Search results for: Vector control
4341 Optimal Control Strategies for Speed Control of Permanent-Magnet Synchronous Motor Drives
Authors: Roozbeh Molavi, Davood A. Khaburi
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The permanent magnet synchronous motor (PMSM) is very useful in many applications. Vector control of PMSM is popular kind of its control. In this paper, at first an optimal vector control for PMSM is designed and then results are compared with conventional vector control. Then, it is assumed that the measurements are noisy and linear quadratic Gaussian (LQG) methodology is used to filter the noises. The results of noisy optimal vector control and filtered optimal vector control are compared to each other. Nonlinearity of PMSM and existence of inverter in its control circuit caused that the system is nonlinear and time-variant. With deriving average model, the system is changed to nonlinear time-invariant and then the nonlinear system is converted to linear system by linearization of model around average values. This model is used to optimize vector control then two optimal vector controls are compared to each other. Simulation results show that the performance and robustness to noise of the control system has been highly improved.Keywords: Kalman filter, Linear quadratic Gaussian (LQG), Linear quadratic regulator (LQR), Permanent-Magnet synchronousmotor (PMSM).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30004340 Space Vector PWM and Model Predictive Control for Voltage Source Inverter Control
Authors: Irtaza M. Syed, Kaamran Raahemifar
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In this paper, we present a comparative assessment of Space Vector Pulse Width Modulation (SVPWM) and Model Predictive Control (MPC) for two-level three phase (2L-3P) Voltage Source Inverter (VSI). VSI with associated system is subjected to both control techniques and the results are compared. Matlab/Simulink was used to model, simulate and validate the control schemes. Findings of this study show that MPC is superior to SVPWM in terms of total harmonic distortion (THD) and implementation.
Keywords: Model Predictive Control, Space Vector Pulse Width Modulation, Voltage Source Inverter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 45074339 Open-Loop Vector Control of Induction Motor with Space Vector Pulse Width Modulation Technique
Authors: Karchung, S. Ruangsinchaiwanich
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This paper presents open-loop vector control method of induction motor with space vector pulse width modulation (SVPWM) technique. Normally, the closed loop speed control is preferred and is believed to be more accurate. However, it requires a position sensor to track the rotor position which is not desirable to use it for certain workspace applications. This paper exhibits the performance of three-phase induction motor with the simplest control algorithm without the use of a position sensor nor an estimation block to estimate rotor position for sensorless control. The motor stator currents are measured and are transformed to synchronously rotating (d-q-axis) frame by use of Clarke and Park transformation. The actual control happens in this frame where the measured currents are compared with the reference currents. The error signal is fed to a conventional PI controller, and the corrected d-q voltage is generated. The controller outputs are transformed back to three phase voltages and are fed to SVPWM block which generates PWM signal for the voltage source inverter. The open loop vector control model along with SVPWM algorithm is modeled in MATLAB/Simulink software and is experimented and validated in TMS320F28335 DSP board.
Keywords: Electric drive, induction motor, open-loop vector control, space vector pulse width modulation technique.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 9424338 Vector Control of Multimotor Drive
Authors: Archana S. Nanoty, A. R. Chudasama
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Three-phase induction machines are today a standard for industrial electrical drives. Cost, reliability, robustness and maintenance free operation are among the reasons these machines are replacing dc drive systems. The development of power electronics and signal processing systems has eliminated one of the greatest disadvantages of such ac systems, which is the issue of control. With modern techniques of field oriented vector control, the task of variable speed control of induction machines is no longer a disadvantage. The need to increase system performance, particularly when facing limits on the power ratings of power supplies and semiconductors, motivates the use of phase number other than three, In this paper a novel scheme of connecting two, three phase induction motors in parallel fed by two inverters; viz. VSI and CSI and their vector control is presented.Keywords: Field oriented control, multiphase induction motor, power electronics converter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 33744337 Interpreting the Out-of-Control Signals of Multivariate Control Charts Employing Neural Networks
Authors: Francisco Aparisi, José Sanz
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Multivariate quality control charts show some advantages to monitor several variables in comparison with the simultaneous use of univariate charts, nevertheless, there are some disadvantages. The main problem is how to interpret the out-ofcontrol signal of a multivariate chart. For example, in the case of control charts designed to monitor the mean vector, the chart signals showing that it must be accepted that there is a shift in the vector, but no indication is given about the variables that have produced this shift. The MEWMA quality control chart is a very powerful scheme to detect small shifts in the mean vector. There are no previous specific works about the interpretation of the out-of-control signal of this chart. In this paper neural networks are designed to interpret the out-of-control signal of the MEWMA chart, and the percentage of correct classifications is studied for different cases.
