Showing papers in "Journal of The Franklin Institute-engineering and Applied Mathematics in 2011"

Comparative performance analysis of artificial bee colony algorithm for automatic voltage regulator (AVR) system

Abstract: In this study, Artificial Bee Colony (ABC) algorithm is applied to the Automatic Voltage Regulator (AVR) system for obtaining optimal control. The tuning performance of this algorithm and its contribution to the robustness of the control system are also extensively and comparatively investigated. In the performance analysis, Particle Swarm Optimization (PSO) algorithm and Differential Evolution (DE) algorithm are used for the purpose of comparison. These analyses are realized by benefiting from different analysis methods such as transient response analysis, root locus analysis, bode analysis and statistically Receiver Operating Characteristic (ROC) analysis. Afterwards, the robustness analysis is applied to the AVR system, which is tuned by ABC algorithm in order to determine its response to changes in the system parameters. At the end of the study, it is shown that the ABC algorithm is successfully applied to the AVR system for improving the performance of the controller and shows a better tuning capability than the other similar population based optimization algorithms for this control application.

Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations

Abstract: This paper considers existence, uniqueness and the global asymptotic stability of fuzzy cellular neural networks with mixed delays. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delays and continuously distributed delays. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, some sufficient conditions ensuring global asymptotic stability of the equilibrium point are derived, which are dependent on both the discrete and distributed time delays. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the feasibility of the result.

H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance

Abstract: Finite-time stability concerns the boundness of system during a fixed finite-time interval. For switched systems, finite-time stability property can be affected significantly by switching behavior; however, it was neglected by most previous research. In this paper, the problems of finite-time stability analysis and stabilization for switched nonlinear discrete-time systems are addressed. First, sufficient conditions are given to ensure a class of switched nonlinear discrete-time system subjected to norm bounded disturbance finite-time bounded under arbitrary switching, and then the results are extended to H∞ finite-time boundness of switched nonlinear discrete-time systems. Finally based on the results on finite-time boundness, the state feedback controller is designed to H∞ finite-time stabilize a switched nonlinear discrete-time system. A numerical design example is given to illustrate the proposed results within this paper.

Stabilization for a coupled PDE–ODE control system

Abstract: A control system of an ODE and a diffusion PDE is discussed in this paper. The novelty lies in that the system is coupled. The method of PDE backstepping as well as some special skills is resorted in stabilizing the coupled PDE–ODE control system, which is transformed into an exponentially stable PDE–ODE cascade with an invertible integral transformation. And a state feedback boundary controller is designed. Moreover, an exponentially convergent observer for anti-collocated setup is proposed, and the output feedback boundary control problem is solved. For both the state and output feedback boundary controllers, exponential stability analyses in the sense of the corresponding norms for the resulting closed-loop systems are given through rigid proofs.

Application of numerical inverse Laplace transform algorithms in fractional calculus

Abstract: Laplace transform technique has been considered as an efficient way in solving differential equations with integer-order. But for differential equations with non-integer order, the Laplace transform technique works effectively only for relatively simple equations, because of the difficulties of calculating inversion of Laplace transforms. Motivated by finding an easy way to numerically solve the complicated fractional-order differential equations, we investigate the validity of applying numerical inverse Laplace transform algorithms in fractional calculus. Three numerical inverse Laplace transform algorithms, named Invlap, Gavsteh and NILT, were tested using Laplace transforms of fractional-order equations. Based on the comparison between analytical results and numerical inverse Laplace transform algorithm results, the effectiveness and reliability of numerical inverse Laplace transform algorithms for fractional-order differential equations was confirmed.

A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations

Abstract: In the present paper, a new Legendre wavelet operational matrix of derivative is presented. Shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The application of the proposed operational matrix for solving initial and boundary value problems is explained. Then the scheme is tested for linear and nonlinear singular examples. The obtained results demonstrate efficiency and capability of the proposed method.

Parameter-dependent robust stability for uncertain Markovian jump systems with time delay

Abstract: In this paper, the problem of parameter-dependent robust stability analysis is addressed for uncertain Markovian jump linear systems (MJLSs) with polytopic parameter uncertainties and time-varying delay. By constructing parameter-dependent Lyapunov functional, some sufficient conditions are developed to enable robust exponential mean square stability for the systems. New parameter-dependent robust stability criteria for MJLSs are established in the form of linear matrix inequalities (LMIs), which can be solved efficiently by the interior-point algorithm. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Robust stability analysis for a class of fractional order systems with uncertain parameters

Abstract: The research of robust stability for fractional order linear time-invariant (FO-LTI) interval systems with uncertain parameters has become a hot issue. In this paper, it is the first time to consider robust stability of uncertain parameters FO-LTI interval systems, which have deterministic linear coupling relationship between fractional order and other model parameters. Linear matrix inequalities (LMI) methods are used, and a criterion for checking asymptotical stability of this class of systems is presented. One numerical illustrative example is given to verify the correctness of the conclusions.

