Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 22

Search results for: Hybrid Systems

22 Modeling and Simulation of a Hybrid System Solar Panel and Wind Turbine in the Quingeo Heritage Center in Ecuador

Authors: Juan Portoviejo Brito, Daniel Icaza Alvarez, Christian Castro Samaniego

Abstract:

In this article, we present the modeling, simulations, and energy conversion analysis of the solar-wind system for the Quingeo Heritage Center in Ecuador. A numerical model was constructed based on the 19 equations, it was coded in MATLAB R2017a, and the results were compared with the experimental data of the site. The model is built with the purpose of using it as a computer development for the optimization of resources and designs of hybrid systems in the Parish of Quingeo and its surroundings. The model obtained a fairly similar pattern compared to the data and curves obtained in the field experimentally and detailed in manuscript. It is important to indicate that this analysis has been carried out so that in the near future one or two of these power generation systems can be exploited in a massive way according to the budget assigned by the Parish GAD of Quingeo or other national or international organizations with the purpose of preserving this unique colonial helmet in Ecuador.

Keywords: Hybrid system, wind turbine, modeling, simulation, Smart Grid, Quingeo Azuay Ecuador.

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21 Analysis and Design of Offshore Triceratops under Ultra-Deep Waters

Authors: Srinivasan Chandrasekaran, R. Nagavinothini

Abstract:

Offshore platforms for ultra-deep waters are form-dominant by design; hybrid systems with large flexibility in horizontal plane and high rigidity in vertical plane are preferred due to functional complexities. Offshore triceratops is relatively a new-generation offshore platform, whose deck is partially isolated from the supporting buoyant legs by ball joints. They allow transfer of partial displacements of buoyant legs to the deck but restrain transfer of rotational response. Buoyant legs are in turn taut-moored to the sea bed using pre-tension tethers. Present study will discuss detailed dynamic analysis and preliminary design of the chosen geometric, which is necessary as a proof of validation for such design applications. A detailed numeric analysis of triceratops at 2400 m water depth under random waves is presented. Preliminary design confirms member-level design requirements under various modes of failure. Tether configuration, proposed in the study confirms no pull-out of tethers as stress variation is comparatively lesser than the yield value. Presented study shall aid offshore engineers and contractors to understand suitability of triceratops, in terms of design and dynamic response behaviour.

Keywords: Buoyant legs, dynamic analysis, offshore structures, preliminary design, random waves, triceratops.

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20 Efficiency Validation of Hybrid Cooling Application in Hot and Humid Climate Houses of KSA

Authors: Jamil Hijazi, Stirling Howieson

Abstract:

Reducing energy consumption and CO2 emissions are probably the greatest challenge now facing mankind. From considerations surrounding global warming and CO2 production, it has to be recognized that oil is a finite resource and the KSA like many other oil-rich countries will have to start to consider a horizon where hydro-carbons are not the dominant energy resource. The employment of hybrid ground-cooling pipes in combination with the black body solar collection and radiant night cooling systems may have the potential to displace a significant proportion of oil currently used to run conventional air conditioning plant. This paper presents an investigation into the viability of such hybrid systems with the specific aim of reducing cooling load and carbon emissions while providing all year-round thermal comfort in a typical Saudi Arabian urban housing block. Soil temperatures were measured in the city of Jeddah. A parametric study then was carried out by computational simulation software (DesignBuilder) that utilized the field measurements and predicted the cooling energy consumption of both a base case and an ideal scenario (typical block retro-fitted with insulation, solar shading, ground pipes integrated with hypocaust floor slabs/stack ventilation and radiant cooling pipes embed in floor). Initial simulation results suggest that careful ‘ecological design’ combined with hybrid radiant and ground pipe cooling techniques can displace air conditioning systems, producing significant cost and carbon savings (both capital and running) without appreciable deprivation of amenity.

Keywords: Cooling load, energy efficiency, ground pipe cooling, hybrid cooling strategy, hydronic radiant systems, low carbon emission, passive designs, thermal comfort.

