Search results for: Disturbance robustness
367 Fuel Cell/DC-DC Convertor Control by Sliding Mode Method
Authors: Farzad Abdous
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Fuel cell's system requires regulating circuit for voltage and current in order to control power in case of connecting to other generative devices or load. In this paper Fuel cell system and convertor, which is a multi-variable system, are controlled using sliding mode method. Use of weighting matrix in design procedure made it possible to regulate speed of control. Simulation results show the robustness and accuracy of proposed controller for controlling desired of outputs.Keywords: DC-DC converter, Fuel cell, PEM, Slides mode control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1614366 Influence of Temperature Variations on Calibrated Cameras
Authors: Peter Podbreznik, Božidar Potocnik
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The camera parameters are changed due to temperature variations, which directly influence calibrated cameras accuracy. Robustness of calibration methods were measured and their accuracy was tested. An error ratio due to camera parameters change with respect to total error originated during calibration process was determined. It pointed out that influence of temperature variations decrease by increasing distance of observed objects from cameras.Keywords: camera calibration, perspective projection matrix, epipolar geometry, temperature variation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1859365 Designing Intelligent Adaptive Controller for Nonlinear Pendulum Dynamical System
Authors: R. Ghasemi, M. R. Rahimi Khoygani
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This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller.
Keywords: Adaptive Neural Controller, Nonlinear Dynamical, Neural Network, RBF, Driven Pendulum, Position Control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2592364 Design of Permanent Sensor Fault Tolerance Algorithms by Sliding Mode Observer for Smart Hybrid Powerpack
Authors: Sungsik Jo, Hyeonwoo Kim, Iksu Choi, Hunmo Kim
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In the SHP, LVDT sensor is for detecting the length changes of the EHA output, and the thrust of the EHA is controlled by the pressure sensor. Sensor is possible to cause hardware fault by internal problem or external disturbance. The EHA of SHP is able to be uncontrollable due to control by feedback from uncertain information, on this paper; the sliding mode observer algorithm estimates the original sensor output information in permanent sensor fault. The proposed algorithm shows performance to recovery fault of disconnection and short circuit basically, also the algorithm detect various of sensor fault mode.Keywords: Smart Hybrid Powerpack (SHP), Electro Hydraulic Actuator (EHA), Permanent Sensor fault tolerance, Sliding mode observer (SMO), Graphic User Interface (GUI).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1491363 Simulation of an Active Controlled Vibration Isolation System for Astronaut’s Exercise Platform
Authors: Shield B. Lin, Sameer Abdali
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Computer simulations were performed using MATLAB/Simulink for a vibration isolation system for astronaut’s exercise platform. Simulation parameters initially were based on an on-going experiment in a laboratory at NASA Johnson Space Center. The authors expanded later simulations to include other parameters. A discrete proportional-integral-derivative controller with a low-pass filter commanding a linear actuator served as the active control unit to push and pull a counterweight in balancing the disturbance forces. A spring-damper device is used as an optional passive control unit. Simulation results indicated such design could achieve near complete vibration isolation with small displacements of the exercise platform.Keywords: Control, counterweight, isolation, vibration.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 508362 Static Voltage Stability Assessment Considering the Power System Contingencies using Continuation Power Flow Method
Authors: Mostafa Alinezhad, Mehrdad Ahmadi Kamarposhti
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According to the increasing utilization in power system, the transmission lines and power plants often operate in stability boundary and system probably lose its stable condition by over loading or occurring disturbance. According to the reasons that are mentioned, the prediction and recognition of voltage instability in power system has particular importance and it makes the network security stronger.This paper, by considering of power system contingencies based on the effects of them on Mega Watt Margin (MWM) and maximum loading point is focused in order to analyse the static voltage stability using continuation power flow method. The study has been carried out on IEEE 14-Bus Test System using Matlab and Psat softwares and results are presented.
