Search results for: robust design.

Authors: Michal Polanský, C. Ardil

Abstract:

This paper shows a new method for design of fuzzy observers for Takagi-Sugeno systems. The method is based on Linear matrix inequalities (LMIs) and it allows to insert H constraint into the design procedure. The speed of estimation can tuned be specification of a decay rate of the observer closed loop system. We discuss here also the influence of parametric uncertainties at the output control system stability.

Keywords: H norm, Linear Matrix Inequalities, Observers, Takagi-Sugeno Systems, Parallel Distributed Compensation

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Authors: A. Abbasi Moshaii, M. Soltan Rezaee, M. Mohammadi Moghaddam

Abstract:

Control of some mechanisms is hard because of their complex dynamic equations. If part of the complexity is resulting from uncertainties, an efficient way for solving that is robust control. By this way, the control procedure could be simple and fast and finally, a simple controller can be designed. One kind of these mechanisms is 3-RRR which is a parallel mechanism and has three revolute joints. This paper aims to robust control a 3-RRR planner mechanism and it presents that this could be used for other mechanisms. So, a significant problem in mechanisms control could be solved. The relevant diagrams are drawn and they show the correctness of control process.

Keywords: 3-RRR, dynamic equations, mechanisms control, structural uncertainty.

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Authors: Charles Chikwendu Okpala, Christopher Chukwutoo Ihueze

Abstract:

As a technique that reduces variation in a product by lessening the sensitivity of the design to sources of variation, rather than by controlling their sources, Taguchi Robust Design entails the designing of ideal goods, by developing a product that has minimal variance in its characteristics and also meets the desired exact performance. This paper examined the concept of the manufacturing approach and its application to brake pad product of an automotive parts manufacturing company. Although the firm claimed that only defects, excess inventory, and over-production were the few wastes that grossly affect their productivity and profitability, a careful study and analysis of their manufacturing processes with the application of Single Minute Exchange of Dies (SMED) tool showed that the waste of waiting is the fourth waste that bedevils the firm. The selection of the Taguchi L9 orthogonal array which is based on the four parameters and the three levels of variation for each parameter revealed that with a range of 2.17, that waiting is the major waste that the company must reduce in order to continue to be viable. Also, to enhance the company’s throughput and profitability, the wastes of over-production, excess inventory, and defects with ranges of 2.01, 1.46, and 0.82, ranking second, third, and fourth respectively must also be reduced to the barest minimum. After proposing -33.84 as the highest optimum Signal-to-Noise ratio to be maintained for the waste of waiting, the paper advocated for the adoption of all the tools and techniques of Lean Production System (LPS), and Continuous Improvement (CI), and concluded by recommending SMED in order to drastically reduce set up time which leads to unnecessary waiting.

Keywords: Taguchi Robust Design, signal to noise ratio, Single Minute Exchange of Dies, lean production system, waste.

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Authors: S. Veera Ragavan, V. Ganapathy

Abstract:

Many environment specific methods and systems for Robot Navigation exist. However vast strides in the evolution of navigation technologies and system techniques create the need for a general unified framework that is scalable, modular and dynamic. In this paper a Unified Framework for a Robust Conflict-free Robot Navigation System that can be used for either a structured or unstructured and indoor or outdoor environments has been proposed. The fundamental design aspects and implementation issues encountered during the development of the module are discussed. The results of the deployment of three major peripheral modules of the framework namely the GSM based communication module, GIS Module and GPS module are reported in this paper.

Keywords: Localization, Sensor Fusion, Mapping, GIS, GPS, and Autonomous Mobile Robot Navigation.

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Authors: M. Almeshal, M. O. Tokhi, K. M. Goher

Abstract:

A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.

Keywords: double inverted pendulum, modelling, robust control, simulation,

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Authors: Riku Hayashida, Tomoaki Hashimoto

Abstract:

This paper provides a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. Underwater robots are expected to be used for various work assignments. The large variety of applications of underwater robots motivates researchers to develop control systems and technologies for underwater robots. Several control methods have been proposed so far for the stabilization of nominal system model of underwater robots with no parameter uncertainty. Parameter uncertainties are considered to be obstacles in implementation of the such nominal control methods for underwater robots. The objective of this study is to establish a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: Robust control, stabilization method, underwater robot, parameter uncertainty.