Differential evolution algorithm for SSSC-based damping controller design considering time delay

Abstract: Power-system stability improvement by a static synchronous series compensator (SSSC)-based damping controller is thoroughly investigated in this paper. Both local and remote signals with associated time delays are considered in the present study. The design problem of the proposed controller is formulated as an optimization problem, and differential evolution (DE) algorithm is employed to search for the optimal controller parameters. The performances of the proposed controllers are evaluated under different disturbances for both single-machine infinite-bus power system and multi-machine power system. The performance of the proposed controllers with variations in the signal transmission delays has also been investigated. Simulation results are presented and compared with a recently published modern heuristic optimization technique under various disturbances to show the effectiveness and robustness of the proposed approach. The performances of the proposed controllers are also evaluated under N −2 contingency situation.

A design of fine motion assist equipment for disabled hand in robotic rehabilitation system

Abstract: This paper reports a newly designed system intended to aid in hand rehabilitation The motion assistance equipment consists of three parts: mechanisms for the fingers and thumb, a base of these mechanisms, and a motion assistance mechanism for the wrist The structure of each mechanism is designed to achieve independent, fine motion assistance, especially, for the individual fingers First, the features of each mechanism in the equipment are explained Next, the control systems are introduced, which are constructed to realize a self-motion control strategy (ie, the motion is controlled by its user) Using this control system, the transient response and steady state characteristics of the motion assistance mechanisms for the thumb are evaluated Consequently, the possibility of practical application is found in regard to some improved points

A switched system approach to H∞ control of networked control systems with time-varying delays

Abstract: This paper is concerned with the H ∞ control problem for a class of networked control systems (NCSs) with time-varying delay that is less than one sampling period. By applying a new working mode of the actuator and considering state feedback controllers, a new discrete-time switched system model is proposed to describe the NCS. Based on the obtained switched system model, a sufficient condition is derived for the closed-loop NCS to be exponentially stable and ensure a prescribed H ∞ performance level. The obtained condition establishes relations among the delay length, the delay variation frequency, and the system performances of the closed-loop NCS. Moreover, a convex optimization problem is formulated to design the H ∞ controllers which minimize the H ∞ performance level. An illustrative example is given to show the effectiveness of the proposed results.

A collocation method using Hermite polynomials for approximate solution of pantograph equations

Abstract: In this paper, a numerical method based on polynomial approximation, using Hermite polynomial basis, to obtain the approximate solution of generalized pantograph equations with variable coefficients is presented. The technique we have used is an improved collocation method. Some numerical examples, which consist of initial conditions, are given to illustrate the reality and efficiency of the method. In addition, some numerical examples are presented to show the properties of the given method; the present method has been compared with other methods and the results are discussed.

Convection–radiation from a continuously moving fin of variable thermal conductivity

Abstract: The homotopy analysis method (HAM) is applied to generate an analytic solution for heat transfer in a moving fin of variable thermal conductivity which is losing heat by simultaneous convection and radiation to its surroundings. The accuracy of the analytic solution is validated by comparing it with the direct numerical solution of the problem. The analytic solution is found to be accurate to at least three places of decimal for a wide range of values of the parameters that are commonly encountered in thermal processing application. Graphs displaying the results are interpreted in physical terms.

A symmetric image encryption scheme based on combination of nonlinear chaotic maps

Abstract: During the recent years several chaotic image encryption algorithms have been proposed, but most of them encountered some drawbacks such as small key space, low speed, lack of robustness and low security. In this paper, we have proposed an image algorithm based on the combination of a one-dimensional polynomial chaotic map and a piecewise nonlinear chaotic map. Theoretical analysis and computer simulations, both confirm that the new algorithm possesses high security, robust fast encryption speed for practical image encryption and solves the problem of small key space.

Polynomial based differential quadrature method for numerical solution of nonlinear Burgers' equation

Abstract: Nonlinear Burgers' equation is solved using polynomial based differential quadrature method (PDQ). Numerical simulations are studied for three well known test problems, namely shock-like solution, travelling wave and sinusoidal disturbance solutions of Burgers' equation. Obtained numerical results of the first and the third test problems are compared with some earlier numerical results. Discrete root mean square error norm and maximum error norm are computed for the first two test problems and a comparison with some earlier works is given.