Keywords: Contingency, Continuation Power Flow, Static Voltage Stability, Voltage Collapse.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2214361 A Statistical Identification Approach by the Boundary Field Changes
Authors: Rumena D. Stancheva, Ilona I. Iatcheva
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In working mode some unexpected changes could be arise in inner structure of electromagnetic device. They influence modification in electromagnetic field propagation map. The field values at an observed boundary are also changed. The development of the process has to be watched because the arising structural changes would provoke the device to be gone out later. The probabilistic assessment of the state is possible to be made. The numerical assessment points if the resulting changes have only accidental character or they are due to the essential inner structural disturbances. The presented application example is referring to the 200MW turbine-generator. A part of the stator core end teeth zone is simulated broken. Quasi three-dimensional electromagnetic and temperature field are solved applying FEM. The stator core state diagnosis is proposed to be solved as an identification problem on the basis of a statistical criterion.Keywords: Identification, structural disturbance, statistical criterion.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1291360 Stabilization Technique for Multi-Inputs Voltage Sense Amplifiers in Node Sharing Converters
Authors: Sanghoon Park, Ki-Jin Kim, Kwang-Ho Ahn
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This paper discusses the undesirable charge transfer through the parasitic capacitances of the input transistors in a multi-inputs voltage sense amplifier. Its intrinsic rail-to-rail voltage transitions at the output nodes inevitably disturb the input sides through the capacitive coupling between the outputs and inputs. Then, it can possible degrade the stabilities of the reference voltage levels. Moreover, it becomes more serious in multi-channel systems by altering them for other channels, and so degrades the linearity of the overall systems. In order to alleviate the internal node voltage transition, the internal node stabilization techniques are proposed. It achieves 45% and 40% improvements for node stabilization and input referred disturbance, respectively.
Keywords: Voltage sense amplifier, multi-inputs, voltage transition, node stabilization, and biasing circuits.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2464359 On The Design of Robust Governors of Steam Power Systems Using Polynomial and State-Space Based H∞ Techniques: A Comparative Study
Authors: Rami A. Maher, Ibraheem K. Ibraheem
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This work presents a comparison study between the state-space and polynomial methods for the design of the robust governor for load frequency control of steam turbine power systems. The robust governor is synthesized using the two approaches and the comparison is extended to include time and frequency domains performance, controller order, and uncertainty representation, weighting filters, optimality and sub-optimality. The obtained results are represented through tables and curves with reasons of similarities and dissimilarities.
Keywords: Robust control, load frequency control, steam turbine, H∞-norm, system uncertainty, load disturbance.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2062358 Engine Power Effects on Support Interference
Authors: B.J.C. Horsten, L.L.M. Veldhuis
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Renewed interest in propeller propulsion on aircraft configurations combined with higher propeller loads lead to the question how the effects of the propulsion on model support disturbances should be accounted for. In this paper, the determination of engine power effects on support interference of sting-mounted models is demonstrated by a measurement on a four-engine turboprop aircraft. CFD results on a more generic model are presented in order to clarify the possible mechanism behind engine power effects on support interference. The engine slipstream induces a local change in angle of sideslip at the model sting thereby influencing the sting near-field and far-field effects. Whether or not the net result of these changes in the disturbance pattern leads to a significant engine power effect depends on the configuration of the wind tunnel model and the test setup.Keywords: CFD, engine power effects, measurements, support interference.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1481357 Performance of Power System Stabilizer (UNITROL D) in Benghazi North Power Plant
Authors: T. Hussein
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The use of power system stabilizers (PSSs) to damp power system swing mode of oscillations is practical important. Our purpose is to retune the power system stabilizer (PSS1A) parameters in Unitrol D produced by ABB– was installed in 1995in Benghazi North Power Plants (BNPPs) at General Electricity Company of Libya (GECOL). The optimal values of the power system stabilizer (PSS1A) parameters are determined off-line by a particle swarm optimization technique (PSO). The objective is to damp the local and inter-area modes of oscillations that occur following power system disturbances. The retuned power system stabilizer (PSS1A) can cope with large disturbance at different operating points and has enhanced power system stability.Keywords: Static excitation system, particle swarm optimization (PSO), power system stabilizer (PSS).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2430356 Object Alignment for Military Optical Surveillance