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Authors: Seungwoo Kim, Hyojune Chae, Yongrae Jung, Jongwook Kim

Abstract:

Recent medical studies have investigated the importance of enteral feeding and the use of feeding pumps for recovering patients unable to feed themselves or gain nourishment and nutrients by natural means. The most of enteral feeding system uses a peristaltic tube pump. A peristaltic pump is a form of positive displacement pump in which a flexible tube is progressively squeezed externally to allow the resulting enclosed pillow of fluid to progress along it. The squeezing of the tube requires a precise and robust controller of the geared motor to overcome parametric uncertainty of the pumping system which generates due to a wide variation of friction and slip between tube and roller. So, this paper proposes fuzzy adaptive controller for the robust control of the peristaltic tube pump. This new adaptive controller uses a fuzzy multi-layered architecture which has several independent fuzzy controllers in parallel, each with different robust stability area. Out of several independent fuzzy controllers, the most suited one is selected by a system identifier which observes variations in the controlled system parameter. This paper proposes a design procedure which can be carried out mathematically and systematically from the model of a controlled system. Finally, the good control performance, accurate dose rate and robust system stability, of the developed feeding pump is confirmed through experimental and clinic testing.

Keywords: Enteral Feeding Pump, Peristaltic Tube Pump, Fuzzy Adaptive Control, Fuzzy Multi-layered Controller, Look-up Table..

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Authors: Pulak Swain, A. K. Ojha

Abstract:

Portfolio optimization is based on dealing with the problems of efficient asset allocation. Risk and Expected return are two conflicting criteria in such problems, where the investor prefers the return to be high and the risk to be low. Using multi-objective approach we can solve those type of problems. However the information which we have for the input parameters are generally ambiguous and the input values can fluctuate around some nominal values. We can not ignore the uncertainty in input values, as they can affect the asset allocation drastically. So we use Robust Optimization approach to the problems where the input parameters comes under box uncertainty. In this paper, we solve the multi criteria robust problem with the help of  E- constraint method.

Keywords: Portfolio optimization, multi-objective optimization, E-constraint method, box uncertainty, robust optimization.

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Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

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

Abstract:

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: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

Abstract:

The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

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Authors: L. Khoshnevisan, H. R. Momeni, A. Ashraf-Modarres

Abstract:

One of the robust fault detection filter (RFDF) designing method is based on sliding-mode theory. The main purpose of our study is to introduce an innovative simplified reference residual model generator to formulate the RFDF as a sliding-mode observer without any manipulation package or transformation matrix, through which the generated residual signals can be evaluated. So the proposed design is more explicit and requires less design parameters in comparison with approaches requiring changing coordinates. To the best author's knowledge, this is the first time that the sliding mode technique is applied to detect actuator and sensor faults in a real boiler. The designing procedure is proposed in a drum boiler in Synvendska Kraft AB Plant in Malmo, Sweden as a multivariable and strongly coupled system. It is demonstrated that both sensor and actuator faults can robustly be detected. Also sensor faults can be diagnosed and isolated through this method.

Keywords: Boiler, fault detection, robustness, simplified sliding-mode observer.

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Authors: Jagadish H. Pujar, S. F. Kodad

Abstract:

Recent developments in Soft computing techniques, power electronic switches and low-cost computational hardware have made it possible to design and implement sophisticated control strategies for sensorless speed control of AC motor drives. Such an attempt has been made in this work, for Sensorless Speed Control of Induction Motor (IM) by means of Direct Torque Fuzzy Control (DTFC), PI-type fuzzy speed regulator and MRAS speed estimator strategy, which is absolutely nonlinear in its nature. Direct torque control is known to produce quick and robust response in AC drive system. However, during steady state, torque, flux and current ripple occurs. So, the performance of conventional DTC with PI speed regulator can be improved by implementing fuzzy logic techniques. Certain important issues in design including the space vector modulated (SVM) 3-Ф voltage source inverter, DTFC design, generation of reference torque using PI-type fuzzy speed regulator and sensor less speed estimator have been resolved. The proposed scheme is validated through extensive numerical simulations on MATLAB. The simulated results indicate the sensor less speed control of IM with DTFC and PI-type fuzzy speed regulator provides satisfactory high dynamic and static performance compare to conventional DTC with PI speed regulator.

Keywords: Sensor-less Speed Estimator, Fuzzy Logic Control(FLC), SVM, DTC, DTFC, IM, fuzzy speed regulator.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

In this paper, the robust exponential stability problem of uncertain discrete-time recurrent neural networks with timevarying delay is investigated. By constructing a new augmented Lyapunov-Krasovskii function, some new improved stability criteria are obtained in forms of linear matrix inequality (LMI). Compared with some recent results in literature, the conservatism of the new criteria is reduced notably. Two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neutral networks, time-varying delays.

