Search results for: Sustainable control

Authors: Sanjeeb Kumar Kar

Abstract:

The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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

Abstract:

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

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

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Authors: Shonal Singh, Bibhya Sharma, Jito Vanualailai

Abstract:

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

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

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Authors: Sushovan Sarkar, Debabrata Mazumder

Abstract:

Solid waste management in steel industry is broadly classified in “4 Rs” i.e. reduce, reuse, recycle and restore the materials. Reuse and recycling the entire solid waste generated in the process of steel making is a viable solution in targeting a clean, green and zero waste technology leading to sustainable development of the steel industry. Solid waste management has gained importance in steel industry in view of its uncertainty, volatility and speculation due to world competitive standards, rising input costs, scarcity of raw materials and solid waste generated like in other sectors. The challenges that the steel Industry faces today are the requirement of a sustainable development by meeting the needs of our present generation without compromising the ability of future generations. Technologies are developed not only for gainful utilization of solid wastes in manufacture of conventional products but also for conversion of same in to completely new products.

Keywords: Reuse, recycle, solid waste, sustainable development.

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Authors: Keivan Karimlou, Nemat Hassani, Abdollah Rashidi Mehrabadi

Abstract:

Climate change, industrial bloom, population growth and mismanagement are the most important factors that lead to water shortages around the world. Water shortages often lead to forced immigration, war, and thirst and hunger, especially in developing countries. One of the simplest solutions to solve the water shortage issues around the world is transferring water from one watershed to another; however it may not be a suitable solution. Water managers around the world use supply and demand management methods to decrease the incidence of water shortage in a sustainable manner. But as a matter of economic constraints, they must define a method to select the best possible action to reduce and limit water shortages. The following paper recognizes different kinds of criteria to select the best possible policy for reducing water shortage in mega cities by examining a comprehensive literature review.

Keywords: Criteria, management, shortage, sustainable, water.

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Authors: Li Jie, Zhang Wei

Abstract:

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

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

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

Abstract:

Neural networks offer an alternative approach both for identification and control of nonlinear processes in process engineering. The lack of software tools for the design of controllers based on neural network models is particularly pronounced in this field. SIMULINK is properly a widely used graphical code development environment which allows system-level developers to perform rapid prototyping and testing. Such graphical based programming environment involves block-based code development and offers a more intuitive approach to modeling and control task in a great variety of engineering disciplines. In this paper a SIMULINK based Neural Tool has been developed for analysis and design of multivariable neural based control systems. This tool has been applied to the control of a high purity distillation column including non linear hydrodynamic effects. The proposed control scheme offers an optimal response for both theoretical and practical challenges posed in process control task, in particular when both, the quality improvement of distillation products and the operation efficiency in economical terms are considered.

Keywords: Distillation, neural networks, software tools, identification, control.

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Authors: Tomoaki Hashimoto

Abstract:

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

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

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Authors: Nguyen Thi Thu Trang

Abstract:

Climate change and sea level rise is one of the greatest challenges facing human beings in the 21^st century. Because of sea level rise, several low-lying coastal areas around the globe are at risk of being completely submerged, disappearing under water. Particularly in Viet Nam, the rise in sea level is predicted to result in more frequent and even permanently inundated coastal plains. As a result, land reserving fund of coastal cities is going to be narrowed in near future, while construction ground is becoming increasingly limited due to a rapid growth in population. Faced with this reality, the solutions are being discussed not only in tradition view such as accommodation is raised or moved to higher areas, or “living with the water”, but also forwards to “living on the water”. Therefore, the concept of a sustainable floating community with floating houses based on the precious value of long term historical tradition of water dwellings in Viet Nam would be a sustainable solution for adaptation of climate change and sea level rise in the coastal areas. The sustainable floating community is comprised of sustainability in four components: architecture, environment, socio-economic and living quality. This research paper is focused on sustainability in architectural component of floating community. Through detailed architectural analysis of current floating houses and floating communities in Viet Nam, this research not only accumulates precious values of traditional architecture that need to be preserved and developed in the proposed concept, but also illustrates its weaknesses that need to address for optimal design of the future sustainable floating communities. Based on these studies the research would provide guidelines with appropriate architectural solutions for the concept of sustainable floating community with floating housing units that are adapted to climate change and sea level rise in Viet Nam.

