Search results for: linear quadratic control

Authors: T. Hussein

Abstract:

In this paper, determining the optimal proportionalintegral- derivative (PID) controller gains of an single-area load frequency control (LFC) system using genetic algorithm (GA) is presented. The LFC is notoriously difficult to control optimally using conventionally tuning a PID controller because the system parameters are constantly changing. It is for this reason the GA as tuning strategy was applied. The simulation has been conducted in MATLAB Simulink package for single area power system. the simulation results shows the effectiveness performance of under various disturbance.

Keywords: Load Frequency Control (LFC), PID controller and Genetic Algorithm (GA).

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Authors: Abolfazl Mohammadijoo

Abstract:

In this paper, we are investigating sliding mode control approach for trajectory tracking of a two-link-manipulator with wheeled mobile robot in its base. The main challenge of this work is dynamic interaction between mobile base and manipulator which makes trajectory tracking more difficult than n-link manipulators with fixed base. Another challenging part of this work is to avoid chattering phenomenon of sliding mode control that makes lots of damages for actuators in real industrial cases. The results show the effectiveness of sliding mode control approach for desired trajectory.

Keywords: Mobile manipulator, sliding mode control, dynamic interaction, mobile robotics.

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Authors: Seong-Ho Song, Ki-Seob Kim, Seon-Woo Lee, Seop-Hyeong Park

Abstract:

Based on a theoretical erbium-doped fiber amplifier (EDFA) model, we have proposed an application of disturbance observer(DOB) with proportional/integral/differential(PID) controller to EDFA for minimizing gain-transient time of wavelength -division-multiplexing (WDM) multi channels in optical amplifier in channel add/drop networks. We have dramatically reduced the gain-transient time to less than 30μsec by applying DOB with PID controller to the control of amplifier gain. The proposed DOB-based gain control algorithm for EDFA was implemented as a digital control system using TI's DSP(TMS320C28346) chip and experimental results of the system verify the excellent performance of the proposed gain control methodology.

Keywords: EDFA, Disturbance observer, gain control, WDM.

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Authors: S. Ariffin, K. Hasnan, R.H. Weston

Abstract:

A new generation of manufacturing machines so-called MIMCA (modular and integrated machine control architecture) capable of handling much increased complexity in manufacturing control-systems is presented. Requirement for more flexible and effective control systems for manufacturing machine systems is investigated and dimensioned-which highlights a need for improved means of coordinating and monitoring production machinery and equipment used to- transport material. The MIMCA supports simulation based on machine modeling, was conceived by the authors to address the issues. Essentially MIMCA comprises an organized unification of selected architectural frameworks and modeling methods, which include: NISTRCS, UMC and Colored Timed Petri nets (CTPN). The unification has been achieved; to support the design and construction of hierarchical and distributed machine control which realized the concurrent operation of reusable and distributed machine control components; ability to handle growing complexity; and support requirements for real- time control systems. Thus MIMCA enables mapping between 'what a machine should do' and 'how the machine does it' in a well-defined but flexible way designed to facilitate reconfiguration of machine systems.

Keywords: Machine control, architectures, Petri nets, modularity, modeling, simulation.

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Authors: Surinder Deswal, Mahesh Pal

Abstract:

An Artificial Neural Network based modeling technique has been used to study the influence of different combinations of meteorological parameters on evaporation from a reservoir. The data set used is taken from an earlier reported study. Several input combination were tried so as to find out the importance of different input parameters in predicting the evaporation. The prediction accuracy of Artificial Neural Network has also been compared with the accuracy of linear regression for predicting evaporation. The comparison demonstrated superior performance of Artificial Neural Network over linear regression approach. The findings of the study also revealed the requirement of all input parameters considered together, instead of individual parameters taken one at a time as reported in earlier studies, in predicting the evaporation. The highest correlation coefficient (0.960) along with lowest root mean square error (0.865) was obtained with the input combination of air temperature, wind speed, sunshine hours and mean relative humidity. A graph between the actual and predicted values of evaporation suggests that most of the values lie within a scatter of ±15% with all input parameters. The findings of this study suggest the usefulness of ANN technique in predicting the evaporation losses from reservoirs.

