Search results for: PID/PD controllers

Authors: Seungchul Lee, Minjeong Kim, Iman Janghorban Esfahani, Jeong Tai Kim, ChangKyoo Yoo

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It is hard to maintain the effluent quality of the wastewater treatment plants (WWTPs) under with fixed types of operational control because of continuously changed influent flow rate and pollutant load. The aims of this study is development of multi-loop multi-objective control (ML-MOC) strategy in plant-wide scope targeting four objectives: 1) maximization of nutrient removal efficiency, 2) minimization of operational cost, 3) maximization of CH4 production in anaerobic digestion (AD) for CH4 reuse as a heat source and energy source, and 4) minimization of N2O gas emission to cope with global warming. First, benchmark simulation mode is modified to describe N2O dynamic in biological process, namely benchmark simulation model for greenhouse gases (BSM2G). Then, three types of single-loop proportional-integral (PI) controllers for DO controller, NO3 controller, and CH4 controller are implemented. Their optimal set-points of the controllers are found by using multi-objective genetic algorithm (MOGA). Finally, multi loop-MOC in BSM2G is implemented and evaluated in BSM2G. Compared with the reference case, the ML-MOC with the optimal set-points showed best control performances than references with improved performances of 34%, 5% and 79% of effluent quality, CH4 productivity, and N2O emission respectively, with the decrease of 65% in operational cost.

Keywords: Benchmark simulation model for greenhouse gas, multi-loop multi-objective controller, multi-objective genetic algorithm, wastewater treatment plant

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Authors: Mohamed Amine Haraoubia, Abdelaziz Hamzaoui, Najib Essounbouli

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The pursuit of the MPPT has led to the development of many kinds of controllers, one of which is the Fuzzy Logic Controller, which has proven its worth. To further tune this controller this paper will discuss and analyze the use of Genetic Algorithms to tune the Fuzzy Logic Controller. It will provide an introduction to both systems, and test their compatibility and performance.

Keywords: fuzzy logic controller, fuzzy logic, genetic algorithm, maximum power point, maximum power point tracking

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Authors: Adel Salem Bahakeem, Ahmad Jamal, Mir Md. Maruf Morshed, Elwaleed Awad Khidir

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Direct Current (DC) servo motors, or simply DC motors, play an important role in many industrial applications such as manufacturing of plastics, precise positioning of the equipment, and operating computer-controlled systems where speed of feed control, maintaining the position, and ensuring to have a constantly desired output is very critical. These parameters can be controlled with the help of control systems such as the Proportional Integral Derivative (PID) controller. The aim of the current work is to investigate the effects of Proportional (P) and Integral (I) controllers on the steady state and transient response of the DC motor. The controller gains are varied to observe their effects on the error, damping, and stability of the steady and transient motor response. The current investigation is conducted experimentally on a servo trainer CE 110 using analog PI controller CE 120 and theoretically using Simulink in MATLAB. Both experimental and theoretical work involves varying integral controller gain to obtain the response to a steady-state input, varying, individually, the proportional and integral controller gains to obtain the response to a step input function at a certain frequency, and theoretically obtaining the proportional and integral controller gains for desired values of damping ratio and response frequency. Results reveal that a proportional controller helps reduce the steady-state and transient error between the input signal and output response and makes the system more stable. In addition, it also speeds up the response of the system. On the other hand, the integral controller eliminates the error but tends to make the system unstable with induced oscillations and slow response to eliminate the error. From the current work, it is desired to achieve a stable response of the servo motor in terms of its angular velocity subjected to steady-state and transient input signals by utilizing the strengths of both P and I controllers.