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Authors: Feifei Lee, Qiu Chen, Koji Kotani, Tadahiro Ohmi

Abstract:

In this paper, we present an improved fast and robust search algorithm for copy detection using histogram-based features for short MPEG video clips from large video database. There are two types of histogram features used to generate more robust features. The first one is based on the adjacent pixel intensity difference quantization (APIDQ) algorithm, which had been reliably applied to human face recognition previously. An APIDQ histogram is utilized as the feature vector of the frame image. Another one is ordinal histogram feature which is robust to color distortion. Furthermore, by Combining with a temporal division method, the spatial and temporal features of the video sequence are integrated to realize fast and robust video search for copy detection. Experimental results show the proposed algorithm can detect the similar video clip more accurately and robust than conventional fast video search algorithm.

Keywords: Fast search, Copy detection, Adjacent pixel intensity difference quantization (APIDQ), DC image, Histogram feature.

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Authors: Mareli Hattingh, I. Jaco Van der Walt, Frans B. Waanders

Abstract:

A waste-to-energy plasma system was designed by Necsa for commercial use to create electricity from unsorted municipal waste. Fly ash particles must be removed from the syngas stream at operating temperatures of 1000 °C and recycled back into the reactor for complete combustion. A 2D2D high efficiency cyclone separator was chosen for this purpose. During this study, two cyclone design methods were explored: The Classic Empirical Method (smaller cyclone) and the Flow Characteristics Method (larger cyclone). These designs were optimized with regard to efficiency, so as to remove at minimum 90% of the fly ash particles of average size 10 μm by 50 μm. Wood was used as feed source at a concentration of 20 g/m³ syngas. The two designs were then compared at room temperature, using Perspex test units and three feed gases of different densities, namely nitrogen, helium and air. System conditions were imitated by adapting the gas feed velocity and particle load for each gas respectively. Helium, the least dense of the three gases, would simulate higher temperatures, whereas air, the densest gas, simulates a lower temperature. The average cyclone efficiencies ranged between 94.96% and 98.37%, reaching up to 99.89% in individual runs. The lowest efficiency attained was 94.00%. Furthermore, the design of the smaller cyclone proved to be more robust, while the larger cyclone demonstrated a stronger correlation between its separation efficiency and the feed temperatures. The larger cyclone can be assumed to achieve slightly higher efficiencies at elevated temperatures. However, both design methods led to good designs. At room temperature, the difference in efficiency between the two cyclones was almost negligible. At higher temperatures, however, these general tendencies are expected to be amplified so that the difference between the two design methods will become more obvious. Though the design specifications were met for both designs, the smaller cyclone is recommended as default particle separator for the plasma system due to its robust nature.

Keywords: Cyclone, design, plasma, renewable energy, solid separation, waste processing.

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Authors: M. Ahmadnezhad, M. Soltanpour

Abstract:

Electrohydraulic servo system have been used in industry in a wide number of applications. Its dynamics are highly nonlinear and also have large extent of model uncertainties and external disturbances. In this paper, a robust back-stepping control (RBSC) scheme is proposed to overcome the problem of disturbances and system uncertainties effectively and to improve the tracking performance of EHS systems. In order to implement the proposed control scheme, the system uncertainties in EHS systems are considered as total leakage coefficient and effective oil volume. In addition, in order to obtain the virtual controls for stabilizing system, the update rule for the system uncertainty term is induced by the Lyapunov control function (LCF). To verify the performance and robustness of the proposed control system, computer simulation of the proposed control system using Matlab/Simulink Software is executed. From the computer simulation, it was found that the RBSC system produces the desired tracking performance and has robustness to the disturbances and system uncertainties of EHS systems.

Keywords: Electro hydraulic servo system, back-stepping control, robust back-stepping control, Lyapunov redesign

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Authors: M. Ahmadnezhad, M. Soltanpour

Abstract:

Electrohydraulic servo system have been used in industry in a wide number of applications. Its dynamics are highly nonlinear and also have large extent of model uncertainties and external disturbances. In this paper, a robust back-stepping control (RBSC) scheme is proposed to overcome the problem of disturbances and system uncertainties effectively and to improve the tracking performance of EHS systems. In order to implement the proposed control scheme, the system uncertainties in EHS systems are considered as total leakage coefficient and effective oil volume. In addition, in order to obtain the virtual controls for stabilizing system, the update rule for the system uncertainty term is induced by the Lyapunov control function (LCF). To verify the performance and robustness of the proposed control system, computer simulation of the proposed control system using Matlab/Simulink Software is executed. From the computer simulation, it was found that the RBSC system produces the desired tracking performance and has robustness to the disturbances and system uncertainties of EHS systems.