Keywords: Artificial neural network, evaporation losses, multiple linear regression, modeling.

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Authors: Markus Mazzola, Gunther Schaaf

Abstract:

A vehicle driving with an Adaptive Cruise Control System (ACC) is usually controlled decentrally, based on the information of radar systems and in some publications based on C2X-Communication (CACC) to guarantee stable platoons. In this paper we present a Model Predictive Control (MPC) design of a centralized, server-based ACC-System, whereby the vehicular platoon is modeled and controlled as a whole. It is then proven that the proposed MPC design guarantees asymptotic stability and hence string stability of the platoon. The Networked MPC design is chosen to be able to integrate system constraints optimally as well as to reduce the effects of communication delay and packet loss. The performance of the proposed controller is then simulated and analyzed in an LTE communication scenario using the LTE/EPC Network Simulator LENA, which is based on the ns-3 network simulator.

Keywords: Adaptive Cruise Control, Centralized Server, Networked Model Predictive Control, String Stability.

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Authors: Lily Ingsrisawang, Tasanee Nacharoen

Abstract:

The problems arising from unbalanced data sets generally appear in real world applications. Due to unequal class distribution, many researchers have found that the performance of existing classifiers tends to be biased towards the majority class. The k-nearest neighbors’ nonparametric discriminant analysis is a method that was proposed for classifying unbalanced classes with good performance. In this study, the methods of discriminant analysis are of interest in investigating misclassification error rates for classimbalanced data of three diabetes risk groups. The purpose of this study was to compare the classification performance between parametric discriminant analysis and nonparametric discriminant analysis in a three-class classification of class-imbalanced data of diabetes risk groups. Data from a project maintaining healthy conditions for 599 employees of a government hospital in Bangkok were obtained for the classification problem. The employees were divided into three diabetes risk groups: non-risk (90%), risk (5%), and diabetic (5%). The original data including the variables of diabetes risk group, age, gender, blood glucose, and BMI were analyzed and bootstrapped for 50 and 100 samples, 599 observations per sample, for additional estimation of the misclassification error rate. Each data set was explored for the departure of multivariate normality and the equality of covariance matrices of the three risk groups. Both the original data and the bootstrap samples showed nonnormality and unequal covariance matrices. The parametric linear discriminant function, quadratic discriminant function, and the nonparametric k-nearest neighbors’ discriminant function were performed over 50 and 100 bootstrap samples and applied to the original data. Searching the optimal classification rule, the choices of prior probabilities were set up for both equal proportions (0.33: 0.33: 0.33) and unequal proportions of (0.90:0.05:0.05), (0.80: 0.10: 0.10) and (0.70, 0.15, 0.15). The results from 50 and 100 bootstrap samples indicated that the k-nearest neighbors approach when k=3 or k=4 and the defined prior probabilities of non-risk: risk: diabetic as 0.90: 0.05:0.05 or 0.80:0.10:0.10 gave the smallest error rate of misclassification. The k-nearest neighbors approach would be suggested for classifying a three-class-imbalanced data of diabetes risk groups.

Keywords: Bootstrap, diabetes risk groups, error rate, k-nearest neighbors.

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Authors: L. Novakova-Marcincinova, J. Novak-Marcincin, M. Janak

Abstract:

The computer aided for design, analysis, control, visualization and simulation of robotized workcells is very interesting in this time. Computer Aided Robot Control (CARC) is a subsystem of the system CIM including the computer aided systems of all activities connected with visualization and working of robotized workcells. There are three basic ideas: current CAD/CAM/CAE systems for design and 3D visualization, special PC based control and simulation systems and Augmented Reality Aided Manufacturing (ARAM) systems. This paper describes example of Open Source software application that can to be utilized at planning of the robotized workcells, visualization and off-line programming the automated processes realized by authors.

Keywords: Intelligent control, augmented reality, robot.