Keywords: DC servo motor, proportional controller, integral controller, controller gain optimization, Simulink

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Authors: Cesar A. Nava-Gaxiola, C. Barrado

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Harmonized with SESAR (Single European Sky Research) initiatives, a new concept related with airspace structures have been introduced in Europe, the Free Route Airspace. The key of free route is based in an airspace where users may freely plan a route between a defined entry and exit waypoint, with the possibility of routing via intermediate points, the free route flights remain subject to air traffic control (ATC) for the established separations. Free route airspace does not present anymore fixed airways to airspace users, as a consequence it brings a new paradigm for managing safe separations of aircrafts inside these airspace blocks . Nowadays, several European nations have been introduced the concept, some of them in a complete or partial stage, but finally offering limited benefits to airspace users for this condition. This research evaluates the future scenario of free route implementation across Europe, considering a unique airspace block configuration with a complete upper airspace with free route. The paper is centered in investigating the benefits for airspace users, and the study of possible increments of Air Traffic Controllers task loads with a full application. In this research, fast time simulations are carrying out for discovering how much flight time and distance aircrafts can save with an overall free route establishment. In the other side, the paper explains the evolution of conflicts derivate from possible separation losses between aircrafts in this new environment. Free route conflicts can emerges in any points of the airspace, requiring a great effort for solving it, in comparison with fixed airways, where conflicts normally were found by controllers in known waypoints, and they solved using the fixed network as reference. The airspace configuration modelled in this study take into account the actual navigation waypoints structure, moving into a future scenario, where new ones waypoints are added and new traffic flow patterns appears. In this sense, this research explores the advantages and unknown difficulties that a large scale application of free route concept can carry out in the European airspace.

Keywords: ATC conflicts, efficiency, free route airspace, SESAR

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Authors: Jorge Rodriguez-Guerra, Carlos Calleja, Aron Pujana, Iker Elorza, Ana Maria Macarulla

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Society demands more reliable manufacturing processes capable of producing high quality products in shorter production cycles. New control algorithms have been studied to satisfy this paradigm, in which Fault-Tolerant Control (FTC) plays a significant role. It is suitable to detect, isolate and adapt a system when a harmful or faulty situation appears. In this paper, a general overview about FTC characteristics are exposed; highlighting the properties a system must ensure to be considered faultless. In addition, a research to identify which are the main FTC techniques and a classification based on their characteristics is presented in two main groups: Active Fault-Tolerant Controllers (AFTCs) and Passive Fault-Tolerant Controllers (PFTCs). AFTC encompasses the techniques capable of re-configuring the process control algorithm after the fault has been detected, while PFTC comprehends the algorithms robust enough to bypass the fault without further modifications. The mentioned re-configuration requires two stages, one focused on detection, isolation and identification of the fault source and the other one in charge of re-designing the control algorithm by two approaches: fault accommodation and control re-design. From the algorithms studied, one has been selected and applied to a case study based on an industrial hydraulic-press. The developed model has been embedded under a real-time validation platform, which allows testing the FTC algorithms and analyse how the system will respond when a fault arises in similar conditions as a machine will have on factory. One AFTC approach has been picked up as the methodology the system will follow in the fault recovery process. In a first instance, the fault will be detected, isolated and identified by means of a neural network. In a second instance, the control algorithm will be re-configured to overcome the fault and continue working without human interaction.

Keywords: fault-tolerant control, electro-hydraulic actuator, fault detection and isolation, control re-design, real-time

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Authors: Graziano Chesi

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The topological entropy plays a key role in linear dynamical systems, allowing one to establish the existence of stabilizing feedback controllers for linear systems in the presence of communications constraints. This paper addresses the determination of a robust value of the topological entropy in nonlinear dynamical systems, specifically the largest value of the topological entropy over all linearized models in a region of interest of the state space. It is shown that a sufficient condition for establishing upper bounds of the sought robust value of the topological entropy can be given in terms of a semidefinite program (SDP), which belongs to the class of convex optimization problems.

Keywords: non-linear system, communication constraint, topological entropy

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Authors: Jaydip M. Desai, Antonio Valdevit, Arthur Ritter

