Search results for: feedforward control

Authors: Jin-Wei Liang, Hung-Yi Chen, Lung Lin

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In this paper feedforward controller is designed to eliminate nonlinear hysteresis behaviors of a piezoelectric stack actuator (PSA) driven system. The control design is based on inverse Prandtl-Ishlinskii (P-I) hysteresis model identified using particle swarm optimization (PSO) technique. Based on the identified P-I model, both the inverse P-I hysteresis model and feedforward controller can be determined. Experimental results obtained using the inverse P-I feedforward control are compared with their counterparts using hysteresis estimates obtained from the identified Bouc-Wen model. Effectiveness of the proposed feedforward control scheme is demonstrated. To improve control performance feedback compensation using traditional PID scheme is adopted to integrate with the feedforward controller.

Keywords: the Bouc-Wen hysteresis model, particle swarm optimization, Prandtl-Ishlinskii model, automation engineering

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Authors: U. Yavas, M. Gokasan

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Control of diesel engine’s air path has drawn a lot of attention due to its multi input-multi output, closed coupled, non-linear relation. Today, precise control of amount of air to be combusted is a must in order to meet with tight emission limits and performance targets. In this study, passenger car size diesel engine is modeled by AVL Boost RT, and then simulated with standard, industry level PID controllers. Finally, linear model predictive control is designed and simulated. This study shows the importance of modeling and control of diesel engines with flexible algorithm development in computer based systems.

Keywords: predictive control, engine control, engine modeling, PID control, feedforward compensation

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Authors: Rihab Hamdi, Amel Hadri Hamida, Fatiha Khelili, Sakina Zerouali, Ouafae Bennis

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This paper features a comparative study performance of sliding mode controller (SMC) for closed-loop voltage control of direct current to direct current (DC-DC) three-cells buck converter connected in parallel, operating in continuous conduction mode (CCM), based on pulse-width modulation (PWM) with SMC based on hysteresis modulation (HM) where an adaptive feedforward technique is adopted. On one hand, for the PWM-based SM, the approach is to incorporate a fixed-frequency PWM scheme which is effectively a variant of SM control. On the other hand, for the HM-based SM, oncoming an adaptive feedforward control that makes the hysteresis band variable in the hysteresis modulator of the SM controller in the aim to restrict the switching frequency variation in the case of any change of the line input voltage or output load variation are introduced. The results obtained under load change, input change and reference change clearly demonstrates a similar dynamic response of both proposed techniques, their effectiveness is fast and smooth tracking of the desired output voltage. The PWM-based SM technique has greatly improved the dynamic behavior with a bit advantageous compared to the HM-based SM technique, as well as provide stability in any operating conditions. Simulation studies in MATLAB/Simulink environment have been performed to verify the concept.

Keywords: DC-DC converter, hysteresis modulation, parallel multi-cells converter, pulse-width modulation, robustness, sliding mode control

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Authors: Natalia Espinosa, Arthur Amorim, Rudolf Huebner

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Epilepsy is a chronic neural disease and around 50 million people in the world suffer from this disease, however, in many cases, the individual acquires resistance to the medication, which is known as drug-resistant epilepsy, where a detection system is necessary. This paper showed the development of an automatic system for seizure detection based on artificial neural networks (ANN), which are common techniques of machine learning. Discrete Wavelet Transform (DWT) is used for decomposing electroencephalogram (EEG) signal into main brain waves, with these frequency bands is extracted features for training a feedforward neural network with backpropagation, finally made a pattern classification, seizure or non-seizure. Obtaining 95% accuracy in epileptic EEG and 100% in normal EEG.

Keywords: Artificial Neural Network (ANN), Discrete Wavelet Transform (DWT), Epilepsy Detection , Seizure.

