, we model the retailer's inventory system as a cost minimization problem to determine the retailer's optimal cycle time and optimal order quantity. Three theorems are developed to efficiently determine the optimal replenishment policy for the retailer. Finally, numerical examples are given to illustrate these theorems and obtained a lot of managerial insights.

Third-Body Perturbation Using a Single Averaged Model: Application in Nonsingular Variables

Abstract: The Lagrange's planetary equations written in terms of the classical orbital elements have the disadvantage of singularities in eccentricity and inclination. These singularities are due to the mathematical model used and do not have physical reasons. In this paper, we studied the third-body perturbation using a single averaged model in nonsingular variables. The goal is to develop a semianalytical study of the perturbation caused in a spacecraft by a third body using a single averaged model to eliminate short-period terms caused by the motion of the spacecraft. This is valid if no resonance occurs with the moon or the sun. Several plots show the time histories of the Keplerian elements of equatorial and circular orbits, which are the situations with singularities. In this paper, the expansions are limited only to second order in eccentricity and for the ratio of the semimajor axis of the perturbing and perturbed bodies and to the fourth order for the inclination.

Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method

Abstract: 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).