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Robotic surgery is used to enhance minimally invasive surgical procedure. It provides greater degree of freedom for surgical tools but lacks of haptic feedback system to provide sense of touch to the surgeon. Surgical robots work on master-slave operation, where user is a master and robotic arms are the slaves. Current, surgical robots provide precise control of the surgical tools, but heavily rely on visual feedback, which sometimes cause damage to the inner organs. The goal of this research was to design and develop a real-time simulink based robotic system to study force feedback mechanism during instrument-object interaction. Setup includes three Velmex XSlide assembly (XYZ Stage) for three dimensional movement, an end effector assembly for forceps, electronic circuit for four strain gages, two Novint Falcon 3D gaming controllers, microcontroller board with linear actuators, MATLAB and Simulink toolboxes. Strain gages were calibrated using Imada Digital Force Gauge device and tested with a hard-core wire to measure instrument-object interaction in the range of 0-35N. Designed simulink model successfully acquires 3D coordinates from two Novint Falcon controllers and transfer coordinates to the XYZ stage and forceps. Simulink model also reads strain gages signal through 10-bit analog to digital converter resolution of a microcontroller assembly in real time, converts voltage into force and feedback the output signals to the Novint Falcon controller for force feedback mechanism. Experimental setup allows user to change forward kinematics algorithms to achieve the best-desired movement of the XYZ stage and forceps. This project combines haptic technology with surgical robot to provide sense of touch to the user controlling forceps through machine-computer interface.

Keywords: surgical robot, haptic feedback, MATLAB, strain gage, simulink

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Authors: Mujde Turkkan, Nurkan Yagiz

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The vibrations, caused by the irregularities of the road surface, are to be suppressed via suspension systems. In this paper, sliding mode control for a half bus model with air suspension system is presented. The bus is modelled as five degrees of freedom (DoF) system. The mathematical model of the half bus is developed using Lagrange Equations. For time domain analysis, the bus model is assumed to travel at certain speed over the bump road. The numerical results of the analysis indicate that the sliding mode controllers can be effectively used to suppress the vibrations and to improve the ride comfort of the busses.

Keywords: active suspension system, air suspension, bus model, sliding mode control

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Authors: Tesfaye Alamirew Dessie

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Our study focuses on developing a Model Predictive Controller (MPC) and evaluating it against a traditional PID for a pasteurization process. Utilizing system identification from the experimental data, the dynamics of the pasteurization process were calculated. Using best fit with data validation, residual, and stability analysis, the quality of several model architectures was evaluated. The validation data fit the auto-regressive with exogenous input (ARX322) model of the pasteurization process by roughly 80.37 percent. The ARX322 model structure was used to create MPC and PID control techniques. After comparing controller performance based on settling time, overshoot percentage, and stability analysis, it was found that MPC controllers outperform PID for those parameters.

Keywords: MPC, PID, ARX, pasteurization

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Authors: Wesam Jasim, Dongbing Gu

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This paper presents an iterative linear quadratic regulator optimal control technique to solve the problem of quadrotors path tracking. The dynamic motion equations are represented based on unit quaternion representation and include some modelled aerodynamical effects as a nonlinear part. Simulation results prove the ability and effectiveness of iLQR to stabilize the quadrotor and successfully track different paths. It also shows that iLQR controller outperforms LQR controller in terms of fast convergence and tracking errors.

Keywords: iLQR controller, optimal control, path tracking, quadrotor UAVs

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Authors: Hajara Abdulkarim Aliyu, Abdulbasid Ismail Isa

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This research paper studies electrohydraulic system for its role in position and motion control system and develops as mathematical model describing the behaviour of the system. The research further proposes Fuzzy logic and conventional PID controllers in order to achieve both accurate positioning of the payload and overall improvement of the system performance. The simulation result shows Fuzzy logic controller has a superior tracking performance and high disturbance rejection efficiency for its shorter settling time, less overshoot, smaller values of integral of absolute and deviation errors over the conventional PID controller at all the testing conditions.

Keywords: electrohydraulic, fuzzy logic, modelling, NZ-PID

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Authors: H. Tédjini, Y. Meslem, B. Guesbaoui, A. Safa

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Flexible AC Transmission Systems (FACTS) are potentially becoming more flexible and more economical local controllers in the power system; and because of the high MVA ratings, it would be expensive to provide independent, equal, regulated DC voltage sources to power the multilevel converters which are presently proposed for STATCOMs. DC voltage sources can be derived from the DC link capacitances which are charged by the rectified ac power. In this paper a new stronger control combined of nonlinear control based Lyapunov’s theorem and Ant Colony Algorithm (ACA) to maintain stability of multilevel STATCOM and the utility.