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19 Hybrid Heat Pump for Micro Heat Network

Authors: J. M. Counsell, Y. Khalid, M. J. Stewart

Abstract:

Achieving nearly zero carbon heating continues to be identified by UK government analysis as an important feature of any lowest cost pathway to reducing greenhouse gas emissions. Heat currently accounts for 48% of UK energy consumption and approximately one third of UK’s greenhouse gas emissions. Heat Networks are being promoted by UK investment policies as one means of supporting hybrid heat pump based solutions. To this effect the RISE (Renewable Integrated and Sustainable Electric) heating system project is investigating how an all-electric heating sourceshybrid configuration could play a key role in long-term decarbonisation of heat.  For the purposes of this study, hybrid systems are defined as systems combining the technologies of an electric driven air source heat pump, electric powered thermal storage, a thermal vessel and micro-heat network as an integrated system.  This hybrid strategy allows for the system to store up energy during periods of low electricity demand from the national grid, turning it into a dynamic supply of low cost heat which is utilized only when required. Currently a prototype of such a system is being tested in a modern house integrated with advanced controls and sensors. This paper presents the virtual performance analysis of the system and its design for a micro heat network with multiple dwelling units. The results show that the RISE system is controllable and can reduce carbon emissions whilst being competitive in running costs with a conventional gas boiler heating system.

Keywords: Gas boilers, heat pumps, hybrid heating and thermal storage, renewable integrated& sustainable electric.

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18 Overview of Different Approaches Used in Optimal Operation Control of Hybrid Renewable Energy Systems

Authors: K. Kusakana

Abstract:

A hybrid energy system is a combination of renewable energy sources with back up, as well as a storage system used to respond to given load energy requirements. Given that the electrical output of each renewable source is fluctuating with changes in weather conditions, and since the load demand also varies with time; one of the main attributes of hybrid systems is to be able to respond to the load demand at any time by optimally controlling each energy source, storage and back-up system. The induced optimization problem is to compute the optimal operation control of the system with the aim of minimizing operation costs while efficiently and reliably responding to the load energy requirement. Current optimization research and development on hybrid systems are mainly focusing on the sizing aspect. Thus, the aim of this paper is to report on the state-of-the-art of optimal operation control of hybrid renewable energy systems. This paper also discusses different challenges encountered, as well as future developments that can help in improving the optimal operation control of hybrid renewable energy systems.

Keywords: Renewable energies, hybrid systems, optimization, operation control.

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17 Optimal Design and Intelligent Management of Hybrid Power System

Authors: Reza Sedaghati

Abstract:

Given the increasing energy demand in the world as well as limited fossil energy fuel resources, it is necessary to use renewable energy resources more than ever. Developing a hybrid energy system is suggested to overcome the intermittence of renewable energy resources such as sun and wind, in which the excess electrical energy can be converted and stored. While these resources store the energy, they can provide a more reliable system that is really suitable for off-grid applications. In hybrid systems, a methodology for optimal sizing of power generation systems components is of great importance in terms of economic aspects and efficiency. In this study, a hybrid energy system is designed to supply an off-grid sample load pattern with the aim of supplying necessary energy and minimizing the total production cost throughout the system life as well as increasing the reliability. For this purpose, the optimal size and the cost function of these resources is determined and minimized using evolutionary algorithms and system efficiency is studied with real-time load and meteorological information of Kazerun, a city in southern Iran under different conditions.

Keywords: Hybrid energy system, intelligent method, optimal size, minimal.

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16 A Hybrid System of Hidden Markov Models and Recurrent Neural Networks for Learning Deterministic Finite State Automata

Authors: Pavan K. Rallabandi, Kailash C. Patidar

Abstract:

In this paper, we present an optimization technique or a learning algorithm using the hybrid architecture by combining the most popular sequence recognition models such as Recurrent Neural Networks (RNNs) and Hidden Markov models (HMMs). In order to improve the sequence/pattern recognition/classification performance by applying a hybrid/neural symbolic approach, a gradient descent learning algorithm is developed using the Real Time Recurrent Learning of Recurrent Neural Network for processing the knowledge represented in trained Hidden Markov Models. The developed hybrid algorithm is implemented on automata theory as a sample test beds and the performance of the designed algorithm is demonstrated and evaluated on learning the deterministic finite state automata.

Keywords: Hybrid systems, Hidden Markov Models, Recurrent neural networks, Deterministic finite state automata.