Effects of axial and residual stresses on thermoelastic damping in capacitive micro-beam resonators

Abstract: This paper deals with effects of residual and axial stresses on thermoelastic damping (TED) in micro-beam resonators. Equations of coupled thermoelastic case for a capacitive micro-beam resonator have been governed using two dimensional non-Fourier heat conduction model based on continuum theory frame. A Galerkin based finite element formulation has been used to analyze TED for the first mode of vibration of the micro-beam resonator with both ends clamped and isothermal. Effect of axial stresses owing to stretching of the micro-beam on the TED ratio has been investigated. As results illustrate, this effect gets importance only when the resonator is vibrating about a large static deflection due to a bias DC voltage close to the pull-in voltage of the resonator, otherwise it can be neglected in calculations. Effect of compressive and tensile residual stresses has been also studied. The results show that compressive (tensile) residual stresses increase (decrease) the TED ratio considerably. The residual stresses effect has been also studied for various values of the micro-beam thicknesses. The results illustrate that the effect of residual stress on the TED ratio decreases by increasing the thickness of the micro-beam. The results show that, applying DC voltages near the pull-in voltage increases energy dissipation due to the TED considerably, therefore, there is a limitation for applied DC voltage for resonators, since residual stresses change the pull-in voltage of the resonator, hence, existing residual stresses can change the interval of the applied voltage limitation.

A robust vector control for induction motor drives with an adaptive sliding-mode control law

Abstract: A novel adaptive sliding-mode control system is proposed in order to control the speed of an induction motor drive. This design employs the so-called vector (or field oriented) control theory for the induction motor drives. The sliding-mode control is insensitive to uncertainties and presents an adaptive switching gain to relax the requirement for the bound of these uncertainties. The switching gain is adapted using a simple algorithm which does not imply a high computational load. Stability analysis based on Lyapunov theory is also performed in order to guarantee the closed loop stability. Finally, simulation results show not only that the proposed controller provides high-performance dynamic characteristics, but also that this scheme is robust with respect to plant parameter variations and external load disturbances.

A novel technique for optimal placement of piezoelectric actuators on smart structures

Abstract: The problem of positioning of actuators and sensors on smart materials has been a point of interest in recent years. This is due to the fact that in many practical applications there are limitations in space, weight, etc. of the smart structures, which make the problem of positioning more complex. In addition, it is required that the actuators/sensors have the best possible performance. The development of smart structures technology in recent years has provided numerous opportunities for vibration control applications. The use of piezoelectric ceramics or polymers has shown great promise in the development of this technology. The employment of piezoelectric material as actuators in vibration control is beneficial because these actuators only excite the elastic modes of the structures without exciting the rigid-body modes. This is important since very often only elastic motions of the structures are needed to be controlled. The purpose of this paper is to introduce a novel approach developed for optimizing the location of piezoelectric actuators for vibration suppression of flexible structures. A flexible fin with bonded piezoelectric actuators is considered in this study. The frequency response function (FRF) of the system is then recorded and maximization of the FRF peaks is considered as the objective function of the optimization algorithm to find the optimal placement of the piezoelectric actuators on the smart fin. Three multi-layer perceptron neural networks are employed to perform surface fitting to the discrete data generated by the finite element method (FEM). Invasive weed optimization (IWO), a novel numerical stochastic optimization algorithm, is then employed to maximize the weighted summation of FRF peaks. Results indicate an accurate surface fitting for the FRF peak data and an optimal placement of the piezoelectric actuators for vibration suppression is achieved.

Controllability of fractional-order partial neutral functional integrodifferential inclusions with infinite delay

Abstract: In this paper, a sufficient condition is established for the controllability of fractional-order partial neutral functional integrodifferential inclusions with infinite delay in Banach spaces. The approach used is analytic semigroups and fractional powers of closed operators and nonlinear alternative of Leray–Schauder type for multivalued maps due to D. O'Regan.

Variational approach to some damped Dirichlet nonlinear impulsive differential equations

Abstract: We use critical point theory and variational methods to investigate the solutions of a Dirichlet boundary value problem for damped nonlinear impulsive differential equations. The conditions for the existence of solution are established.