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

This paper is concerned with the stability problem with two additive time-varying delay components. By choosing one augmented Lyapunov-Krasovskii functional, using some new zero equalities, and combining linear matrix inequalities (LMI) techniques, two new sufficient criteria ensuring the global stability asymptotic stability of DNNs is obtained. These stability criteria are present in terms of linear matrix inequalities and can be easily checked. Finally, some examples are showed to demonstrate the effectiveness and less conservatism of the proposed method.

Keywords: Neural networks, Globally asymptotic stability, LMI approach, Additive time-varying delays.

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Authors: M. Umabharathi, S. Vijayabaskar

Abstract:

Evolutionary Fuzzy PID Speed Controller for Permanent Magnet Synchronous Motor (PMSM) is developed to achieve the Speed control of PMSM in Closed Loop operation and to deal with the existence of transients. Consider a Fuzzy PID control design problem, based on common control Engineering Knowledge. If the transient error is big, that Good transient performance can be obtained by increasing the P and I gains and decreasing the D gains. To autotune the control parameters of the Fuzzy PID controller, the Evolutionary Algorithms (EA) are developed. EA based Fuzzy PID controller provides better speed control and guarantees the closed loop stability. The Evolutionary Fuzzy PID controller can be implemented in real time Applications without any concern about instabilities that leads to system failure or damage.

Keywords: Evolutionary Algorithm (EA), Fuzzy system, Genetic Algorithm (GA), Membership, Permanent Magnet Synchronous Motor (PMSM).

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Authors: Davod Khojasteh Salkuyeh, Sayyed Hasan Azizi

Abstract:

We study the semiconvergence of Gauss-Seidel iterative methods for the least squares solution of minimal norm of rank deficient linear systems of equations. Necessary and sufficient conditions for the semiconvergence of the Gauss-Seidel iterative method are given. We also show that if the linear system of equations is consistent, then the proposed methods with a zero vector as an initial guess converge in one iteration. Some numerical results are given to illustrate the theoretical results.

Keywords: rank deficient least squares problems, AOR iterativemethod, Gauss-Seidel iterative method, semiconvergence.

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Authors: M. Siosemarde, M. Byzedi

Abstract:

Saturated hydraulic conductivity of Soil is an important property in processes involving water and solute flow in soils. Saturated hydraulic conductivity of soil is difficult to measure and can be highly variable, requiring a large number of replicate samples. In this study, 60 sets of soil samples were collected at Saqhez region of Kurdistan province-IRAN. The statistics such as Correlation Coefficient (R), Root Mean Square Error (RMSE), Mean Bias Error (MBE) and Mean Absolute Error (MAE) were used to evaluation the multiple linear regression models varied with number of dataset. In this study the multiple linear regression models were evaluated when only percentage of sand, silt, and clay content (SSC) were used as inputs, and when SSC and bulk density, Bd, (SSC+Bd) were used as inputs. The R, RMSE, MBE and MAE values of the 50 dataset for method (SSC), were calculated 0.925, 15.29, -1.03 and 12.51 and for method (SSC+Bd), were calculated 0.927, 15.28,-1.11 and 12.92, respectively, for relationship obtained from multiple linear regressions on data. Also the R, RMSE, MBE and MAE values of the 10 dataset for method (SSC), were calculated 0.725, 19.62, - 9.87 and 18.91 and for method (SSC+Bd), were calculated 0.618, 24.69, -17.37 and 22.16, respectively, which shows when number of dataset increase, precision of estimated saturated hydraulic conductivity, increases.

Keywords: dataset, precision, saturated hydraulic conductivity, soil and statistics.

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Authors: Jintana Khemprasit, Vatcharaporn Esichaikul

Abstract:

Crime is a major societal problem for most of the world's nations. Consequently, the police need to develop new methods to improve their efficiency in dealing with these ever increasing crime rates. Two of the common difficulties that the police face in crime control are crime investigation and the provision of crime information to the general public to help them protect themselves. Crime control in police operations involves the use of spatial data, crime data and the related crime data from different organizations (depending on the nature of the analysis to be made). These types of data are collected from several heterogeneous sources in different formats and from different platforms, resulting in a lack of standardization. Moreover, there is no standard framework for crime data collection, integration and dissemination through mobile devices. An investigation into the current situation in crime control was carried out to identify the needs to resolve these issues. This paper proposes and investigates the use of service oriented architecture (SOA) and the mobile spatial information service in crime control. SOA plays an important role in crime control as an appropriate way to support data exchange and model sharing from heterogeneous sources. Crime control also needs to facilitate mobile spatial information services in order to exchange, receive, share and release information based on location to mobile users anytime and anywhere.