Authors: Oscar J.G. Somsen, Fok Bolderheij
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Electro-optical devices are increasingly used for military sea-, land- and air applications to detect, recognize and track objects. Typically, these devices produce video information that is presented to an operator. However, with increasing availability of electro-optical devices the data volume is becoming very large, creating a rising need for automated analysis. In a military setting, this typically involves detecting and recognizing objects at a large distance, i.e. when they are difficult to distinguish from background and noise. One may consider combining multiple images from a video stream into a single enhanced image that provides more information for the operator. In this paper we investigate a simple algorithm to enhance simulated images from a military context and investigate how the enhancement is affected by various types of disturbance.Keywords: Electro-Optics, Automated Image alignment
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1615355 Optimal Speed Controller Design of the Two-Inertia Stabilization System
Authors: Byoung-Uk Nam, Hag-Seong Kim, Ho-Jung Lee, Dong-Hyun Kim
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This paper focuses on systematic analysis and controller design of the two-inertia STABILIZATION system, considering the angular motion on a base body. This approach is essential to the stabilization system to aim at a target under three or six degrees of freedom base motion. Four controllers, such as conventional PDF(Pseudo-Derivative Feedback) controller with motor speed feedback, PDF controller with load speed feedback, modified PDF controller with motor-load speed feedback and feedforward controller added to modified PDF controller, are suggested to improve reference tracking and disturbance rejection performance. Characteristics and performance of each controller are analyzed and validated by simulation in the case of the modified PDF controller with and without a feedforward controller.Keywords: Two-Inertia stabilization System, ITAE criterion, Speed Control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2687354 Characteristic Function in Estimation of Probability Distribution Moments
Authors: Vladimir S. Timofeev
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In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.
Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2254353 Nonlinear Controller for Fuzzy Model of Double Inverted Pendulums
Authors: I. Zamani, M. H. Zarif
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In this paper a method for designing of nonlinear controller for a fuzzy model of Double Inverted Pendulum is proposed. This system can be considered as a fuzzy large-scale system that includes offset terms and disturbance in each subsystem. Offset terms are deterministic and disturbances are satisfied a matching condition that is mentioned in the paper. Based on Lyapunov theorem, a nonlinear controller is designed for this fuzzy system (as a model reference base) which is simple in computation and guarantees stability. This idea can be used for other fuzzy large- scale systems that include more subsystems Finally, the results are shown.
Keywords: Controller, Fuzzy Double Inverted Pendulums, Fuzzy Large-Scale Systems, Lyapunov Stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2514352 Stability Bound of Ruin Probability in a Reduced Two-Dimensional Risk Model
Authors: Zina Benouaret, Djamil Aissani
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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 889351 A New Nonlinear Excitation Controller for Transient Stability Enhancement in Power Systems
Authors: M. Ouassaid, A. Nejmi, M. Cherkaoui, M. Maaroufi
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The very nonlinear nature of the generator and system behaviour following a severe disturbance precludes the use of classical linear control technique. In this paper, a new approach of nonlinear control is proposed for transient and steady state stability analysis of a synchronous generator. The control law of the generator excitation is derived from the basis of Lyapunov stability criterion. The overall stability of the system is shown using Lyapunov technique. The application of the proposed controller to simulated generator excitation control under a large sudden fault and wide range of operating conditions demonstrates that the new control strategy is superior to conventional automatic voltage regulator (AVR), and show very promising results.Keywords: Excitation control, Lyapunov technique, non linearcontrol, synchronous generator, transient stability, voltage regulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2614350 Repetitive Control and Feedback Dithering Modulation of a DC/AC Converter
Authors: Sing-Han Wang, Shiang-Hwua Yu, Chih-Po Yang
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Repetitive control and feedback dithering modulation are applied to a single-phase voltage source inverter, with an aim to eliminate harmonics and stabilize the inverter under load variations. The proposed control and modulation scheme comprise multiple loops of feedback, which helps improve inverter performance and robustness. Experimental results show that the designed inverter exhibits very low distortion at its output with THD of about 0.3% under different load variations.