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Authors: Yansong Zhang, Xueyuan Li, Junjie Zhou, Xufeng Yin, Shihua Yuan, Shuxian Liu

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Aiming at the verification of control algorithms for skid-steering vehicles, a vehicle simulation model of 6×6 electric skid-steering unmanned vehicle was established based on Trucksim and Simulink. The original transmission and steering mechanism of Trucksim are removed, and the electric skid-steering model and a closed-loop controller for the vehicle speed and yaw rate are built in Simulink. The simulation results are compared with the ones got by theoretical formulas. The results show that the predicted tire mechanics and vehicle kinematics of Trucksim-Simulink simulation model are closed to the theoretical results. Therefore, it can be used as an effective approach to study the dynamic performance and control algorithm of skid-steering vehicle. In this paper, a method of motion control based on feed forward control is also designed. The simulation results show that the feed forward control strategy can make the vehicle follow the target yaw rate more quickly and accurately, which makes the vehicle have more maneuverability.

Keywords: skid-steering, Trucksim-Simulink, feedforward control, dynamics

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Authors: Ashish Payal, C. S. Rai, B. V. R. Reddy

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With the increasing use and application of Wireless Sensor Networks (WSN), need has arisen to explore them in more effective and efficient manner. An important area which can bring efficiency to WSNs is the localization process, which refers to the estimation of the position of wireless sensor nodes in an ad hoc network setting, in reference to a coordinate system that may be internal or external to the network. In this paper, we have done comparison and analysed Sigmoidal Feedforward Artificial Neural Networks (SFFANNs) and Radial Basis Function (RBF) networks for developing localization framework in WSNs. The presented work utilizes the Received Signal Strength Indicator (RSSI), measured by static node on 100 x 100 m² grid from three anchor nodes. The comprehensive evaluation of these approaches is done using MATLAB software. The simulation results effectively demonstrate that FFANNs based sensor motes will show better localization accuracy as compared to RBF.

Keywords: localization, wireless sensor networks, artificial neural network, radial basis function, multi-layer perceptron, backpropagation, RSSI, GPS

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Authors: Hadi Rouhi Belvirdi, Davoud Beheshtizadeh

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The increasing demand for sustainable construction materials has led to a growing interest in high-strength recycled concrete (HSRC). Utilizing recycled materials not only reduces waste but also minimizes the depletion of natural resources. This study explores the application of artificial intelligence (AI) techniques to model and predict the properties of HSRC. In the past two decades, the production levels in various industries and, consequently, the amount of waste have increased significantly. Continuing this trend will undoubtedly cause irreparable damage to the environment. For this reason, engineers have been constantly seeking practical solutions for recycling industrial waste in recent years. This research utilized the results of the compressive strength of 90-day high-strength recycled concrete. The method for creating recycled concrete involved replacing sand with crushed glass and using glass powder instead of cement. Subsequently, a feedforward artificial neural network was employed to model the compressive strength results for 90 days. The regression and error values obtained indicate that this network is suitable for modeling the compressive strength data.

Keywords: high-strength recycled concrete, feedforward artificial neural network, regression, construction materials

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Authors: Oktay Nusratov, Ramin Rzaev, Aydin Goyushov

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Fuzzy inference method based approach to the forming of modular intellectual system of assessment the quality of communication services is proposed. Developed under this approach the basic fuzzy estimation model takes into account the recommendations of the International Telecommunication Union in respect of the operation of packet switching networks based on IP-protocol. To implement the main features and functions of the fuzzy control system of quality telecommunication services it is used multilayer feedforward neural network.

Keywords: quality of communication, IP-telephony, fuzzy set, fuzzy implication, neural network

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Authors: Musaab Mohammed Ahmed Ali, Vladimir Vodichev

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work deals with an universal control technique or single controller for linear and nonlinear stabilization and tracing control systems. These systems may be structured as SISO and MIMO. Parameters of controlled plants can vary over a wide range. Introduced a novel control systems design method, construction of stable platform orbits using derivative balance, solved transfer function stability preservation problem of linear system under partial substitution of a rational function. Universal controller is proposed as a polar system with the multiple orbits to simplify design procedure, where each orbit represent single order of controller transfer function. Designed controller consist of proportional, integral, derivative terms and multiple feedback and feedforward loops. The controller parameters synthesis method is presented. In generally, controller parameters depend on new polynomial equation where all parameters have a relationship with each other and have fixed values without requirements of retuning. The simulation results show that the proposed universal controller can stabilize infinity number of linear and nonlinear plants and shaping desired previously ordered performance. It has been proven that sensor errors and poor performance will be completely compensated and cannot affect system performance. Disturbances and noises effect on the controller loop will be fully rejected. Technical and economic effect of using proposed controller has been investigated and compared to adaptive, predictive, and robust controllers. The economic analysis shows the advantage of single controller with fixed parameters to drive infinity numbers of plants compared to above mentioned control techniques.