Keywords: Electro hydraulic servo system, back-stepping control, robust back-stepping control, Lyapunov redesign.

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Authors: Ahtesham Javaid, Costin S. Bildea

Abstract:

The design and plantwide control of an integrated plant where the endothermic 1,4-butanediol dehydrogenation and the exothermic furfural hydrogenation is simultaneously performed in a single reactor is studied. The reactions can be carried out in an adiabatic reactor using small hydrogen excess and with reduced parameter sensitivity. The plant is robust and flexible enough to allow different production rates of γ-butyrolactone and 2-methyl furan, keeping high product purities. Rigorous steady state and dynamic simulations performed in AspenPlus and AspenDynamics to support the conclusions.

Keywords: Dehydrogenation and hydrogenation, Reaction coupling, Design and control, Process integration.

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Authors: J. Fernandez de Canete, S. Gonzalez-Perez, P. del Saz-Orozco, I. Garcia-Moral

Abstract:

Robust stability and performance are the two most basic features of feedback control systems. The harmonic balance analysis technique enables to analyze the stability of limit cycles arising from a neural network control based system operating over nonlinear plants. In this work a robust stability analysis based on the harmonic balance is presented and applied to a neural based control of a non-linear binary distillation column with unstructured uncertainty. We develop ways to describe uncertainty in the form of neglected nonlinear dynamics and high harmonics for the plant and controller respectively. Finally, conclusions about the performance of the neural control system are discussed using the Nyquist stability margin together with the structured singular values of the uncertainty as a robustness measure.

Keywords: Robust stability, neural network control, unstructured uncertainty, singular values, distillation column.

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Authors: Oscar Fernandez-Flores, Tony Speer, Rodney Day

Abstract:

This paper identifies five key design characteristics of production scheduling software systems in printed circuit board (PCB) manufacturing. The authors consider that, in addition to an effective scheduling engine, a scheduling system should be able to process a preventative maintenance calendar, to give the user the flexibility to handle data using a variety of electronic sources, to run simulations to support decision-making, and to have simple and customisable graphical user interfaces. These design considerations were the result of a review of academic literature, the evaluation of commercial applications and a compilation of requirements of a PCB manufacturer. It was found that, from those systems that were evaluated, those that effectively addressed all five characteristics outlined in this paper were the most robust of all and could be used in PCB manufacturing.

Keywords: Decision-making, ERP, PCB, scheduling.

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Authors: Hazem M. Al-Mofleh, John E. Daniels, Joseph W. McKean

Abstract:

In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates.

Keywords: Asymptotic relative efficiency, non-linear rank-based, robust, rank estimates, variogram.

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Authors: M. M. Fateh, A. Izadbakhsh

Abstract:

A robust control approach is proposed for a high speed manipulator using a hybrid computed torque control approach in the state space. The high-speed manipulator is driven by permanent magnet dc motors to track a trajectory in the joint space in the presence of disturbances. Tracking problem is analyzed in the state space where the completed models are considered for actuators. The proposed control approach can guarantee the stability and a satisfactory tracking performance. A two-link elbow manipulator driven by electrical actuators is simulated and results are shown to satisfy conditions under technical specifications.

Keywords: Computed torque, manipulator, robust control, state space.

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Authors: Sarah Odofin, Zhiwei Gao, Sun Kai

Abstract:

Operations, maintenance and reliability of wind turbines have received much attention over the years due to the rapid expansion of wind farms. This paper explores early fault diagnosis technique for a 5MW wind turbine system subjected to multiple faults, where genetic optimization algorithm is employed to make the residual sensitive to the faults, but robust against disturbances. The proposed technique has a potential to reduce the downtime mostly caused by the breakdown of components and exploit the productivity consistency by providing timely fault alarms. Simulation results show the effectiveness of the robust fault detection methods used under Matlab/Simulink/Gatool environment.

Keywords: Disturbance robustness, fault monitoring and detection, genetic algorithm and observer technique.

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Authors: G. Khamooshian

Abstract:

One of the main points of application of the mechanisms of the series and parallel is the subject of managing them. The control of this mechanism and similar mechanisms is one that has always been the intention of the scholars. On the other hand, modeling the behavior of the system is difficult due to the large number of its parameters, and it leads to complex equations that are difficult to solve and eventually difficult to control. In this paper, a six-linkage robot has been presented that could be used in different areas such as medical robots. Using these robots needs a robust control. In this paper, the system equations are first found, and then the system conversion function is written. A new controller has been designed for this robot which could be used in other parallel robots and could be very useful. Parallel robots are so important in robotics because of their stability, so methods for control of them are important and the robust controller, especially in parallel robots, makes a sense.