Keywords: Static Compensator (STATCOM), ant colony optimization (ACO), lyapunov control theory, Decoupled power control, neutral point clamped (NPC)

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Authors: Tatipamula Samiksha Goud, .A.Naveena, M.sresta

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Traffic congestion is a major issue in many cities throughout the world, particularly in urban areas, and it is past time to switch from a fixed timer mode to an automated system. The current traffic signalling system is a fixed-time system that is inefficient if one lane is more functional than the others. A structure for an intelligent traffic control system is being designed to address this issue. When traffic density is higher on one side of a junction, the signal's green time is extended in comparison to the regular time. This study suggests a technique in which the signal's time duration is assigned based on the amount of traffic present at the time. Infrared sensors can be used to do this.

Keywords: infrared sensors, micro-controllers, LEDs, oscillators

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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: H. E. Keshta, A. A. Ali

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Three phase grid-tied inverters are widely employed in micro-grids (MGs) as interphase between DC and AC systems. These inverters are usually controlled through standard decoupled d–q vector control strategy based on proportional integral (PI) controllers. Recently, advanced meta-heuristic optimization techniques have been used instead of deterministic methods to obtain optimum PI controller parameters. This paper provides a comparative study between the performance of the global Porcellio Scaber algorithm (GPSA) based PI controller and Manta Ray foraging optimization (MRFO) based PI controller.

Keywords: micro-grids, optimization techniques, grid-tied inverter control, PI controller

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Authors: Iyai Davies, Olivier L. C. Haas

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In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability

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Authors: Mohammad Reza Rahimi Khoygani, Reza Ghasemi

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In this paper, designing direct adaptive neural controller is applied for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) is used for the Neural network (NN). The adaptive neural controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are the merits of this paper. The promising performance of the proposed controllers investigates in simulation results.

Keywords: adaptive control, pendulum dynamical system, nonlinear control, adaptive neural controller, nonlinear dynamical, neural network, RBF, driven pendulum, position control

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Authors: Reyhane Hamed Kamran

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Early stage morphogenesis requires the execution of complex systems that direct the nearby conduct of gatherings of cells. The organization of such instruments has been, for the most part, deciphered through the recognizable proof of moderated groups of flagging pathways that spatially and transiently control cell conduct. In any case, how this data is handled to control cell shape and cell elements is an open territory of examination. The structure that rises up out of differing controls, for example, cell science, material science, and formative science, focuses to bond and cortical actin arranges as controllers of cell surface mechanics. In this specific circumstance, a scope of formative marvels can be clarified by the guideline of cell surface pressure.

Keywords: cell, tissue damage, morphogenesis, cell conduct

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Authors: Narin Salehiyan

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Early stage morphogenesis requires the execution of complex systems that direct the nearby conduct of gatherings of cells. The organization of such instruments has been, for the most part, deciphered through the recognizable proof of moderated groups of flagging pathways that spatially and transiently control cell conduct. In any case, how this data is handled to control cell shape and cell elements is an open territory of examination. The structure that rises up out of differing controls, for example, cell science, material science and formative science, focuses to bond and cortical actin arranges as controllers of cell surface mechanics. In this specific circumstance, a scope of formative marvels can be clarified by the guideline of cell surface pressure.

Keywords: cell, tissue damage, morphogenesis, cell conduct

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Authors: S. M. Yasir Arafat

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Driving models are needed by many researchers to improve traffic safety and to advance autonomous vehicle design. To be most useful, a driving model must state specifically what information is needed and how it is processed. So we developed an “Obstacle Avoidance and Detection Autonomous Car” based on sensor application. The ever increasing technological demands of today call for very complex systems, which in turn require highly sophisticated controllers to ensure that high performance can be achieved and maintained under adverse conditions. Based on a developed model of brakes operation, the controller of braking system operation has been designed. It has a task to enable solution to the problem of the better controlling of braking system operation in a more accurate way then it was the case now a day.