Keywords: Feedback dithering modulation, repetitive control, state feedback, inverter, harmonics elimination.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2141349 Cost-Optimized SSB Transmitter with High Frequency Stability and Selectivity
Authors: J. P. Dubois
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Single side band modulation is a widespread technique in communication with significant impact on communication technologies such as DSL modems and ATSC TV. Its widespread utilization is due to its bandwidth and power saving characteristics. In this paper, we present a new scheme for SSB signal generation which is cost efficient and enjoys superior characteristics in terms of frequency stability, selectivity, and robustness to noise. In the process, we develop novel Hilbert transform properties.
Keywords: Crystal filter, frequency drift, frequency mixing, Hilbert transform, phasing, selectivity, single side band AM.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1412348 An Incomplete Factorization Preconditioner for LMS Adaptive Filter
Authors: Shazia Javed, Noor Atinah Ahmad
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In this paper an efficient incomplete factorization preconditioner is proposed for the Least Mean Squares (LMS) adaptive filter. The proposed preconditioner is approximated from a priori knowledge of the factors of input correlation matrix with an incomplete strategy, motivated by the sparsity patter of the upper triangular factor in the QRD-RLS algorithm. The convergence properties of IPLMS algorithm are comparable with those of transform domain LMS(TDLMS) algorithm. Simulation results show efficiency and robustness of the proposed algorithm with reduced computational complexity.
Keywords: Autocorrelation matrix, Cholesky's factor, eigenvalue spread, Markov input.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1793347 Fuzzy Cost Support Vector Regression
Authors: Hadi Sadoghi Yazdi, Tahereh Royani, Mehri Sadoghi Yazdi, Sohrab Effati
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In this paper, a new version of support vector regression (SVR) is presented namely Fuzzy Cost SVR (FCSVR). Individual property of the FCSVR is operation over fuzzy data whereas fuzzy cost (fuzzy margin and fuzzy penalty) are maximized. This idea admits to have uncertainty in the penalty and margin terms jointly. Robustness against noise is shown in the experimental results as a property of the proposed method and superiority relative conventional SVR.
Keywords: Support vector regression, Fuzzy input, Fuzzy cost.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1372346 A Study on using N-Pattern Chains of Design Patterns based on Software Quality Metrics
Authors: Niloofar Khedri, Masoud Rahgozar, MahmoudReza Hashemi
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Design patterns describe good solutions to common and reoccurring problems in program design. Applying design patterns in software design and implementation have significant effects on software quality metrics such as flexibility, usability, reusability, scalability and robustness. There is no standard rule for using design patterns. There are some situations that a pattern is applied for a specific problem and this pattern uses another pattern. In this paper, we study the effect of using chain of patterns on software quality metrics.Keywords: Design Patterns, Design patterns' Relationship, Software quality Metrics, Software Engineering.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1578345 The Reliability of the Improved e-N Method for Transition Prediction as Checked by PSE Method
Authors: Caihong Su
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Transition prediction of boundary layers has always been an important problem in fluid mechanics both theoretically and practically, yet notwithstanding the great effort made by many investigators, there is no satisfactory answer to this problem. The most popular method available is so-called e-N method which is heavily dependent on experiments and experience. The author has proposed improvements to the e-N method, so to reduce its dependence on experiments and experience to a certain extent. One of the key assumptions is that transition would occur whenever the velocity amplitude of disturbance reaches 1-2% of the free stream velocity. However, the reliability of this assumption needs to be verified. In this paper, transition prediction on a flat plate is investigated by using both the improved e-N method and the parabolized stability equations (PSE) methods. The results show that the transition locations predicted by both methods agree reasonably well with each other, under the above assumption. For the supersonic case, the critical velocity amplitude in the improved e-N method should be taken as 0.013, whereas in the subsonic case, it should be 0.018, both are within the range 1-2%.Keywords: Boundary layer, e-N method, PSE, Transition
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1508344 Modeling and Control of Two Manipulators Handling a Flexible Beam
Authors: Amer S. Al-Yahmadi, T.C. Hsia
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This paper seeks to develop simple yet practical and efficient control scheme that enables cooperating arms to handle a flexible beam. Specifically the problem studied herein is that of two arms rigidly grasping a flexible beam and such capable of generating forces/moments in such away as to move a flexible beam along a predefined trajectory. The paper develops a sliding mode control law that provides robustness against model imperfection and uncertainty. It also provides an implicit stability proof. Simulation results for two three joint arms moving a flexible beam, are presented to validate the theoretical results.Keywords: Sliding mode control, cooperative manipulators.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1635343 A Robust Audio Fingerprinting Algorithm in MP3 Compressed Domain