Keywords: Crime Control, Geographic Information System (GIS), Mobile GIS, Service Oriented Architecture (SOA).

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Authors: Kréhi Serge Agbli, Samuel Portebos, Michaël Salomon

Abstract:

Here a methodology is considered aiming at evaluating the economic benefit of the provision of a primary frequency control unit using a Battery Energy Storage System (BESS). In this methodology, two control types (basic and hysteresis) are implemented and the corresponding minimum energy storage system power allowing to maintain the frequency drop inside a given threshold under a given contingency is identified and compared using DigSilent’s PowerFactory software. Following this step, the corresponding energy storage capacity (in MWh) is calculated. As PowerFactory is dedicated to dynamic simulation for transient analysis, a first order model related to the IEEE 9 bus grid used for the analysis under PowerFactory is characterized and implemented on MATLAB-Simulink. Primary frequency control is simulated using the two control types over one-month grid's frequency deviation data on this Simulink model. This simulation results in the energy throughput both basic and hysteresis BESSs. It emerges that the 15 minutes operation band of the battery capacity allocated to frequency control is sufficient under the considered disturbances. A sensitivity analysis on the width of the control deadband is then performed for the two control types. The deadband width variation leads to an identical sizing with the hysteresis control showing a better frequency control at the cost of a higher delivered throughput compared to the basic control. An economic analysis comparing the cost of the sized BESS to the potential revenues is then performed.

Keywords: Battery Energy Storage System, electrical network frequency stability, frequency control unit, PowerFactory.

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Authors: Apinan Aurasopon, Worawat Sa-ngiavibool

Abstract:

This paper proposes a feed-forward control in a halfbridge resonant dc link inverter. The configuration of feed-forward control is based on synchronous sigma-delta modulation and the halfbridge resonant dc link inverter consists of two inductors, one capacitor and two power switches. The simulation results show the proposed technique can reject non-ideal dc bus improving the total harmonic distortion.

Keywords: Feed-forward control, Resonant dc link inverter, Synchronous sigma-delta modulation.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of stability criteria for neural networks with two additive time-varying delays.A new Lyapunov-Krasovskii function is constructed and some new delay dependent stability criterias are derived in the terms of linear matrix inequalities(LMI), zero equalities and reciprocally convex approach.The several stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Stability, Neural networks, Linear Matrix Inequalities (LMI) , Lyapunov function, Time-varying delays

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Authors: Wayne Goodridge, Alexander Nikov, Ashok Sahai

Abstract:

Multi criteria decision making (MCDM) methods like analytic hierarchy process, ELECTRE and multi-attribute utility theory are critically studied. They have irregularities in terms of the reliability of ranking of the best alternatives. The Routing Decision Support (RDS) algorithm is trying to improve some of their deficiencies. This paper gives a mathematical verification that the RDS algorithm conforms to the test criteria for an effective MCDM method when a linear preference function is considered.

Keywords: Decision support systems, linear preference function, multi-criteria decision-making algorithm, analytic hierarchy process.

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Authors: Selim Yannier, Asif Sabanovic, Ahmet Onat, Muhammet Bastan

Abstract:

In this work, we suggested a new approach for the control of a mobile robot capable of being a building block of an intelligent agent. This approach includes obstacle avoidance and goal tracking implemented as two different sliding mode controllers. A geometry based behavior arbitration is proposed for fusing the two outputs. Proposed structure is tested on simulations and real robot. Results have confirmed the high performance of the method.

Keywords: Autonomous Mobile Robot, Behavior Based Control, Fast Local Obstacle Avoidance, Sliding Mode Control.