Keywords: Multivariate quality control, Artificial Intelligence, Neural Networks, Computer Applications
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24904336 Discrete Vector Control for Induction Motor Drives with the Rotor Time Constant Update
Authors: A.Larabi, M.S. Boucherit
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In this paper, we investigated vector control of an induction machine taking into account discretization problems of the command. In the purpose to show how to include in a discrete model of this current control and with rotor time constant update. The results of simulation obtained are very satisfaisant. That was possible thanks to the good choice of the values of the parameters of the regulators used which shows, the founded good of the method used, for the choice of the parameters of the discrete regulators. The simulation results are presented at the end of this paper.
Keywords: Induction motor, discrete vector control, PIRegulator, transformation of park, PWM.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15044335 Optimal Space Vector Control for Permanent Magnet Synchronous Motor based on Nonrecursive Riccati Equation
Authors: Marian Gaiceanu, Emil Rosu
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In this paper the optimal control strategy for Permanent Magnet Synchronous Motor (PMSM) based drive system is presented. The designed full optimal control is available for speed operating range up to base speed. The optimal voltage space-vector assures input energy reduction and stator loss minimization, maintaining the output energy in the same limits with the conventional PMSM electrical drive. The optimal control with three components is based on the energetically criteria and it is applicable in numerical version, being a nonrecursive solution. The simulation results confirm the increased efficiency of the optimal PMSM drive. The properties of the optimal voltage space vector are shown.Keywords: Matlab/Simulink, optimal control, permanent magnet synchronous motor, Riccati equation, space vector PWM
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20154334 The Optimal Indirect Vector Controller Design via an Adaptive Tabu Search Algorithm
Authors: P. Sawatnatee, S. Udomsuk, K-N. Areerak, K-L. Areerak, A. Srikaew
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The paper presents how to design the indirect vector control of three-phase induction motor drive systems using the artificial intelligence technique called the adaptive tabu search. The results from the simulation and the experiment show that the drive system with the controller designed from the proposed method can provide the best output speed response compared with those of the conventional method. The controller design using the proposed technique can be used to create the software package for engineers to achieve the optimal controller design of the induction motor speed control based on the indirect vector concept.
Keywords: Indirect Vector Control, Induction Motor, Adaptive Tabu Search, Control Design, Artificial Intelligence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19224333 Support Vector Machines Approach for Detecting the Mean Shifts in Hotelling-s T2 Control Chart with Sensitizing Rules
Authors: Tai-Yue Wang, Hui-Min Chiang, Su-Ni Hsieh, Yu-Min Chiang
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In many industries, control charts is one of the most frequently used tools for quality management. Hotelling-s T2 is used widely in multivariate control chart. However, it has little defect when detecting small or medium process shifts. The use of supplementary sensitizing rules can improve the performance of detection. This study applied sensitizing rules for Hotelling-s T2 control chart to improve the performance of detection. Support vector machines (SVM) classifier to identify the characteristic or group of characteristics that are responsible for the signal and to classify the magnitude of the mean shifts. The experimental results demonstrate that the support vector machines (SVM) classifier can effectively identify the characteristic or group of characteristics that caused the process mean shifts and the magnitude of the shifts.Keywords: Hotelling's T2 control chart, Neural networks, Sensitizing rules, Support vector machines.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18664332 Maximum Wind Power Extraction Strategy and Decoupled Control of DFIG Operating in Variable Speed Wind Generation Systems
Authors: Abdellatif Kasbi, Abderrafii Rahali
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This paper appraises the performances of two control scenarios, for doubly fed induction generator (DFIG) operating in wind generation system (WGS), which are the direct decoupled control (DDC) and indirect decoupled control (IDC). Both control scenarios studied combines vector control and Maximum Power Point Tracking (MPPT) control theory so as to maximize the captured power through wind turbine. Modeling of DFIG based WGS and details of both control scenarios have been presented, a proportional integral controller is employed in the active and reactive power control loops for both control methods. The performance of the both control scenarios in terms of power reference tracking and robustness against machine parameters inconstancy has been shown, analyzed and compared, which can afford a reference to the operators and engineers of a wind farm. All simulations have been implemented via MATLAB/Simulink.