Keywords: derivative balance, fixed parameters, stable platform, universal control

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Authors: Muhammad A. Alsubaie, Mubarak K. H. Alhajri, Tarek S. Altowaim

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A repetitive controller designed to accommodate periodic disturbances via state feedback is discussed. Periodic disturbances can be represented by a time delay model in a positive feedback loop acting on system output. A direct use of the small gain theorem solves the periodic disturbances problem via 1) isolating the delay model, 2) finding the overall system representation around the delay model and 3) designing a feedback controller that assures overall system stability and tracking error convergence. This paper addresses uncertainty conditions for the repetitive controller designed in state feedback in either past error feedforward or current error feedback using singular values. The uncertainty investigation is based on the overall system found and the stability condition associated with it; depending on the scheme used, to set an upper/lower limit weighting parameter. This creates a region that should not be exceeded in selecting the weighting parameter which in turns assures performance improvement against system uncertainty. Repetitive control problem can be described in lifted form. This allows the usage of singular values principle in setting the range for the weighting parameter selection. The Simulation results obtained show a tracking error convergence against dynamic system perturbation if the weighting parameter chosen is within the range obtained. Simulation results also show the advantage of weighting parameter usage compared to the case where it is omitted.

Keywords: model mismatch, repetitive control, singular values, state feedback

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Authors: Oyebade K. Oyedotun

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The cardiotocogram is a technical recording of the heartbeat rate and uterine contractions of a fetus during pregnancy. During pregnancy, several complications can occur to both the mother and the fetus; hence it is very crucial that medical experts are able to find technical means to check the healthiness of the mother and especially the fetus. It is very important that the fetus develops as expected in stages during the pregnancy period; however, the task of monitoring the health status of the fetus is not that which is easily achieved as the fetus is not wholly physically available to medical experts for inspection. Hence, doctors have to resort to some other tests that can give an indication of the status of the fetus. One of such diagnostic test is to obtain cardiotocograms of the fetus. From the analysis of the cardiotocograms, medical experts can determine the status of the fetus, and therefore necessary medical interventions. Generally, medical experts classify examined cardiotocograms into ‘normal’, ‘suspect’, or ‘pathological’. This work presents an artificial neural network based decision support system which can filter cardiotocograms data, producing the corresponding statuses of the fetuses. The capability of artificial neural network to explore the cardiotocogram data and learn features that distinguish one class from the others has been exploited in this research. In this research, feedforward and radial basis neural networks were trained on a publicly available database to classify the processed cardiotocogram data into one of the three classes: ‘normal’, ‘suspect’, or ‘pathological’. Classification accuracies of 87.8% and 89.2% were achieved during the test phase of the trained network for the feedforward and radial basis neural networks respectively. It is the hope that while the system described in this work may not be a complete replacement for a medical expert in fetus status evaluation, it can significantly reinforce the confidence in medical diagnosis reached by experts.