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Authors: Shonal Singh, Bibhya Sharma, Jito Vanualailai

Abstract:

This paper considers the design of a motion planner that will simultaneously accomplish control and motion planning of a n-link nonholonomic mobile manipulator, wherein, a n-link holonomic manipulator is coupled with a nonholonomic mobile platform, within an obstacle-ridden environment. This planner, derived from the Lyapunov-based control scheme, generates collision-free trajectories from an initial configuration to a final configuration in a constrained environment cluttered with stationary solid objects of different shapes and sizes. We demonstrate the efficiency of the control scheme and the resulting acceleration controllers of the mobile manipulator with results through computer simulations of an interesting scenario.

Keywords: Artificial potential fields, Lyapunov-based control scheme, Lyapunov stability, nonholonomic manipulator, minimum distance technique, kinodynamic constraints.

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Authors: Li Jie, Zhang Wei

Abstract:

In this paper, the problem of posture stabilization for a kinematic model of differential drive robots is studied. A more complex model of the kinematics of differential drive robots is used for the design of stabilizing control. This model is formulated in terms of the physical parameters of the system such as the radius of the wheels, and velocity of the wheels are the control inputs of it. In this paper, the framework of Lyapunov-based control design has been used to solve posture stabilization problem for the comprehensive model of differential drive robots. The results of the simulations show that the devised controller successfully solves the posture regulation problem. Finally, robustness and performance of the controller have been studied under system parameter uncertainty.

Keywords: Differential drive robots, nonlinear control, Lyapunov-based control design, posture regulation.

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Authors: Tooraj Hakim Elahi, Abdolamir Nekoubin

Abstract:

In many applications, magnetic suspension systems are required to operate over large variations in air gap. As a result, the nonlinearities inherent in most types of suspensions have a significant impact on performance. Specifically, it may be difficult to design a linear controller which gives satisfactory performance, stability, and disturbance rejection over a wide range of operating points. in this paper an optimal controller based on discontinuous mathematical model of the system for an electromagnetic suspension system which is applied in magnetic trains has been designed . Simulations show that the new controller can adapt well to the variance of suspension mass and gap, and keep its dynamic performance, thus it is superior to the classic controller.

Keywords: Magnetic Levitation, optimal controller, mass and gap

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Authors: Qingqing Wang, Shouming Zhong

Abstract:

Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural networks, Globally asymptotic stability , LMI approach , IIA approach , Time-varying delay.

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Authors: Tomoaki Hashimoto

Abstract:

Recently, optimal control problems subject to probabilistic constraints have attracted much attention in many research field. Although probabilistic constraints are generally intractable in optimization problems, several methods haven been proposed to deal with probabilistic constraints. In most methods, probabilistic constraints are transformed to deterministic constraints that are tractable in optimization problems. This paper examines a method for transforming probabilistic constraints into deterministic constraints for a class of probabilistic constrained optimal control problems.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints.

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Authors: Fariba Azizi, Firoozeh Haghighi, Viliam Makis

Abstract:

In this paper, we propose a method to model the relationship between failure time and degradation for a simple step stress test where underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to shorten failure time of products and a tampered failure rate (TFR) model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates (MLEs) of the model parameters are obtained through an expectation-maximization (EM) algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real example is analyzed to illustrate the application of the proposed methods.

Keywords: Expectation-maximization (EM) algorithm, cause of failure, intensity, linear degradation path, masked data, reliability function.

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Authors: Badr M. Alshammari, A. Rabeh, A. K. Mohamed

Abstract:

This paper presents the modeling and the control of a grid-connected photovoltaic system (PVS). Firstly, the MPPT control of the PVS and its associated DC/DC converter has been analyzed in order to extract the maximum of available power. Secondly, the control system of the grid side converter (GSC) which is a three-phase voltage source inverter (VSI) has been presented. A special attention has been paid to the control algorithms of the GSC converter during grid voltages imbalances. Especially, three different control objectives are to achieve; the mitigation of the grid imbalance adverse effects, at the point of common coupling (PCC), on the injected currents, the elimination of double frequency oscillations in active power flow, and the elimination of double frequency oscillations in reactive power flow. Simulation results of two control strategies have been performed via MATLAB software in order to demonstrate the particularities of each control strategy according to power quality standards.