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15 Adsorptive Waste Heat Based Air-Conditioning Control Strategy for Automotives

Authors: Indrasen Raghupatruni, Michael Glora, Ralf Diekmann, Thomas Demmer

Abstract:

As the trend in automotive technology is fast moving towards hybridization and electrification to curb emissions as well as to improve the fuel efficiency, air-conditioning systems in passenger cars have not caught up with this trend and still remain as the major energy consumers amongst others. Adsorption based air-conditioning systems, e.g. with silica-gel water pair, which are already in use for residential and commercial applications, are now being considered as a technology leap once proven feasible for the passenger cars. In this paper we discuss a methodology, challenges and feasibility of implementing an adsorption based air-conditioning system in a passenger car utilizing the exhaust waste heat. We also propose an optimized control strategy with interfaces to the engine control unit of the vehicle for operating this system with reasonable efficiency supported by our simulation and validation results in a prototype vehicle, additionally comparing to existing implementations, simulation based as well as experimental. Finally we discuss the influence of start-stop and hybrid systems on the operation strategy of the adsorption air-conditioning system.

Keywords: Adsorption air-conditioning, feasibility study, optimized control strategy, prototype vehicle.

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14 Optimal Design of a PV/Diesel Hybrid System for Decentralized Areas through Economic Criteria

Authors: D. Tsuanyo, D. Aussel, Y. Azoumah, P. Neveu

Abstract:

An innovative concept called “Flexy-Energy” is developing at 2iE. This concept aims to produce electricity at lower cost by smartly mix different available energy sources in accordance to the load profile of the region. With a higher solar irradiation and due to the fact that Diesel generator are massively used in sub-Saharan rural areas, PV/Diesel hybrid systems could be a good application of this concept and a good solution to electrify this region, provided they are reliable, cost effective and economically attractive to investors. Presentation of the developed approach is the aims of this paper. The PV/Diesel hybrid system designed consists to produce electricity and/or heat from a coupling between Diesel Diesel generators and PV panels without batteries storage, while ensuring the substitution of gasoil by bio-fuels available in the area where the system will be installed. The optimal design of this system is based on his technical performances; the Life Cycle Cost (LCC) and Levelized Cost of Energy are developed and use as economic criteria. The Net Present Value (NPV), the internal rate of return (IRR) and the discounted payback (DPB) are also evaluated according to dual electricity pricing (in sunny and unsunny hours). The PV/Diesel hybrid system obtained is compared to the standalone Diesel Diesel generators. The approach carried out in this paper has been applied to Siby village in Mali (Latitude 12 ° 23'N 8 ° 20'W) with 295 kWh as daily demand.This approach provides optimal physical characteristics (size of the components, number of component) and dynamical characteristics in real time (number of Diesel generator on, their load rate, fuel specific consumptions, and PV penetration rate) of the system. The system obtained is slightly cost effective; but could be improved with optimized tariffing strategies.

Keywords: Investments criteria, Optimization, PV hybrid, Sizing, Rural electrification.

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13 A Hybrid Recommendation System Based On Association Rules

Authors: Ahmed Mohammed K. Alsalama

Abstract:

Recommendation systems are widely used in e-commerce applications. The engine of a current recommendation system recommends items to a particular user based on user preferences and previous high ratings. Various recommendation schemes such as collaborative filtering and content-based approaches are used to build a recommendation system. Most of current recommendation systems were developed to fit a certain domain such as books, articles, and movies. We propose1 a hybrid framework recommendation system to be applied on two dimensional spaces (User × Item) with a large number of Users and a small number of Items. Moreover, our proposed framework makes use of both favorite and non-favorite items of a particular user. The proposed framework is built upon the integration of association rules mining and the content-based approach. The results of experiments show that our proposed framework can provide accurate recommendations to users.

Keywords: Data Mining, Association Rules, Recommendation Systems, Hybrid Systems.