Keywords: DFIG, WGS, DDC, IDC, vector control, MPPT.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6954331 Fuzzy Logic Control for a Speed Control of Induction Motor using Space Vector Pulse Width Modulation
Authors: Satean Tunyasrirut, Tianchai Suksri, Sompong Srilad
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This paper presents design and implements a voltage source inverter type space vector pulse width modulation (SVPWM) for control a speed of induction motor. This scheme leads to be able to adjust the speed of the motor by control the frequency and amplitude of the stator voltage, the ratio of stator voltage to frequency should be kept constant. The fuzzy logic controller is also introduced to the system for keeping the motor speed to be constant when the load varies. The experimental results in testing the 0.22 kW induction motor from no-load condition to rated condition show the effectiveness of the proposed control scheme.Keywords: Fuzzy logic control, space vector pulse width modulation, induction motor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 29934330 Space-Vector PWM Inverter Feeding a Permanent-Magnet Synchronous Motor
Authors: A. Maamoun, Y. M. Alsayed, A. Shaltout
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The paper presents a space-vector pulse width modulation (SVPWM) inverter feeding a permanent-magnet synchronous motor (PMSM). The SVPWM inverter enables to feed the motor with a higher voltage with low harmonic distortions than the conventional sinusoidal PWM inverter. The control strategy of the inverter is the voltage / frequency control method, which is based on the space-vector modulation technique. The proposed PMSM drive system involving the field-oriented control scheme not only decouples the torque and flux which provides faster response but also makes the control task easy. The performance of the proposed drive is simulated. The advantages of the proposed drive are confirmed by the simulation results.
Keywords: permanent-magnet synchronous motor, space-vectorPWM inverter, voltage/frequency control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 66904329 Optimal Control Strategy for High Performance EV Interior Permanent Magnet Synchronous Motor
Authors: Mehdi Karbalaye Zadeh, Ehsan M. Siavashi
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The controllable electrical loss which consists of the copper loss and iron loss can be minimized by the optimal control of the armature current vector. The control algorithm of current vector minimizing the electrical loss is proposed and the optimal current vector can be decided according to the operating speed and the load conditions. The proposed control algorithm is applied to the experimental PM motor drive system and this paper presents a modern approach of speed control for permanent magnet synchronous motor (PMSM) applied for Electric Vehicle using a nonlinear control. The regulation algorithms are based on the feedback linearization technique. The direct component of the current is controlled to be zero which insures the maximum torque operation. The near unity power factor operation is also achieved. More over, among EV-s motor electric propulsion features, the energy efficiency is a basic characteristic that is influenced by vehicle dynamics and system architecture. For this reason, the EV dynamics are taken into account.Keywords: PMSM, Electric Vehicle, Optimal control, Traction.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17544328 Synthesis of a Control System of a Deterministic Chaotic Process in the Class of Two-Parameter Structurally Stable Mappings
Authors: M. Beisenbi, A. Sagymbay, S. Beisembina, A. Satpayeva
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In this paper, the problem of unstable and deterministic chaotic processes in control systems is considered. The synthesis of a control system in the class of two-parameter structurally stable mappings is demonstrated. This is realized via the gradient-velocity method of Lyapunov vector functions. It is shown that the gradient-velocity method of Lyapunov vector functions allows generating an aperiodic robust stable system with the desired characteristics. A simple solution to the problem of synthesis of control systems for unstable and deterministic chaotic processes is obtained. Moreover, it is applicable for complex systems.