Keywords: Renewable energies, photovoltaic systems, DC link, voltage source inverter, space vector SVPWM, unbalanced voltage dips, symmetrical components.

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Authors: Ismail Algelli Sassi Ehtiwesh, Željko Đurović

Abstract:

The main goal of the study is to analyze all relevant properties of the electro hydraulic systems and based on that to make a proper choice of the control strategy that may be used for the control of the servomechanism system. A combination of electronic and hydraulic systems is widely used since it combines the advantages of both. Hydraulic systems are widely spread because of their properties as accuracy, flexibility, high horsepower-to-weight ratio, fast starting, stopping and reversal with smoothness and precision, and simplicity of operations. On the other hand, the modern control of hydraulic systems is based on control of the circuit fed to the inductive solenoid that controls the position of the hydraulic valve. Since this circuit may be easily handled by PWM (Pulse Width Modulation) signal with a proper frequency, the combination of electrical and hydraulic systems became very fruitful and usable in specific areas as airplane and military industry. The study shows and discusses the experimental results obtained by the control strategy (classical feedback (PID) & neural network) using MATLAB and SIMULINK [1]. Finally, the special attention was paid to the possibility of neuro-controller design and its application to control of electro-hydraulic systems and to make comparative with classical control.

Keywords: Electro-hydraulic systems, PID, Neural network controller.

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Authors: Lianglin Xiong, Shouming Zhong, Mao Ye

Abstract:

This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.

Keywords: Switched neutral system, piecewise Lyapunov functional, nonlinear perturbation, Lyapunov-Metzler linear matrix inequality.

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Authors: Roengruen P., Tipsuwanporn V., Puawade P., Numsomran A.

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Smith Predictor control is theoretically a good solution to the problem of controlling the time delay systems. However, it seldom gets use because it is almost impossible to find out a precise mathematical model of the practical system and very sensitive to uncertain system with variable time-delay. In this paper is concerned with a design method of smith predictor for temperature control system by Coefficient Diagram Method (CDM). The simulation results show that the control system with smith predictor design by CDM is stable and robust whilst giving the desired time domain system performance.

Keywords: CDM, Smith Predictor, temperature process

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Authors: Ephraim Gower, Thato Tsalaile, Monageng Kgwadi, Malcolm Hawksford.

Abstract:

In this paper, the statistical properties of filtered or convolved signals are considered by deriving the resulting density functions as well as the exact mean and variance expressions given a prior knowledge about the statistics of the individual signals in the filtering or convolution process. It is shown that the density function after linear convolution is a mixture density, where the number of density components is equal to the number of observations of the shortest signal. For circular convolution, the observed samples are characterized by a single density function, which is a sum of products.

Keywords: Circular Convolution, linear Convolution, mixture density function.

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Authors: Vijaya K. Srivastava, Davide Spinello

Abstract:

This paper presents performance of two robust gradient-based heuristic optimization procedures based on 3ⁿ enumeration and tunneling approach to seek global optimum of constrained integer problems. Both these procedures consist of two distinct phases for locating the global optimum of integer problems with a linear or non-linear objective function subject to linear or non-linear constraints. In both procedures, in the first phase, a local minimum of the function is found using the gradient approach coupled with hemstitching moves when a constraint is violated in order to return the search to the feasible region. In the second phase, in one optimization procedure, the second sub-procedure examines 3ⁿ integer combinations on the boundary and within hypercube volume encompassing the result neighboring the result from the first phase and in the second optimization procedure a tunneling function is constructed at the local minimum of the first phase so as to find another point on the other side of the barrier where the function value is approximately the same. In the next cycle, the search for the global optimum commences in both optimization procedures again using this new-found point as the starting vector. The search continues and repeated for various step sizes along the function gradient as well as that along the vector normal to the violated constraints until no improvement in optimum value is found. The results from both these proposed optimization methods are presented and compared with one provided by popular MS Excel solver that is provided within MS Office suite and other published results.

Keywords: Constrained integer problems, enumerative search algorithm, Heuristic algorithm, tunneling algorithm.

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