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12 Hybrid System Configurations and Charging Strategies for Isolated Electric Tuk-Tuk Charging Station in South Africa

Authors: L. Bokopane, K. Kusakana, H. J. Vermaark

Abstract:

The success of renewable powered electric vehicle charging station in isolated areas depends highly on the availability and sustainability of renewable resources all year round at a selected location. The main focus of this paper is to discuss the possible charging strategies that could be implemented to find the best possible configuration of an electric Tuk-Tuk charging station at a given location within South Africa. The charging station is designed, modeled and simulated to evaluate its performances. The technoeconomic analysis of different feasible supply configurations of the charging station using renewable energies is simulated using HOMER software and the results compared in order to select the best possible charging strategies in terms of cost of energy consumed.

Keywords: Electric Tuk-Tuk, Renewable energy, Energy Storage, Hybrid systems, HOMER.

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11 FACTS Based Stabilization for Smart Grid Applications

Authors: Adel M. Sharaf, Foad H. Gandoman

Abstract:

Nowadays, Photovoltaic-PV Farms/ Parks and large PV-Smart Grid Interface Schemes are emerging and commonly utilized in Renewable Energy distributed generation. However, PVhybrid- Dc-Ac Schemes using interface power electronic converters usually has negative impact on power quality and stabilization of modern electrical network under load excursions and network fault conditions in smart grid. Consequently, robust FACTS based interface schemes are required to ensure efficient energy utilization and stabilization of bus voltages as well as limiting switching/fault onrush current condition. FACTS devices are also used in smart grid- Battery Interface and Storage Schemes with PV-Battery Storage hybrid systems as an elegant alternative to renewable energy utilization with backup battery storage for electric utility energy and demand side management to provide needed energy and power capacity under heavy load conditions. The paper presents a robust interface PV-Li-Ion Battery Storage Interface Scheme for Distribution/Utilization Low Voltage Interface using FACTS stabilization enhancement and dynamic maximum PV power tracking controllers. Digital simulation and validation of the proposed scheme is done using MATLAB/Simulink software environment for Low Voltage- Distribution/Utilization system feeding a hybrid Linear-Motorized inrush and nonlinear type loads from a DC-AC Interface VSC-6- pulse Inverter Fed from the PV Park/Farm with a back-up Li-Ion Storage Battery.

Keywords: AC FACTS, Smart grid, Stabilization, PV-Battery Storage, Switched Filter-Compensation (SFC).

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10 Diagnosis of the Heart Rhythm Disorders by Using Hybrid Classifiers

Authors: Sule Yucelbas, Gulay Tezel, Cuneyt Yucelbas, Seral Ozsen

Abstract:

In this study, it was tried to identify some heart rhythm disorders by electrocardiography (ECG) data that is taken from MIT-BIH arrhythmia database by subtracting the required features, presenting to artificial neural networks (ANN), artificial immune systems (AIS), artificial neural network based on artificial immune system (AIS-ANN) and particle swarm optimization based artificial neural network (PSO-NN) classifier systems. The main purpose of this study is to evaluate the performance of hybrid AIS-ANN and PSO-ANN classifiers with regard to the ANN and AIS. For this purpose, the normal sinus rhythm (NSR), atrial premature contraction (APC), sinus arrhythmia (SA), ventricular trigeminy (VTI), ventricular tachycardia (VTK) and atrial fibrillation (AF) data for each of the RR intervals were found. Then these data in the form of pairs (NSR-APC, NSR-SA, NSR-VTI, NSR-VTK and NSR-AF) is created by combining discrete wavelet transform which is applied to each of these two groups of data and two different data sets with 9 and 27 features were obtained from each of them after data reduction. Afterwards, the data randomly was firstly mixed within themselves, and then 4-fold cross validation method was applied to create the training and testing data. The training and testing accuracy rates and training time are compared with each other.

As a result, performances of the hybrid classification systems, AIS-ANN and PSO-ANN were seen to be close to the performance of the ANN system. Also, the results of the hybrid systems were much better than AIS, too. However, ANN had much shorter period of training time than other systems. In terms of training times, ANN was followed by PSO-ANN, AIS-ANN and AIS systems respectively. Also, the features that extracted from the data affected the classification results significantly.

Keywords: AIS, ANN, ECG, hybrid classifiers, PSO.