Keywords: decision support, cardiotocogram, classification, neural networks

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Authors: M.Rüştü Karaman, İsmail İşeri, Kadir Saltalı, A.Reşit Brohi, Ayhan Horuz, Mümin Dizman

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Considerable relations has recently been given to the environmental hazardous caused by agricultural chemicals such as excess fertilizers. In this study, a neural network approach was investigated in the prediction of potential nitrate pollution across different land-use patterns by using a feedforward multilayered computer model of artificial neural network (ANN) with proper training. Periodical concentrations of some anions, especially nitrate (NO3-), and cations were also detected in drainage waters collected from the drain pipes placed in irrigated tomato field, unirrigated wheat field, fallow and pasture lands. The soil samples were collected from the irrigated tomato field and unirrigated wheat field on a grid system with 20 m x 20 m intervals. Site specific nitrate concentrations in the soil samples were measured for ANN based simulation of nitrate leaching potential from the land profiles. In the application of ANN model, a multi layered feedforward was evaluated, and data sets regarding with training, validation and testing containing the measured soil nitrate values were estimated based on spatial variability. As a result of the testing values, while the optimal structures of 2-15-1 was obtained (R2= 0.96, P < 0.01) for unirrigated field, the optimal structures of 2-10-1 was obtained (R2= 0.96, P < 0.01) for irrigated field. The results showed that the ANN model could be successfully used in prediction of the potential leaching levels of nitrate, based on different land use patterns. However, for the most suitable results, the model should be calibrated by training according to different NN structures depending on site specific soil parameters and varied agricultural managements.

Keywords: artificial intelligence, ANN, drainage water, nitrate pollution

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Authors: A. Oukaci, R. Toufouti, D. Dib, l. Atarsia

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This article presents a multitude of alternative techniques to control the vector control, namely the nonlinear control and sliding mode control. Moreover, the implementation of their control law applied to the high-performance to the induction motor with the objective to improve the tracking control, ensure stability robustness to parameter variations and disturbance rejection. Tests are performed numerical simulations in the Matlab/Simulink interface, the results demonstrate the efficiency and dynamic performance of the proposed strategy.

Keywords: Induction Motor (IM), Non-linear Control (NLC), Sliding Mode Control (SMC), nonlinear sliding surface

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Authors: Ying Li, Yan Li

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A new algorithm for single hidden layer feedforward neural networks (SLFN), Orthogonal Basis Extreme Learning (OBEL) algorithm, is proposed and the algorithm derivation is given in the paper. The algorithm can decide both the NNs parameters and the neuron number of hidden layer(s) during training while providing extreme fast learning speed. It will provide a practical way to develop NNs. The simulation results of function approximation showed that the algorithm is effective and feasible with good accuracy and adaptability.

Keywords: neural network, orthogonal basis extreme learning, function approximation

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Authors: S. Curteanu, F. Leon, M. Gavrilescu, S. A. Floria

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Optimization algorithms inspired from human behavior were applied in this approach, associated with neural networks models. The algorithms belong to human behaviors of learning and cooperation and human competitive behavior classes. For the first class, the main strategies include: random learning, individual learning, and social learning, and the selected algorithms are: simplified human learning optimization (SHLO), social learning optimization (SLO), and teaching-learning based optimization (TLBO). For the second class, the concept of learning is associated with competitiveness, and the selected algorithms are sports-inspired algorithms (with Football Game Algorithm, FGA and Volleyball Premier League, VPL) and Imperialist Competitive Algorithm (ICA). A real process, the synthesis of polyacrylamide-based multicomponent hydrogels, where some parameters are difficult to obtain experimentally, is considered as a case study. Reaction yield and swelling degree are predicted as a function of reaction conditions (acrylamide concentration, initiator concentration, crosslinking agent concentration, temperature, reaction time, and amount of inclusion polymer, which could be starch, poly(vinyl alcohol) or gelatin). The experimental results contain 175 data. Artificial neural networks are obtained in optimal form with biologically inspired algorithm; the optimization being perform at two level: structural and parametric. Feedforward neural networks with one or two hidden layers and no more than 25 neurons in intermediate layers were obtained with values of correlation coefficient in the validation phase over 0.90. The best results were obtained with TLBO algorithm, correlation coefficient being 0.94 for an MLP(6:9:20:2) – a feedforward neural network with two hidden layers and 9 and 20, respectively, intermediate neurons. Good results obtained prove the efficiency of the optimization algorithms. More than the good results, what is important in this approach is the simulation methodology, including neural networks and optimization biologically inspired algorithms, which provide satisfactory results. In addition, the methodology developed in this approach is general and has flexibility so that it can be easily adapted to other processes in association with different types of models.

