Search results for: nonlinear optimization with constraints

Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

Abstract:

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Kanica Goel, Nilam

Abstract:

Infectious diseases are a leading cause of death worldwide and hence a great challenge for every nation. Thus, it becomes utmost essential to prevent and reduce the spread of infectious disease among humans. Mathematical models help to better understand the transmission dynamics and spread of infections. For this purpose, in the present article, we have proposed a nonlinear time-delayed SVIRS (Susceptible-Vaccinated-Infected-Recovered-Susceptible) mathematical model with nonlinear type incidence rate and nonlinear type treatment rate. Analytical study of the model shows that model exhibits two types of equilibrium points, namely, disease-free equilibrium and endemic equilibrium. Further, for the long-term behavior of the model, stability of the model is discussed with the help of basic reproduction number R₀ and we showed that disease-free equilibrium is locally asymptotically stable if the basic reproduction number R₀ is less than one and unstable if the basic reproduction number R₀ is greater than one for the time lag τ≥0. Furthermore, when basic reproduction number R₀ is one, using center manifold theory and Casillo-Chavez and Song theorem, we showed that the model undergoes transcritical bifurcation. Moreover, numerical simulations are being carried out using MATLAB 2012b to illustrate the theoretical results.

Keywords: nonlinear incidence rate, nonlinear treatment rate, stability, time delayed SVIRS epidemic model

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Since the modernism, movement, and appearance of modern architecture, an aggressive desire for a general design theory in the theoretical works of architects in the form of books and essays emerges. Since Robert Venturi and Denise Scott Brown’s published complexity and contradiction in architecture in 1966, the discourse of complexity and volumetric composition has been an important and controversial issue in the discipline. Ever since various theories and essays were involved in this discourse, this paper attempt to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. As a result, we identify chaotic architecture as the correlation of chaos theory and architecture as an independent nonlinear design theory with specific characteristics and properties.

Keywords: architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology

Procedia PDF Downloads 347

Authors: Azim Khodadadi, Sahar Sadaat Vakili, Ebrahim Babaei

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This study presents a numerical method to optimize the failure rate and repair time of a typical radial distribution system. Failure rate and repair time are effective parameters in customer and energy based indices of reliability. Decrease of these parameters improves reliability indices. Thus, system stability will be boost. The penalty functions indirectly reflect the cost of investment which spent to improve these indices. Constraints on customer and energy based indices, i.e. SAIFI, SAIDI, CAIDI and AENS have been considered by using a new method which reduces optimization algorithm controlling parameters. Imperialist Competitive Algorithm (ICA) used as main optimization technique and particle swarm optimization (PSO), simulated annealing (SA) and differential evolution (DE) has been applied for further investigation. These algorithms have been implemented on a test system by MATLAB. Obtained results have been compared with each other. The optimized values of repair time and failure rate are much lower than current values which this achievement reduced investment cost and also ICA gives better answer than the other used algorithms.

Keywords: imperialist competitive algorithm, failure rate, repair time, radial distribution network

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

Abstract:

This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: nonlinear optics, plasmonic waveguide, chalcogenide, propagation equation

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Authors: Dongkyu Lee, Thanh Banh Thien, Soomi Shin

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In the present study, the isogeometric topology optimization is proposed for cracked structures through using Solid Isotropic Material with Penalization (SIMP) as a design model. Design density variables defined in the variable space are used to approximate the element analysis density by the bivariate B-spline basis functions. The mathematical formulation of topology optimization problem solving minimum structural compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Stiffness and adjoint sensitivity formulations linked to strain energy of cracked structure are proposed in terms of design density variables. Numerical examples demonstrate interactions of topology optimization to structures design with cracks.