A family of proportionate normalized subband adaptive filter algorithms

Abstract: In this paper, the concept of proportionate adaptation is extended to the normalized subband adaptive filter (NSAF), and seven proportionate normalized subband adaptive filter algorithms are established. The proposed algorithms are proportionate normalized subband adaptive filter (PNSAF), μ ‐law PNSAF (MPNSAF), improved PNSAF (IPNSAF), the improved IPNSAF (IIPNSAF), the set-membership IPNSAF (SM-IPNSAF), the selective partial update IPNSAF (SPU-IPNSAF), and SM-SPU-IPNSAF which are suitable for sparse system identification in network echo cancellation. When the impulse response of the echo path is sparse, the PNSAF has initial faster convergence than NSAF but slows down dramatically after initial convergence. The MPNSAF algorithm has fast convergence speed during the whole adaptation. The IPNSAF algorithm is suitable for both sparse and dispersive impulse responses. The SM-IPNSAF exhibits good performance with significant reduction in the overall computational complexity compared with the ordinary IPNSAF. In SPU-IPNSAF, the filter coefficients are partially updated rather than the entire filter at every adaptation. In SM-SPU-IPNSAF algorithm, the concepts of SM and SPU are combined which leads to a reduction in computational complexity. The simulation results show good performance of the proposed algorithms.

Optimized frequency-based foundation design for wind turbine towers utilizing soil–structure interaction

Abstract: This study illustrates design optimization for multiple wind towers located at different villages in Alaska. The towers are supported by two different types of foundations: large mat or deep piles foundations. Initially, a reinforced concrete (RC) mat foundation was proposed. Where soil conditions required it, a pile foundation solution was devised utilizing a 30 in thick RC mat containing an embedded steel grillage of W18 beams and supported by 20–24 in grouted or un-grouted piles. For faster installation and lower construction cost, all-steel foundations were proposed for these remote Alaska sites. The new all-steel design was found to reduce the natural frequencies of the structural system due to softening the foundation. Thus, the tower–foundation system could potentially become near-resonant with the operational frequencies of the wind turbine. Consequently, the likelihood of structural damage or even the collapse is increased. A detailed 3D finite-element model of the tower–foundation–pile system with RC foundation was created using SAP2000. Soil springs were included in the model based on soil properties obtained from the geotechnical investigation. The natural frequency from the model was verified against the tower manufacturer analytical and experimental values. When piles were used, numerous iterations were carried out to eliminate the need for the RC and optimize the design. An optimized design was achieved with enough separation between the natural and operational frequencies. The design successfully avoids damage to the structural system, while eliminating the need for any RC in most cases.

Stability analysis for switched genetic regulatory networks: An average dwell time approach

Abstract: In this correspondence, the problem of exponential stability for switched genetic regulatory networks (GRNs) with time delays is investigated. The GRNs are composed of N modes and the network switches from one mode to another. By employing the piecewise Lyapunov functional method combined with the average dwell time approach and by using a novel Lyapunov–Krasovskii functional (LKF), sufficient criteria are given to ensure the exponential stability for the switched GRNs with constant and time-varying delays, respectively. These criteria are proved to be much less conservative than the most recent results, since the results reported in this paper not only depend on the delay bounds, but also depend on the partitioning. All the conditions presented here are in the form of matrix inequalities which are easy to be verified via the Matlab toolbox. Two examples are provided in the end of this paper to illustrate the effectiveness of the obtained theoretical results.

Observer-based fault-tolerant control for a class of networked control systems with transfer delays

Abstract: In this paper, an observer-based fault-tolerant control (FTC) method is proposed for a class of networked control systems (NCSs) with transfer delays. Markov chain is employed to characterize the transfer delays. Then, such kind of networked control systems are modelled as Markovian jump systems. An observer-based FTC scheme using the delayed state information and the estimated fault value is presented to guarantee the stability of the faulty systems. An inverted pendulum example is used to illustrate the efficiency of the proposed method.

Simultaneous recovery model for aircraft and passengers

Abstract: Usually some unforeseen events make airlines to reconstruct their schedules. A mathematical model for airlines schedule recovery which recovers aircrafts and disrupted passengers simultaneously is presented in this study. Aircraft recovery decisions affect on passengers but disrupted passengers and recovering them were not explicitly considered in the most previous aircraft recovery models so recovery of these two resources – aircrafts and passengers – concurrently is one of our contributions. The modeling is based on defining the recovery scope as well as employing aircraft rotations and passengers’ itineraries instead of flights. These are two of our other contributions. Our model examines possible flight re-timing, aircraft swapping, ferrying, utilization of reserve aircrafts, cancellation, and passenger reassignment to generate an efficient schedule recovery plan. Model parameters are user-specific therefore it helps airlines to apply their policies in the model. Defining the recovery scope reduces the problem size and ensures that the schedule returns to normal within a certain time. The objective is in the form of cost minimization which involves three kinds of cost—operational aircraft recovery, flight cancellation, and delay as well as disrupted passengers. A data set with two disruption scenarios is used to test the proposed model. The computational results show that it is capable of handling the simultaneous aircraft and passenger recovery problem successfully. & 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Mixed H2/H∞ approach to fault detection of discrete linear repetitive processes