Keywords: Control system synthesis, deterministic chaotic processes, Lyapunov vector function, robust stability, structurally stable mappings.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3634327 Fuzzy Logic Speed Control of Three Phase Induction Motor Drive
Authors: P.Tripura, Y.Srinivasa Kishore Babu
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This paper presents an intelligent speed control system based on fuzzy logic for a voltage source PWM inverter-fed indirect vector controlled induction motor drive. Traditional indirect vector control system of induction motor introduces conventional PI regulator in outer speed loop; it is proved that the low precision of the speed regulator debases the performance of the whole system. To overcome this problem, replacement of PI controller by an intelligent controller based on fuzzy set theory is proposed. The performance of the intelligent controller has been investigated through digital simulation using MATLAB-SIMULINK package for different operating conditions such as sudden change in reference speed and load torque. The simulation results demonstrate that the performance of the proposed controller is better than that of the conventional PI controller.Keywords: Fuzzy Logic, Intelligent controllers, Conventional PI controller, Induction motor drives, indirect vector control, Speed control
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 64804326 DTC-SVM Scheme for Induction Motors Fedwith a Three-level Inverter
Authors: Ehsan Hassankhan, Davood A. Khaburi
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Direct Torque Control is a control technique in AC drive systems to obtain high performance torque control. The conventional DTC drive contains a pair of hysteresis comparators. DTC drives utilizing hysteresis comparators suffer from high torque ripple and variable switching frequency. The most common solution to those problems is to use the space vector depends on the reference torque and flux. In this Paper The space vector modulation technique (SVPWM) is applied to 2 level inverter control in the proposed DTC-based induction motor drive system, thereby dramatically reducing the torque ripple. Then the controller based on space vector modulation is designed to be applied in the control of Induction Motor (IM) with a three-level Inverter. This type of Inverter has several advantages over the standard two-level VSI, such as a greater number of levels in the output voltage waveforms, Lower dV/dt, less harmonic distortion in voltage and current waveforms and lower switching frequencies. This paper proposes a general SVPWM algorithm for three-level based on standard two-level SVPWM. The proposed scheme is described clearly and simulation results are reported to demonstrate its effectiveness. The entire control scheme is implemented with Matlab/Simulink.Keywords: Direct torque control, space vector Pulsewidthmodulation(SVPWM), neutral point clamped(NPC), two-levelinverter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 43864325 Model Predictive Fuzzy Control of Air-ratio for Automotive Engines
Authors: Hang-cheong Wong, Pak-kin Wong, Chi-man Vong, Zhengchao Xie, Shaojia Huang
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Automotive engine air-ratio plays an important role of emissions and fuel consumption reduction while maintains satisfactory engine power among all of the engine control variables. In order to effectively control the air-ratio, this paper presents a model predictive fuzzy control algorithm based on online least-squares support vector machines prediction model and fuzzy logic optimizer. The proposed control algorithm was also implemented on a real car for testing and the results are highly satisfactory. Experimental results show that the proposed control algorithm can regulate the engine air-ratio to the stoichiometric value, 1.0, under external disturbance with less than 5% tolerance.Keywords: Air-ratio, Fuzzy logic, online least-squares support vector machine, model predictive control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17964324 Vector Control Using Series Iron Loss Model of Induction, Motors and Power Loss Minimization
Authors: Kheldoun Aissa, Khodja Djalal Eddine
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The iron loss is a source of detuning in vector controlled induction motor drives if the classical rotor vector controller is used for decoupling. In fact, the field orientation will not be satisfied and the output torque will not truck the reference torque mostly used by Loss Model Controllers (LMCs). In addition, this component of loss, among others, may be excessive if the vector controlled induction motor is driving light loads. In this paper, the series iron loss model is used to develop a vector controller immune to iron loss effect and then an LMC to minimize the total power loss using the torque generated by the speed controller.Keywords: Field Oriented Controller, Induction Motor, Loss ModelController, Series Iron Loss.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 26904323 Multi Switched Split Vector Quantizer
Authors: M. Satya Sai Ram, P. Siddaiah, M. Madhavi Latha