Keywords: artificial neural networks, human behaviors of learning and cooperation, human competitive behavior, optimization algorithms

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Authors: Khalil Aghapouramin, Mostafa Ranjbar

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Run- to- Run (R2 R) control was developed in order to monitor and control different semiconductor manufacturing processes based upon the fundamental engineering frameworks. This technology allows rectification in the optimum direction. This control always had a significant potency in which was appeared in a variety of processes. The term run to run refers to the case where the act of control would take with the aim of getting batches of silicon wafers which produced in a manufacturing process. In the present work, a brief review about run-to-run control investigated which mainly is effective in the manufacturing process.

Keywords: Run-to-Run (R2R) control, manufacturing, process in engineering, manufacturing controls

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Authors: Luiz F. J. Maia

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This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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Authors: Khaing Yadana Swe, Lillie Dewan

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At present, the cascade PID control is widely used to control the super-heating temperature (main steam temperature). As the main steam temperature has the characteristics of large inertia, large time-delay, and time varying, etc., conventional PID control strategy can not achieve good control performance. In order to overcome the bad performance and deficiencies of main steam temperature control system, Model Free Adaptive Control (MFAC) P cascade control system is proposed in this paper. By substituting MFAC in PID of the main control loop of the main steam temperature control, it can overcome time delays, non-linearity, disturbance and time variation.

Keywords: model-free adaptive control, cascade control, adaptive control, PID

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

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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: Alia Abdul Ghaffar, Tom Richardson

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A model reference adaptive control and a fixed gain LQR control were implemented in the height controller of a quadrotor that has parametric uncertainties due to the act of picking up an object of unknown dimension and mass. It is shown that an adaptive control, unlike a fixed gain control, is capable of ensuring a stable tracking performance under such condition, although adaptive control suffers from several limitations. The combination of both adaptive and fixed gain control in the controller architecture results in an enhanced tracking performance in the presence of parametric uncertainties.

Keywords: UAV, quadrotor, robotic arm augmentation, model reference adaptive control, LQR control

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Authors: Zongyan Li, Matt Best

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This paper presents an optimization method for reducing the number of input channels and the complexity of the feed-forward NARX neural network (NN) without compromising the accuracy of the NN model. By utilizing the correlation analysis method, the most significant regressors are selected to form the input layer of the NN structure. An application of vehicle dynamic model identification is also presented in this paper to demonstrate the optimization technique and the optimal input layer structure and the optimal number of neurons for the neural network is investigated.

Keywords: correlation analysis, F-ratio, levenberg-marquardt, MSE, NARX, neural network, optimisation

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Authors: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

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Authors: Heung Sun Yoon, Jong Tae Kim

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In this paper, we present an activity diagram model for double-loop control self-adaptive braking system. Since activity diagram helps to improve visibility of self-adaption, we can easily find where improvement is needed on double-loop control. Double-loop control is adopted since the design conditions and actual conditions can be different. The system is reconfigured in runtime by using double-loop control. We simulated to verify and validate our model by using MATLAB. We compared single-loop control model with double-loop control model. Simulation results show that double-loop control provides more consistent brake power control than single-loop control.

Keywords: activity diagram, automotive, braking system, double-loop, self-adaptive, UML, vehicle

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Authors: Fouad Berrabah, Saad Salah, Zaamouche Fares

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In this paper, the Direct Torque Control (DTC) Control and the Sliding Mode Control for induction motor are presented and compared. The performance of the two control schemes is evaluated in terms of torque and current ripple, and transient response to variations of the torque , speed and robustness, trajectory tracking. In order to identify the more suitable solution for any application, both techniques are analyzed mathematically and simulation results are compared which advantages and drawbacks are discussed.