Abstract: Linear repetitive processes (LRPs) are a distinct class of two-dimensional (2-D) systems, which have extensive applications in the practical industry, such as, long-wall coal cutting and metal rolling operations. This paper is concerned with the problem of mixed H 2 / H ∞ filter design for discrete LRPs with its application to fault detection. Our attention is focused on the design of a fault-detection filter for generating a residual signal which can be processed to decide whether or not a fault has occurred in the process. A sufficient condition of the mixed H 2 / H ∞ performance for the fault-detection process is proposed. The solvability condition for a desired fault-detection filter is also established, and the corresponding fault-detection filter design is cast into a convex optimization problem which can be efficiently handled by using the standard softwares. A numerical example is given to demonstrate the effectiveness of the proposed design procedures.

Frequency dependent dynamic properties from resonant column and cyclic triaxial tests

Abstract: The resonant column (RC) and cyclic triaxial (CT) devices are commonly used for the measurement of soils’ dynamic properties. The results of these tests do not agree when extrapolated to similar strain levels. The main objectives of this paper are to evaluate the effect of excitation frequency on the dynamic properties of soils, and to provide a methodology to reconcile shear modulus values obtained from RC and CT tests. The effect of frequency on the dynamic properties is evaluated using the new non-resonance (NR) method in the RC device and CT tests. Sand specimens with varying percentages of bentonite–water mixture and a clay specimen are tested. The results obtained from RC tests utilizing the NR method indicate significant change in shear modulus with frequency. The extrapolation of shear modulus from the conventional RC results to shear strains used in CT is significantly overestimated. The extrapolations improved when the results were corrected for frequency effect inferred from the NR method. & 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

MIMO fuzzy sliding mode controlled dual arm robot in load transportation

Abstract: The control problem of the cooperative motion of a two-link dual arm robot during handling and transportation of an object was studied in this paper. Since these types of robots are frequently preferred for hazardous applications such as transportation of radioactive materials and disposal of explosives, a robust non-chattering sliding mode controller (SMC) improved by a multiple-input multiple-output (MIMO) fuzzy logic unit was applied to the robot to track the desired trajectory with high accuracy and transport the load safely. In order to assess the performance of the proposed MIMO fuzzy sliding mode controller (MIMO-FSMC) in presence of parameter variations and external disturbances, a sudden load variation and noise were introduced to the robot system. If compared with classical SMC, tracking errors with smaller magnitudes and faster convergence to zero were obtained by using the proposed MIMO-FSMC. Numerical results suggest that this type of control method may safely be used for cooperative motion control of dual arm robots in load handling and transport applications in hazardous environments with high accuracy.

Handling multi-lean measures with simulation and simulated annealing

Abstract: This paper describes a simulation-based approach for developing a lean production system of multi-lean measures. Three lean measures are defined to characterize the leanness of the underlying production system: productivity, cycle time, and work-in-process inventory. An optimized setting to certain operational parameters is determined so that a best tradeoff of the three lean measures is reached. The problem formulation results in a multi-objective optimization problem with no closed-form definition of problem objective functions and constraints. The solution approach utilizes Discrete Event Simulation (DES) to deploy lean techniques and model lean measures under process variability and plant constraints and dynamics. A direct search method (i.e., Simulated Annealing (SA)) is used to search of problem domain. A model-based Value Mapping (VM) is used for combining the conflicting multi-lean measures and guiding the SA search for optima. The DES model is also used to develop a future state dynamic Value Stream Map (VSM) of the optimized production process. The approach is applied to an example production system where the capacity of material handling conveyors and the size of maintenance crew are optimized to develop a lean system in terms of three lean measures. Little’s formula is used to verify the simulation assessment of lean measures. Optimization results are also used to demonstrate the conflict among lean measures, the impact of process variability on lean measures, and the role of VM in reaching an efficient tradeoff of multi-lean measures.

An LMS adaptive algorithm with a new step-size control equation

Abstract: In this paper, we introduce a new variable step-size LMS (VSSLMS) adaptive algorithm. The algorithm step-size equations estimate an optimal derived step-size and are controlled by only one parameter. Mean-square performance analysis is provided for zero-mean stationary Gaussian input signal, and a simple expression that predicts the algorithm steady state misadjustment is derived for small step-size fluctuations. The algorithm is compared with other well-known VSSLMS algorithms through simulation experiments, which demonstrate the performance advantages of the proposed algorithm over these algorithms.