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Vector quantization is a powerful tool for speech coding applications. This paper deals with LPC Coding of speech signals which uses a new technique called Multi Switched Split Vector Quantization, This is a hybrid of two product code vector quantization techniques namely the Multi stage vector quantization technique, and Switched split vector quantization technique,. Multi Switched Split Vector Quantization technique quantizes the linear predictive coefficients in terms of line spectral frequencies. From results it is proved that Multi Switched Split Vector Quantization provides better trade off between bitrate and spectral distortion performance, computational complexity and memory requirements when compared to Switched Split Vector Quantization, Multi stage vector quantization, and Split Vector Quantization techniques. By employing the switching technique at each stage of the vector quantizer the spectral distortion, computational complexity and memory requirements were greatly reduced. Spectral distortion was measured in dB, Computational complexity was measured in floating point operations (flops), and memory requirements was measured in (floats).Keywords: Unconstrained vector quantization, Linear predictiveCoding, Split vector quantization, Multi stage vector quantization, Switched Split vector quantization, Line Spectral Frequencies.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17304322 Experimental Implementation of Model Predictive Control for Permanent Magnet Synchronous Motor
Authors: Abdelsalam A. Ahmed
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Fast speed drives for Permanent Magnet Synchronous Motor (PMSM) is a crucial performance for the electric traction systems. In this paper, PMSM is derived with a Model-based Predictive Control (MPC) technique. Fast speed tracking is achieved through optimization of the DC source utilization using MPC. The technique is based on predicting the optimum voltage vector applied to the driver. Control technique is investigated by comparing to the cascaded PI control based on Space Vector Pulse Width Modulation (SVPWM). MPC and SVPWM-based FOC are implemented with the TMS320F2812 DSP and its power driver circuits. The designed MPC for a PMSM drive is experimentally validated on a laboratory test bench. The performances are compared with those obtained by a conventional PI-based system in order to highlight the improvements, especially regarding speed tracking response.Keywords: Permanent magnet synchronous motor, mode predictive control, optimization of DC source utilization, cascaded PI control, space vector pulse width modulation, TMS320F2812 DSP.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 30874321 Self-Organizing Control Systems for Unstable and Deterministic Chaotic Processes
Authors: M. A. Beisenbi, N. M. Kissikova, S. E. Beisembina, S. T. Suleimenova, S. A. Kaliyeva
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The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector-functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.
Keywords: Gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4384320 ABURAS Index: A Statistically Developed Index for Dengue-Transmitting Vector Population Prediction
Authors: Hani M. Aburas
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“Dengue" is an African word meaning “bone breaking" because it causes severe joint and muscle pain that feels like bones are breaking. It is an infectious disease mainly transmitted by female mosquito, Aedes aegypti, and causes four serotypes of dengue viruses. In recent years, a dramatic increase in the dengue fever confirmed cases around the equator-s belt has been reported. Several conventional indices have been designed so far to monitor the transmitting vector populations known as House Index (HI), Container Index (CI), Breteau Index (BI). However, none of them describes the adult mosquito population size which is important to direct and guide comprehensive control strategy operations since number of infected people has a direct relationship with the vector density. Therefore, it is crucial to know the population size of the transmitting vector in order to design a suitable and effective control program. In this context, a study is carried out to report a new statistical index, ABURAS Index, using Poisson distribution based on the collection of vector population in Jeddah Governorate, Saudi Arabia.Keywords: Poisson distribution, statistical index, prediction, Aedes aegypti.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19064319 Performances Assessment of Direct Torque Controlled IM Drives Using Fuzzy Logic Control and Space Vector Modulation Strategy
Authors: L. Moussaoui, L. Rahmani
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This paper deals with the direct torque control (DTC) of the induction motor. This type of control allows decoupling control between the flux and the torque without the need for a transformation of coordinates. However, as with other hysteresis-based systems, the classical DTC scheme represents a high ripple, in both the electromagnetic torque and the stator flux and a distortion in the stator current. As well, it suffers from variable switching frequency. To solve these problems various modifications, in conventional DTC scheme, have been made during the last decade. Indeed the DTC based on space vector modulation (SVM) has proved to generate very low ripples in torque and flux with constant switching frequency. It also shows almost the same dynamic performances as the classical DTC system. On the other hand, fuzzy logic is considered as an interesting alternative approach for its advantages: Analysis close to the exigencies of user, ability of nonlinear systems control, best dynamic performances and inherent quality of robustness.
Therefore, two fuzzy direct torque control approaches, for the induction motor fed by SVM-voltage source inverter, are proposed in this paper. By using these two approaches of DTC, the advantages of fuzzy logic control, space vector modulation, and direct torque control method are combined. The performances of these DTC schemes are evaluated through digital simulation using Matlab/Simulink platform and fuzzy logic tools. Simulation results illustrate the effectiveness and the superiority of the proposed Fuzzy DTC-SVM schemes in comparison to the classical DTC.