Keywords: induction motor, DTC- MRAS control, sliding mode control, robustness, trajectory tracking

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Authors: Sheng-Tse Wu, Wu-Sung Yao

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In this paper, a drift assist control system is proposed for remote control (RC) cars to get the perfect drift angle. A steering servo control scheme is given powerfully to assist the drift driving. A gyroscope sensor is included to detect the machine's tail sliding and to achieve a better automatic counter-steering to prevent RC car from spinning. To analysis tire traction and vehicle dynamics is used to obtain the dynamic track of RC cars. It comes with a control gain to adjust counter-steering amount according to the sensor condition. An illustrated example of 1:10 RC drift car is given and the real-time control algorithm is realized by Arduino Uno.

Keywords: drift assist control system, remote control cars, gyroscope, vehicle dynamics

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Authors: Othmane Boughazi, Abdelmadjid Boumedienne, Hachemi Glaoui

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This work treats the modeling and simulation of non-linear system behavior of an induction motor using backstepping sliding mode control. First, the direct field oriented control IM is derived. Then, a sliding for direct field oriented control is proposed to compensate the uncertainties, which occur in the control.Finally, the study of Backstepping sliding controls strategy of the induction motor drive. Our non linear system is simulated in MATLAB SIMULINK environment, the results obtained illustrate the efficiency of the proposed control with no overshoot, and the rising time is improved with good disturbances rejections comparing with the classical control law.

Keywords: induction motor, proportional-integral, sliding mode control, backstepping sliding mode control

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Authors: Chen-Fang Tsai, Shin-Li Lu

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Distribution-free control chart is an oncoming area from the statistical process control charts in recent years. Some researchers have developed various nonparametric control charts and investigated the detection capability of these charts. The major advantage of nonparametric control charts is that the underlying process is not specifically considered the assumption of normality or any parametric distribution. In this paper, two nonparametric exponentially weighted moving average (EWMA) control charts based on nonparametric tests, namely NE-S and NE-M control charts, are proposed for monitoring process variability. Generally, weighted moving average (GWMA) control charts are extended by utilizing design and adjustment parameters for monitoring the changes in the process variability, namely NG-S and NG-M control charts. Statistical performance is also investigated on NG-S and NG-M control charts with run rules. Moreover, sensitivity analysis is performed to show the effects of design parameters under the nonparametric NG-S and NG-M control charts.

Keywords: Distribution-free control chart, EWMA control charts, GWMA control charts

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Recently, crystal growth technologies have made progress by the requirement for the high quality of crystal materials. To control the crystal growth dynamics actively by external forces is useuful for reducing composition non-uniformity. In this study, a control method based on model predictive control using thermal inputs is proposed for crystal growth dynamics of semiconductor materials. The control system of crystal growth dynamics considered here is governed by the continuity, momentum, energy, and mass transport equations. To establish the control method for such thermal fluid systems, we adopt model predictive control known as a kind of optimal feedback control in which the control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. The objective of this study is to establish a model predictive control method for crystal growth dynamics of semiconductor materials.

Keywords: model predictive control, optimal control, process control, crystal growth

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Authors: S. Bangphan, P. Bangphan, T.Boonkang

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Quality control helps industries in improvements of its product quality and productivity. Statistical Process Control (SPC) is one of the tools to control the quality of products that turning practice in bringing a department of industrial engineering process under control. In this research, the process control of a turning manufactured at workshops machines. The varying measurements have been recorded for a number of samples of a rice polished cylinder obtained from a number of trials with the turning practice. SPC technique has been adopted by the process is finally brought under control and process capability is improved.

Keywords: rice polished cylinder, statistical process control, control charts, process capability

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Authors: Ran Etgar

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The process of rounding off measurements in continuous variables is commonly encountered. Although it usually has minor effects, sometimes it can lead to poor outcomes in statistical process control using X ̅-chart. The traditional control limits can cause incorrect conclusions if applied carelessly. This study looks into the limitations of classical control limits, particularly the impact of asymmetry. An approach to determining the distribution function of the measured parameter (Y ̅) is presented, resulting in a more precise method to establish the upper and lower control limits. The proposed method, while slightly more complex than Shewhart's original idea, is still user-friendly and accurate and only requires the use of two straightforward tables.

Keywords: quality control, process control, round-off, measurement, rounding error

Procedia PDF Downloads 100