Keywords: 3-RRS, 6 linkage, parallel robot, control.

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Authors: Martin A. Smith, Xiaogang Chen

Abstract:

This paper proposes new algorithms for the computeraided design and manufacture (CAD/CAM) of 3D woven multi-layer textile structures. Existing commercial CAD/CAM systems are often restricted to the design and manufacture of 2D weaves. Those CAD/CAM systems that do support the design and manufacture of 3D multi-layer weaves are often limited to manual editing of design paper grids on the computer display and weave retrieval from stored archives. This complex design activity is time-consuming, tedious and error-prone and requires considerable experience and skill of a technical weaver. Recent research reported in the literature has addressed some of the shortcomings of commercial 3D multi-layer weave CAD/CAM systems. However, earlier research results have shown the need for further work on weave specification, weave generation, yarn path editing and layer binding. Analysis of 3D multi-layer weaves in this research has led to the design and development of efficient and robust algorithms for the CAD/CAM of 3D woven multi-layer textile structures. The resulting algorithmically generated weave designs can be used as a basis for lifting plans that can be loaded onto looms equipped with electronic shedding mechanisms for the CAM of 3D woven multi-layer textile structures.

Keywords: CAD/CAM, Multi-layer, Textile, Weave.

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Authors: Shu Lü, Shouming Zhong, Zixin Liu

Abstract:

In this paper, the robust exponential stability problem of discrete-time uncertain stochastic neural networks with timevarying delays is investigated. By introducing a new augmented Lyapunov function, some delay-dependent stable results are obtained in terms of linear matrix inequality (LMI) technique. Compared with some existing results in the literature, the conservatism of the new criteria is reduced notably. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neural networks, stochastic, time-varying delays.

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Authors: Bokyung Sung, Jungsoo Kim, Jinman Kwun, Junhyung Park, Jihye Ryeo, Ilju Ko

Abstract:

In this paper, we propose a practical digital music matching system that is robust to variation in sound qualities. The proposed system is subdivided into two parts: client and server. The client part consists of the input, preprocessing and feature extraction modules. The preprocessing module, including the music onset module, revises the value gap occurring on the time axis between identical songs of different formats. The proposed method uses delta-grouped Mel frequency cepstral coefficients (MFCCs) to extract music features that are robust to changes in sound quality. According to the number of sound quality formats (SQFs) used, a music server is constructed with a feature database (FD) that contains different sub feature databases (SFDs). When the proposed system receives a music file, the selection module selects an appropriate SFD from a feature database; the selected SFD is subsequently used by the matching module. In this study, we used 3,000 queries for matching experiments in three cases with different FDs. In each case, we used 1,000 queries constructed by mixing 8 SQFs and 125 songs. The success rate of music matching improved from 88.6% when using single a single SFD to 93.2% when using quadruple SFDs. By this experiment, we proved that the proposed method is robust to various sound qualities.

Keywords: Digital Music, Music Matching, Variation in Sound Qualities, Robust Matching method.

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Authors: Markus Reichhartinger, Martin Horn

Abstract:

In this paper, the application of sliding-mode control to a permanent-magnet synchronous motor (PMSM) is presented. The control design is based on a generic mathematical model of the motor. Some dynamics of the motor and of the power amplification stage remain unmodelled. This model uncertainty is estimated in realtime. The estimation is based on the differentiation of measured signals using the ideas of robust exact differentiator (RED). The control law is implemented on an industrial servo drive. Simulations and experimental results are presented and compared to the same control strategy without uncertainty estimation. It turns out that the proposed concept is superior to the same control strategy without uncertainty estimation especially in the case of non-smooth reference signals.

Keywords: sliding-mode control, Permanent-magnet synchronous motor, uncertainty estimation, robust exact differentiator.

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Authors: Azeddine Ghodbane, David Bensoussan, Maher Hammami

Abstract:

In this study, we introduce an alternative adaptive architecture that enhances both time and frequency performance, helpfully mitigating the effects of disturbances from the input plant and external disturbances affecting the output. To facilitate superior performance in both the time and frequency domains, we have developed a user-friendly interactive design methods using the GeoGebra platform.

Keywords: Control theory, decentralized control, sensitivity theory, input-output stability theory, robust multivariable feedback control design.

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