Keywords: Direct torque control, Fuzzy logic control, Induction motor, Switching frequency, Space vector modulation, Torque and flux ripples.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23864318 Simplified Space Vector Based Decoupled Switching Strategy for Indirect Vector Controlled Open-End Winding Induction Motor Drive
Authors: Syed Munvar Ali, V. Vijaya Kumar Reddy, M. Surya Kalavathi
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In this paper, a dual inverter configuration has been implemented for induction motor drive. This isolated dual inverter is capable to produce high quality of output voltage and minimize common mode voltage (CMV). To this isolated dual inverter a decoupled space vector based pulse width modulation (PWM) technique is proposed. Conventional space vector based PWM (SVPWM) techniques require reference voltage vector calculation and sector identification. The proposed decoupled SVPWM technique generates gating pulses from instantaneous phase voltages and gives a CMV of ±vdc/6. To evaluate proposed algorithm MATLAB based simulation studies are carried on indirect vector controlled open end winding induction motor drive.Keywords: Inverter configuration, decoupled SVPWM, common mode voltage, vector control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7204317 Distribution Sampling of Vector Variance without Duplications
Authors: Erna T. Herdiani, Maman A. Djauhari
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In recent years, the use of vector variance as a measure of multivariate variability has received much attention in wide range of statistics. This paper deals with a more economic measure of multivariate variability, defined as vector variance minus all duplication elements. For high dimensional data, this will increase the computational efficiency almost 50 % compared to the original vector variance. Its sampling distribution will be investigated to make its applications possible.Keywords: Asymptotic distribution, covariance matrix, likelihood ratio test, vector variance.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15564316 An Optimal Control Problem for Rigid Body Motions on Lie Group SO(2, 1)
Authors: Nemat Abazari, Ilgin Sager
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In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.
Keywords: Optimal control, Hamiltonian vector field, Darboux vector, maximum principle, lie group, Rigid body motion, Lorentz metric.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13254315 Octonionic Reformulation of Vector Analysis
Authors: Bhupendra C. S. Chauhan, P. S. Bisht, O. P. S. Negi
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According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient, divergence and curl in seven dimension. It is shown that the identity n(n - 1)(n - 3)(n - 7) = 0 is satisfied only for 0, 1, 3 and 7 dimensional vectors. We have tried to write all the vector inequalities and formulas in terms of seven dimensions and it is shown that same formulas loose their meaning in seven dimensions due to non-associativity of octonions. The vector formulas are retained only if we put certain restrictions on octonions and split octonions.Keywords: Octonions, Vector Space and seven dimensions
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11914314 Planning Rigid Body Motions and Optimal Control Problem on Lie Group SO(2, 1)
Authors: Nemat Abazari, Ilgin Sager
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In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimizes the integral of the Lorentz inner product of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.
Keywords: Optimal control, Hamiltonian vector field, Darboux vector, maximum principle, lie group, rigid body motion, Lorentz metric.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15604313 Nonparametric Control Chart Using Density Weighted Support Vector Data Description
Authors: Myungraee Cha, Jun Seok Kim, Seung Hwan Park, Jun-Geol Baek
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In manufacturing industries, development of measurement leads to increase the number of monitoring variables and eventually the importance of multivariate control comes to the fore. Statistical process control (SPC) is one of the most widely used as multivariate control chart. Nevertheless, SPC is restricted to apply in processes because its assumption of data as following specific distribution. Unfortunately, process data are composed by the mixture of several processes and it is hard to estimate as one certain distribution. To alternative conventional SPC, therefore, nonparametric control chart come into the picture because of the strength of nonparametric control chart, the absence of parameter estimation. SVDD based control chart is one of the nonparametric control charts having the advantage of flexible control boundary. However,basic concept of SVDD has been an oversight to the important of data characteristic, density distribution. Therefore, we proposed DW-SVDD (Density Weighted SVDD) to cover up the weakness of conventional SVDD. DW-SVDD makes a new attempt to consider dense of data as introducing the notion of density Weight. We extend as control chart using new proposed SVDD and a simulation study of various distributional data is conducted to demonstrate the improvement of performance.
Keywords: Density estimation, Multivariate control chart, Oneclass classification, Support vector data description (SVDD)
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21104312 Position Vector of a Partially Null Curve Derived from a Vector Differential Equation
Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu
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In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.
Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1154