Keywords: automobile, obstacle, safety, sensing

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Authors: Ghania Zidani, Said Drid, Larbi Chrifi-Alaoui, Abdeslam Benmakhlouf, Souad Chaouch

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In this paper, we focus on the study for path tracking control of unicycle-type Wheeled Mobile Robots (WMR), by applying the Backstepping technic. The latter is a relatively new technic for nonlinear systems. To solve the problem of constraints nonholonomics met in the path tracking of such robots, an adaptive Backstepping based nonlinear controller is developed. The stability of the controller is guaranteed, using the Lyapunov theory. Simulation results show that the proposed controller achieves the objective and ensures good path tracking.

Keywords: Backstepping control, kinematic and dynamic controllers, Lyapunov methods, nonlinear control systems, Wheeled Mobile Robot (WMR).

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Authors: Abdelhalim Kessal

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This paper treats a design of combined control of a single phase power factor correction (PFC). The strategy of the proposed control is based on two parts, the first, for the outer loop (DC output regulated voltage), and the second govern the input current of the converter in order to achieve a sinusoidal form in phase with the grid voltage. Two kinds of regulators are used, Fuzzy controller for the outer loop and predictive controller for the inner loop. The controllers are verified and discussed through simulation under MATLAB/Simulink platform. Also an experimental confirmation is applied. Results present a high dynamic performance under various parameters changes.

Keywords: boost converter, harmonic distortion, Fuzzy, predictive, unity power factor

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Authors: H. Shahid

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Due to Ozone layer depletion on earth, the incoming ultraviolet (UV) radiation is recorded at its high index levels such as 25 in South Peru (13.5° S, 3360 m a.s.l.) Also, the planning of human inhabitation on Mars is under discussion where UV radiations are quite high. The exposure to UV is health hazardous and is avoided by UV filters. On the other hand, artificial UV sources are in use for water thermolysis to generate Hydrogen and Oxygen, which are later used as fuels. This paper presents the utility of employing UVA (315-400nm) and UVB (280-315nm) electromagnetic radiation from the solar spectrum to design and implement an optically active, Hydrogen and Oxygen generation system via thermolysis of desalinated seawater. The proposed system finds its utility on earth and can be deployed in the future on Mars (UVB). In this system, by using Fresnel lens arrays as an optical filter and via active tracking, the ultraviolet light from the sun is concentrated and then allowed to fall on two sub-systems of the proposed system. The first sub-system generates electrical energy by using UV based tandem photovoltaic cells such as GaAs/GaInP/GaInAs/GaInAsP and the second elevates temperature of water to lower the electric potential required to electrolyze the water. An empirical analysis is performed at 30 atm and an electrical potential is observed to be the main controlling factor for the rate of production of Hydrogen and Oxygen and hence the operating point (Q-Point) of the proposed system. The hydrogen production rate in the case of the commercial system in static mode (650ᵒC, 0.6V) is taken as a reference. The silicon oxide electrolyzer cell (SOEC) is used in the proposed (UV) system for the Hydrogen and Oxygen production. To achieve the same amount of Hydrogen as in the case of the reference system, with minimum chamber operating temperature of 850ᵒC in static mode, the corresponding required electrical potential is calculated as 0.3V. However, practically, the Hydrogen production rate is observed to be low in comparison to the reference system at 850ᵒC at 0.3V. However, it has been shown empirically that the Hydrogen production can be enhanced and by raising the electrical potential to 0.45V. It increases the production rate to the same level as is of the reference system. Therefore, 850ᵒC and 0.45V are assigned as the Q-point of the proposed system which is actively stabilized via proportional integral derivative controllers which adjust the axial position of the lens arrays for both subsystems. The functionality of the controllers is based on maintaining the chamber fixed at 850ᵒC (minimum operating temperature) and 0.45V; Q-Point to realize the same Hydrogen production rate as-is for the reference system.