Keywords: Climate change, floating houses, floating community, Viet Nam.

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

Abstract:

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

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

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Authors: Ismail Algelli Sassi Ehtiwesh, Željko Đurović

Abstract:

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

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

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Authors: 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: Hassan Baghgar Bostan Abad, Ali Yazdian Varjani, Taheri Asghar

Abstract:

Variable speed drives are growing and varying. Drives expanse depend on progress in different part of science like power system, microelectronic, control methods, and so on. Artificial intelligent contains hard computation and soft computation. Artificial intelligent has found high application in most nonlinear systems same as motors drive. Because it has intelligence like human but there are no sentimental against human like angriness and.... Artificial intelligent is used for various points like approximation, control, and monitoring. Because artificial intelligent techniques can use as controller for any system without requirement to system mathematical model, it has been used in electrical drive control. With this manner, efficiency and reliability of drives increase and volume, weight and cost of them decrease.

Keywords: Artificial intelligent, electrical motor, intelligent drive and control,

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Authors: Liu Ji-Wei, Pei Yu-Liang, Liu Qian, Han Xiang, Zeng De-Liang

Abstract:

The economic and stable operation was affected seriously by coal quality disturbance for power plants. Based on model analysis, influence of the disturbance can be considered as gain change of control system. Power capability coefficient of coal was constructed to inhibit it. Accuracy of the coefficient was verified by operating data. Then coal quality disturbance free system based on gain scheduling was designed for coordinated control system. Simulation showed that, the strategy improved control quality obviously, and inhibited the coal quality disturbance.

Keywords: coordinate control system, coal quality disturbance, energy coefficient of coal quality, gain scheduling

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Authors: Amir Hossein Daei Sorkhabi, Bita Khazini

Abstract:

In this paper the intelligent control of full automatic car wash using a programmable logic controller (PLC) has been investigated and designed to do all steps of carwashing. The Intelligent control of full automatic carwash has the ability to identify and profile the geometrical dimensions of the vehicle chassis. Vehicle dimension identification is an important point in this control system to adjust the washing brushes position and time duration. The study also tries to design a control set for simulating and building the automatic carwash. The main purpose of the simulation is to develop criteria for designing and building this type of carwash in actual size to overcome challenges of automation. The results of this research indicate that the proposed method in process control not only increases productivity, speed, accuracy and safety but also reduce the time and cost of washing based on dynamic model of the vehicle. A laboratory prototype based on an advanced intelligent control has been built to study the validity of the design and simulation which it’s appropriate performance confirms the validity of this study.

Keywords: Automatic Carwash, Dimension, PLC.

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Authors: Mehdi Karbalaye Zadeh, Ehsan M. Siavashi

Abstract:

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.

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Authors: S. A. Alotaibi, M. A. Al-Ajmi

Abstract:

This work introduces a new concept for controlling the mechanical vibrations via variable stiffness coil spring. The concept relies on fitting a screw though the spring to change the number of active spring coils. A prototype has been built and tested with promising results toward an innovation in the field of vibration control.

Keywords: Variable stiffness, coil spring, vibration control.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

In this paper a PID control strategy using neural network adaptive RASP1 wavelet for WECS-s control is proposed. It is based on single layer feedforward neural networks with hidden nodes of adaptive RASP1 wavelet functions controller and an infinite impulse response (IIR) recurrent structure. The IIR is combined by cascading to the network to provide double local structure resulting in improving speed of learning. This particular neuro PID controller assumes a certain model structure to approximately identify the system dynamics of the unknown plant (WECS-s) and generate the control signal. The results are applied to a typical turbine/generator pair, showing the feasibility of the proposed solution.

Keywords: Adaptive PID Control, RASP1 Wavelets, WindEnergy Conversion Systems.

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Authors: Hanan Rizk

Abstract:

Heat exchanger is a device used to mix liquids having different temperatures. In this case, the temperature control becomes a critical objective. This research work presents the temperature control of the double-pipe heat exchanger (multi-input multi-output (MIMO) system), which is modeled as first-order coupled hyperbolic partial differential equations (PDEs), using conventional and advanced control techniques, and develops appropriate robust control strategy to meet stability requirements and performance objectives. We designed the proportional–integral–derivative (PID) controller and H-infinity controller for a heat exchanger (HE) system. Frequency characteristics of sensitivity functions and open-loop and closed-loop time responses are simulated using MATLAB software and the stability of the system is analyzed using Kalman's test. The simulation results have demonstrated that the H-infinity controller is more efficient than PID in terms of robustness and performance.