Authors: Ruili Zhou, Yuesheng Zhu
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In this paper, a new robust audio fingerprinting algorithm in MP3 compressed domain is proposed with high robustness to time scale modification (TSM). Instead of simply employing short-term information of the MP3 stream, the new algorithm extracts the long-term features in MP3 compressed domain by using the modulation frequency analysis. Our experiment has demonstrated that the proposed method can achieve a hit rate of above 95% in audio retrieval and resist the attack of 20% TSM. It has lower bit error rate (BER) performance compared to the other algorithms. The proposed algorithm can also be used in other compressed domains, such as AAC.Keywords: Audio Fingerprinting, MP3, Modulation Frequency, TSM
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2196342 Software Digital Phase-locked Loop for Induction Motor Speed Control
Authors: Benmabrouk. Zaineb, Ben Hamed. Mouna, Lassad. Sbita
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This article deals to describe the simulation investigation of the digital phase locked loop implemented in software (SDPLL). SDPLL has been developed for speed drives of an induction motor in scalar strategy. A drive was implemented and simulation results are presented to verify the robustness against motor parameter variation and regulation speed.Keywords: Induction motor, Software Digital Phase LockedLoop, Speed control, Simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2525341 A Black-Box Approach in Modeling Valve Stiction
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Several valve stiction models have been proposed in the literature to help understand and study the behavior of sticky valves. In this paper, an alternative black-box modeling approach based on Neural Network (NN) is presented. It is shown that with proper network type and optimum model structures, the performance of the developed NN stiction model is comparable to other established method. The resulting NN model is also tested for its robustness against the uncertainty in the stiction parameter values. Predictive mode operation also shows excellent performance of the proposed model for multi-steps ahead prediction.
Keywords: Control valve stiction, neural network, modeling.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1606340 Conventional and Fuzzy Logic Controllers at Generator Location for Low Frequency Oscillation Damping
Authors: K. Prasertwong, N. Mithulananthan
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This paper investigates and compares performance of various conventional and fuzzy logic based controllers at generator locations for oscillation damping. Performance of combination of conventional and fuzzy logic based controllers also studied by comparing overshoot on the active power deviation response for a small disturbance and damping ratio of the critical mode. Fuzzy logic based controllers can not be modeled in the state space form to get the eigenvalues and corresponding damping ratios of various modes of generators and controllers. Hence, a new method based on tracing envelop of time domain waveform is also presented and used in the paper for comparing performance of controllers. The paper also shows that if the fuzzy based controllers designed separately combining them could not lead to a better performance.Keywords: Automatic voltage regulator, damping ratio, fuzzylogic controller, power system stabilizer.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2011339 A Blind Digital Watermark in Hadamard Domain
Authors: Saeid Saryazdi, Hossein Nezamabadi-pour
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A new blind gray-level watermarking scheme is described. In the proposed method, the host image is first divided into 4*4 non-overlapping blocks. For each block, two first AC coefficients of its Hadamard transform are then estimated using DC coefficients of its neighbor blocks. A gray-level watermark is then added into estimated values. Since embedding watermark does not change the DC coefficients, watermark extracting could be done by estimating AC coefficients and comparing them with their actual values. Several experiments are made and results suggest the robustness of the proposed algorithm.
Keywords: Digital Watermarking, Image watermarking, Information Hiden, Steganography.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2264338 Delay-Dependent H∞ Performance Analysis for Markovian Jump Systems with Time-Varying Delays
Authors: Yucai Ding, Hong Zhu, Shouming Zhong, Yuping Zhang
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This paper considers H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotical stability in mean square and a prescribed H∞ performance index for the considered systems. Two numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed main results. All these results are expected to be of use in the study of stochastic systems with time-varying delays.
Keywords: H∞ performance, Markovian switching, Delaydependent stability, Linear matrix inequality (LMI)
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