Keywords: hydrogen, oxygen, thermolysis, ultraviolet

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Authors: Mohamed Derbeli, Maissa Farhat, Oscar Barambones, Lassaad Sbita

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Conventional controller (PI) applied to a DC/DC boost converter for the improvement and optimization of the Proton Exchange Membrane Fuel Cell (PEMFC) system efficiency, cannot attain a good performance effect. Thus, due to its advantages comparatively with the PI controller, this paper interest is focused on the use of the sliding mode controller (SMC), Stability of the closed loop system is analytically proved using Lyapunov approach for the proposed controller. The model and the controllers are implemented in the MATLAB and SIMULINK environment. A comparison of results indicates that the suggested approach has considerable advantages compared to the traditional controller.

Keywords: DC/DC boost converter, PEMFC, PI controller, sliding mode controller

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Authors: Andrés Gomez-Casseres, Rubén Contreras

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In this paper, a bidirectional boost converter operated in Discontinuous Conduction Mode (DCM) is presented as a suitable power conditioning circuit for tuning of kinetic energy harvesters without the need of a battery. A nonlinear control scheme, composed by two linear controllers, is used to control the average value of the input current, enabling the synthesization of complex loads. The converter, along with the control system, is validated through SPICE simulations using the LTspice tool. The converter model and the controller transfer functions are derived. From the simulation results, it was found that the input current distortion increases with the introduced phase shift and that, such distortion, is almost entirely present at the zero-crossing point of the input voltage.

Keywords: average current control, boost converter, electrical tuning, energy harvesting

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Authors: H. Abderrezek, M. N. Harmas

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DC-DC converters are widely used as reliable power source for many industrial and military applications, computers and electronic devices. Several control methods were developed for DC-DC converters control mostly with asymptotic convergence. Synergetic control (SC) is a proven robust control approach and will be used here in a so-called terminal scheme to achieve finite time convergence. Lyapunov synthesis is adopted to assure controlled system stability. Furthermore particle swarm optimization (PSO) algorithm, based on an integral time absolute of error (ITAE) criterion will be used to optimize controller parameters. Simulation of terminal synergetic control of a DC-DC converter is carried out for different operating conditions and results are compared to classic synergetic control performance, that which demonstrate the effectiveness and feasibility of the proposed control method.

Keywords: DC-DC converter, PSO, finite time, terminal, synergetic control

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Authors: S. M. Hashemy Shahdany

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Equitable water delivery becomes one of the main concerns for water authorities in arid regions. Due to water scarcity, providing reliable amount of water is not possible for most of the irrigation districts in arid regions. In this paper, water level difference control is applied to keep the water level errors equal in adjacent reaches. Distant downstream decentralized configurations of the control method are designed and tested under a realistic scenario shows canal operation under water shortage. The simulation results show that the difference controllers share the water level error among all of the users in a fair way. Therefore, water deficit has a similar influence on downstream as well as upstream and water offtakes.

Keywords: equitable water distribution, precise agriculture, sustainable agriculture, water shortage

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Authors: Sheren H. Salah, Ahmed Y. Ben Sasi

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The inverted pendulum system is a classic control problem that is used in universities around the world. It is a suitable process to test prototype controllers due to its high non-linearities and lack of stability. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. This paper presents the possibility of balancing an inverted pendulum system using sliding mode control (SMC). The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle and cart's position. Therefore, proportional-integral-derivative (PID) is used for comparison. Results have proven SMC control produced better response compared to PID control in both normal and noisy systems.

Keywords: inverted pendulum (IP), proportional-integral derivative (PID), sliding mode control (SMC), systems and control engineering

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Authors: Birs Isabela, Muresan Cristina, Folea Silviu, Prodan Ovidiu

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The wing is one of the most important parts of an airplane because it ensures stability, sustenance and maneuverability of the airplane. Because of its shape, the airplane wing can be simplified to a smart beam. Active vibration suppression is realized using piezoelectric actuators that are mounted on the surface of the beam. This work presents a tuning procedure of fractional order controllers based on a graphical approach of the frequency domain representation. The efficacy of the method is proven by practically testing the controller on a laboratory scale experimental stand.

Keywords: fractional order control, piezoelectric actuators, smart beam, vibration suppression

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Authors: Mojtaba Hakimi-Moghaddam

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Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given.

Keywords: Hurwitz polynomials, Routh-Hurwitz stability criterion, continued fraction expansion, pure imaginary roots

Procedia PDF Downloads 282