Keywords: heat exchanger, multi-input multi-output system, MATLAB simulation, partial differential equations, PID controller, robust control

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Authors: Masataka Ohta

Abstract:

The Internet telephony employs a new type of Internet communication on which a mutual communication is realized by establishing sessions. Session Initiation Protocol (SIP) is used to establish sessions between end-users. For unreliable transmission (UDP), SIP message should be retransmitted when it is lost. The retransmissions increase a load of the SIP signaling network, and sometimes lead to performance degradation when a network is overloaded. The paper proposes an overload control for a SIP signaling network to protect from a performance degradation. Introducing two thresholds in a queue of a SIP proxy server, the SIP proxy server detects a congestion. Once congestion is detected, a SIP signaling network restricts to make new calls. The proposed overload control is evaluated using the network simulator (ns-2). With simulation results, the paper shows the proposed overload control works well.

Keywords: SIP signalling congestion overload control retransmission throughput simulation.

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Authors: Ismail Algelli Sassi Ehtiwesh, Mohamed Ali Elhaj

Abstract:

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

Keywords: Neural-Network controller, Mechatronic, electrohydraulic

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Authors: T. H. Lee, J. H. Park, S. M. Lee, S. C. Lee

Abstract:

In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of load current is the significant one of these for good performance of the SOFC system. In order to keep the constant stack terminal voltage by changing load current, the nonlinear model predictive control (MPC) is proposed in this paper. After primary control method is designed to guarantee the fuel utilization as a proper constant, a nonlinear model predictive control based on the Wiener model is developed to control the stack terminal voltage of the SOFC system. Simulation results verify the possibility of the proposed Wiener model and MPC method to control of SOFC system.

Keywords: SOFC, model predictive control, Wiener model.

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Authors: R. Nayak, T. Panwar, R. Padhye

Abstract:

Protective textiles get soiled, stained and even worn during their use, which may not be usable after a certain period due to the loss of protective performance. They need regular cleaning and maintenance, which helps to extend the durability of the clothing, retains their useful properties and ensures that fresh clothing is ready to wear when needed. Generally, the cleaning processes used for various protective clothing include dry-cleaning (using solvents) or wet cleaning (using water). These cleaning processes can alter the fabric surface properties, dimensions, and physical, mechanical and performance properties. The technology of laundering and dry-cleaning has undergone several changes. Sustainable methods and products are available for faster, safer and improved cleaning of protective textiles. We performed a comprehensive and systematic review of green technologies and eco-friendly products for sustainable cleaning of protective textiles. Special emphasis is given on the care and maintenance procedures of protective textiles for protection from fire, bullets, chemical and other types of protective clothing.

Keywords: Sustainable cleaning, protective textiles, eco-friendly cleaning, ozone laundering, ultrasonic cleaning.

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Authors: Chih-Jian Hu, Chung-Chih Cheng, Hsiao-Yuan Wu., Nien-Tzu Chao

Abstract:

Increasing user comfort and reducing operation costs have always been primary objectives of lighting control strategies in a building. This paper proposes an architecture of the lighting control system for a daylit office. The system consists of the lighting controller, A/D & D/A converter, dimmable LED lights, and the lighting management software. Verification tests are conducted using the proposed system specialized for the interior lighting of a open-plan office. The results showed the proposed architecture of the lighting system would improve the overall system reliability, lower the system cost, and provide ease of installation and maintenance.

Keywords: control, dimming, LED, lighting.

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Authors: Tharunika Sridhar

Abstract:

This paper addresses sustainable eco-connectivity within the telecommunications sector studying its importance to tackle the contemporary challenges and data regulation issues. The paper also investigates the role of Big Data and its integration in this context, specific to telecom industry. One of the major focus areas in this paper is studying and examining the pathways explored, that are state-of-the-art ecological infrastructure solutions and sector-led measures derived from expert analyses and reviews. Additionally, the paper analyses critical factors involving cost-effective route planning, and the development of green telecommunications infrastructure that adds qualitative reasoning to the research idea. Furthermore, the study discusses in detail a potential green roadmap towards sustainability by exploring green routing software, eco-friendly infrastructure and other eco-focused initiatives. The paper is also directed at the special linguistic needs of the telecommunications sector by focusing on targeted select range of telecom environment.