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9 Regional Stability Analysis of Rotor-Ball Bearing and Rotor- Roller Bearing Systems Considering Switching Phenomena

Authors: Jafar Abbaszadeh Chekan, Kaveh Merat, Hassan Zohoor

Abstract:

In this study the regional stability of a rotor system which is supported on rolling bearings with radial clearance is studied. The rotor is assumed to be rigid. Due to radial clearance of bearings and dynamic configuration of system, each rolling elements of bearings has the possibility to be in contact with both of the races (under compression) or lose its contact. As a result, this change in dynamic of the system makes it to be known as switching system which is a type of Hybrid systems. In this investigation by adopting Multiple Lyapunov Function theorem and using Hamiltonian function as a candidate Lyapunov function, the stability of the system is studied. The purpose of this study is to inspect the regional stability of rotor-roller bearing and rotor-ball bearing systems.

Keywords: Stability analysis, Rotor-rolling bearing systems, Switching systems, Multiple Lyapunov Function Method

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8 Identification of a PWA Model of a Batch Reactor for Model Predictive Control

Authors: Gorazd Karer, Igor Skrjanc, Borut Zupancic

Abstract:

The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.

Keywords: Batch reactor, fuzzy clustering, hybrid systems, identification, nonlinear systems, PWA systems.

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7 A New Integer Programming Formulation for the Chinese Postman Problem with Time Dependent Travel Times

Authors: Jinghao Sun, Guozhen Tan, Guangjian Hou

Abstract:

The Chinese Postman Problem (CPP) is one of the classical problems in graph theory and is applicable in a wide range of fields. With the rapid development of hybrid systems and model based testing, Chinese Postman Problem with Time Dependent Travel Times (CPPTDT) becomes more realistic than the classical problems. In the literature, we have proposed the first integer programming formulation for the CPPTDT problem, namely, circuit formulation, based on which some polyhedral results are investigated and a cutting plane algorithm is also designed. However, there exists a main drawback: the circuit formulation is only available for solving the special instances with all circuits passing through the origin. Therefore, this paper proposes a new integer programming formulation for solving all the general instances of CPPTDT. Moreover, the size of the circuit formulation is too large, which is reduced dramatically here. Thus, it is possible to design more efficient algorithm for solving the CPPTDT in the future research.

Keywords: Chinese Postman Problem, Time Dependent, Integer Programming, Upper Bound Analysis.

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6 Application of Artificial Intelligence Techniques for Dissolved Gas Analysis of Transformers-A Review

Authors: Deepika Bhalla, Raj Kumar Bansal, Hari Om Gupta

Abstract:

The gases generated in oil filled transformers can be used for qualitative determination of incipient faults. The Dissolved Gas Analysis has been widely used by utilities throughout the world as the primarily diagnostic tool for transformer maintenance. In this paper, various Artificial Intelligence Techniques that have been used by the researchers in the past have been reviewed, some conclusions have been drawn and a sequential hybrid system has been proposed. The synergy of ANN and FIS can be a good solution for reliable results for predicting faults because one should not rely on a single technology when dealing with real–life applications.

Keywords: Dissolved Gas Analysis, Artificial IntelligenceTechniques, Incipient Faults, Transformer Fault Diagnosis, andHybrid Systems.

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5 Evolutionary Training of Hybrid Systems of Recurrent Neural Networks and Hidden Markov Models

Authors: Rohitash Chandra, Christian W. Omlin

Abstract:

We present a hybrid architecture of recurrent neural networks (RNNs) inspired by hidden Markov models (HMMs). We train the hybrid architecture using genetic algorithms to learn and represent dynamical systems. We train the hybrid architecture on a set of deterministic finite-state automata strings and observe the generalization performance of the hybrid architecture when presented with a new set of strings which were not present in the training data set. In this way, we show that the hybrid system of HMM and RNN can learn and represent deterministic finite-state automata. We ran experiments with different sets of population sizes in the genetic algorithm; we also ran experiments to find out which weight initializations were best for training the hybrid architecture. The results show that the hybrid architecture of recurrent neural networks inspired by hidden Markov models can train and represent dynamical systems. The best training and generalization performance is achieved when the hybrid architecture is initialized with random real weight values of range -15 to 15.

Keywords: Deterministic finite-state automata, genetic algorithm, hidden Markov models, hybrid systems and recurrent neural networks.

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4 A Hybrid Approach to Fault Detection and Diagnosis in a Diesel Fuel Hydrotreatment Process

Authors: Salvatore L., Pires B., Campos M. C. M., De Souza Jr M. B.

Abstract:

It is estimated that the total cost of abnormal conditions to US process industries is around $20 billion dollars in annual losses. The hydrotreatment (HDT) of diesel fuel in petroleum refineries is a conversion process that leads to high profitable economical returns. However, this is a difficult process to control because it is operated continuously, with high hydrogen pressures and it is also subject to disturbances in feed properties and catalyst performance. So, the automatic detection of fault and diagnosis plays an important role in this context. In this work, a hybrid approach based on neural networks together with a pos-processing classification algorithm is used to detect faults in a simulated HDT unit. Nine classes (8 faults and the normal operation) were correctly classified using the proposed approach in a maximum time of 5 minutes, based on on-line data process measurements.

Keywords: Fault detection, hydrotreatment, hybrid systems, neural networks.

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3 Modeling Hybrid Systems with MLD Approach and Analysis of the Model Size and Complexity

Authors: H. Mahboubi, B. Moshiri, A. Khaki Seddigh

Abstract:

Recently, a great amount of interest has been shown in the field of modeling and controlling hybrid systems. One of the efficient and common methods in this area utilizes the mixed logicaldynamical (MLD) systems in the modeling. In this method, the system constraints are transformed into mixed-integer inequalities by defining some logic statements. In this paper, a system containing three tanks is modeled as a nonlinear switched system by using the MLD framework. Comparing the model size of the three-tank system with that of a two-tank system, it is deduced that the number of binary variables, the size of the system and its complexity tremendously increases with the number of tanks, which makes the control of the system more difficult. Therefore, methods should be found which result in fewer mixed-integer inequalities.

Keywords: Hybrid systems, mixed-integer inequalities, mixed logical dynamical systems, multi-tank system.

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2 Hybrid Modeling and Optimal Control of a Two-Tank System as a Switched System

Authors: H. Mahboubi, B. Moshiri, A. Khaki Seddigh

Abstract:

In the past decade, because of wide applications of hybrid systems, many researchers have considered modeling and control of these systems. Since switching systems constitute an important class of hybrid systems, in this paper a method for optimal control of linear switching systems is described. The method is also applied on the two-tank system which is a much appropriate system to analyze different modeling and control techniques of hybrid systems. Simulation results show that, in this method, the goals of control and also problem constraints can be satisfied by an appropriate selection of cost function.

Keywords: Hybrid systems, optimal control, switched systems, two-tank system

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1 Novel Hybrid Approaches For Real Coded Genetic Algorithm to Compute the Optimal Control of a Single Stage Hybrid Manufacturing Systems

Authors: M. Senthil Arumugam, M.V.C. Rao

Abstract:

This paper presents a novel two-phase hybrid optimization algorithm with hybrid genetic operators to solve the optimal control problem of a single stage hybrid manufacturing system. The proposed hybrid real coded genetic algorithm (HRCGA) is developed in such a way that a simple real coded GA acts as a base level search, which makes a quick decision to direct the search towards the optimal region, and a local search method is next employed to do fine tuning. The hybrid genetic operators involved in the proposed algorithm improve both the quality of the solution and convergence speed. The phase–1 uses conventional real coded genetic algorithm (RCGA), while optimisation by direct search and systematic reduction of the size of search region is employed in the phase – 2. A typical numerical example of an optimal control problem with the number of jobs varying from 10 to 50 is included to illustrate the efficacy of the proposed algorithm. Several statistical analyses are done to compare the validity of the proposed algorithm with the conventional RCGA and PSO techniques. Hypothesis t – test and analysis of variance (ANOVA) test are also carried out to validate the effectiveness of the proposed algorithm. The results clearly demonstrate that the proposed algorithm not only improves the quality but also is more efficient in converging to the optimal value faster. They can outperform the conventional real coded GA (RCGA) and the efficient particle swarm optimisation (PSO) algorithm in quality of the optimal solution and also in terms of convergence to the actual optimum value.

Keywords: Hybrid systems, optimal control, real coded genetic algorithm (RCGA), Particle swarm optimization (PSO), Hybrid real coded GA (HRCGA), and Hybrid genetic operators.

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