Keywords: Big Data, telecom, sustainable telecom sector, telecom networks.

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Authors: Juliana C. Alencar, Monica Ferreira do Amaral Porto

Abstract:

The blue-green infrastructure in recent years has been pointed out as a possibility to increase the environmental quality of watersheds. The regulation ecosystem services brought by these areas are many, such as the improvement of the air quality of the air, water, soil, microclimate, besides helping to control the peak flows and to promote the quality of life of the population. This study proposes a blue-green infrastructure scenario for the Jaguaré watershed, located in the western zone of the São Paulo city in Brazil. Based on the proposed scenario, it was verified the impact of the adoption of the blue and green infrastructure in the control of the peak flow of the basin, the benefits for the avifauna that are also reflected in the flora and finally, the quantification of the regulation ecosystem services brought by the adoption of the scenario proposed. A survey of existing green areas and potential areas for expansion and connection of these areas to form a network in the watershed was carried out. Based on this proposed new network of green areas, the peak flow for the proposed scenario was calculated with the help of software, ABC6. Finally, a survey of the ecosystem services contemplated in the proposed scenario was made. It was possible to conclude that the blue and green infrastructure would provide several regulation ecosystem services for the watershed, such as the control of the peak flow, the connection frame between the forest fragments that promoted the environmental enrichment of these fragments, improvement of the microclimate and the provision of leisure areas for the population.

Keywords: Blue and green infrastructure, sustainable drainage, urban waters, ecosystem services.

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Authors: Tae-Yeong Lee, Eun-Ju Yoo, Won-Yeong Choi, Young-Woo Park

Abstract:

This paper presents a 24 watts SEPIC converter design and control using microprocessor. SEPIC converter has advantages of a wide input range and miniaturization caused by the low stress at elements. There is also an advantage that the input and output are isolated in MOSFET-off state. This paper presents the PID control through the SEPIC converter transfer function using a DSP and the protective circuit for fuel cell from the over-current and inverse-voltage by using the characteristic of SEPIC converter. Then it derives them through the experiments.

Keywords: DC-DC Converter, Fuel-Cell, Microprocessor Control, Military Converter, SEPIC Converter

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Authors: M. Mohebbi, K. Shakeri

Abstract:

The effect of different combinations of response feedback on the performance of active control system on nonlinear frames has been studied in this paper. To this end different feedback combinations including displacement, velocity, acceleration and full response feedback have been utilized in controlling the response of an eight story bilinear hysteretic frame which has been subjected to a white noise excitation and controlled by eight actuators which could fully control the frame. For active control of nonlinear frame Newmark nonlinear instantaneous optimal control algorithm has been used which a diagonal matrix has been selected for weighting matrices in performance index. For optimal design of active control system while the objective has been to reduce the maximum drift to below the yielding level, Distributed Genetic Algorithm (DGA) has been used to determine the proper set of weighting matrices. The criteria to assess the effect of each combination of response feedback have been the minimum required control force to reduce the maximum drift to below the yielding drift. The results of numerical simulation show that the performance of active control system is dependent on the type of response feedback where the velocity feedback is more effective in designing optimal control system in comparison with displacement and acceleration feedback. Also using full feedback of response in controller design leads to minimum control force amongst other combinations. Also the distributed genetic algorithm shows acceptable convergence speed in solving the optimization problem of designing active control systems.

Keywords: Active control, Distributed genetic algorithms, Response feedback, Weighting matrices.

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Authors: A. Ramdane, F.Naceri, S. Ramdane

Abstract:

in this work, we present a new strategy of direct adaptive control denoted: Extended minimal controller synthesis (EMCS). This algorithm is designed for an induction motor, which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits. The main motivation of the EMCS control is to enhance the robustness of the MRAC algorithms, i.e. the rejection of bounded effects of rapidly varying external disturbances.

Keywords: Adaptive Control, Simple model reference adaptive control (SMRAC), Extended Minimal Controller synthesis (EMCS), Induction Motor (IM)

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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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