Keywords: topology optimization, isogeometric, NURBS, design

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Authors: Ebrahim Hassan Kapeel, Ahmed Mohsen Kamel, Hossan Hendy, Yehia Z. Elhalwagy

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Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control lawisdesigned for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: UAV dynamic model, attitude control, nonlinear PID, dynamic inversion

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

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In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: grey relational degree, multiple linear regression, membership function, nonlinear programming

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Authors: Lydia Novozhilova, Vladimir Urazhdin

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An optimization problem for reinforced thin-walled vessels under uniform external pressure is considered. The conventional approaches to optimization generally start with pre-defined geometric parameters of the vessels, and then employ analytic or numeric calculations and/or experimental testing to verify functionality, such as stability under the projected conditions. The proposed approach consists of two steps. First, the feasibility domain will be identified in the multidimensional parameter space. Every point in the feasibility domain defines a design satisfying both geometric and functional constraints. Second, an objective function defined in this domain is formulated and optimized. The broader applicability of the suggested methodology is maximized by implementing the Support Vector Machines (SVM) classification algorithm of machine learning for identification of the feasible design region. Training data for SVM classifier is obtained using the Simulation package of SOLIDWORKS®. Based on the data, the SVM algorithm produces a curvilinear boundary separating admissible and not admissible sets of design parameters with maximal margins. Then optimization of the vessel parameters in the feasibility domain is performed using the standard algorithms for the constrained optimization. As an example, optimization of a ring-stiffened closed cylindrical thin-walled vessel with semi-spherical caps under high external pressure is implemented. As a functional constraint, von Mises stress criterion is used but any other stability constraint admitting mathematical formulation can be incorporated into the proposed approach. Suggested methodology has a good potential for reducing design time for finding optimal parameters of thin-walled vessels under uniform external pressure.

Keywords: design parameters, feasibility domain, von Mises stress criterion, Support Vector Machine (SVM) classifier

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Authors: Belloufi Mohammed, Sellami Badreddine

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This paper deals with a new nonlinear modified three-term conjugate gradient algorithm for solving large-scale unstrained optimization problems. The search direction of the algorithms from this class has three terms and is computed as modifications of the classical conjugate gradient algorithms to satisfy both the descent and the conjugacy conditions. An example of three-term conjugate gradient algorithm from this class, as modifications of the classical and well known Hestenes and Stiefel or of the CG_DESCENT by Hager and Zhang conjugate gradient algorithms, satisfying both the descent and the conjugacy conditions is presented. Under mild conditions, we prove that the modified three-term conjugate gradient algorithm with Wolfe type line search is globally convergent. Preliminary numerical results show the proposed method is very promising.

Keywords: unconstrained optimization, three-term conjugate gradient, sufficient descent property, line search

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Authors: M. A. Rubio, A. Urquia

Abstract:

Genetic algorithms (GA) are applied to the solution of high-dimensional optimization problems. Additionally, sensitivity analysis (SA) is usually carried out to determine the effect on optimal solutions of changes in parameter values of the objective function. These two analyses (i.e., optimization and sensitivity analysis) are computationally intensive when applied to high-dimensional functions. The approach presented in this paper consists in performing the SA during the GA execution, by statistically analyzing the data obtained of running the GA. The advantage is that in this case SA does not involve making additional evaluations of the objective function and, consequently, this proposed approach requires less computational effort than conducting optimization and SA in two consecutive steps.

Keywords: optimization, sensitivity, genetic algorithms, model calibration

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Authors: Ali Raheli, Rahim Habibifar, Behzad Mohammadi-Alasti, Mahdi Abbasgholipour

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This paper presents vibration behavior of a FGM micro-beam and its pull-in instability under a nonlinear electrostatic pressure. An exponential function has been applied to show the continuous gradation of the properties along thickness. Nonlinear integro-differential-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static analysis has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points have been shown in the state control space. In order to find the response to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages have been shown. The effects of electrostatic pressure on stability of FGM micro-beams having various amounts of the ceramic constituent have been investigated.

Keywords: FGM, MEMS, nonlinear vibration, electrical, dynamic pull-in voltage

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Authors: Kevin Spencer G. Anglim, Zhenyu Zhang, Qingbin Gao

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Reusable launch vehicles (RLVs) present a more environmentally-friendly approach to accessing space when compared to traditional launch vehicles that are discarded after each flight. This paper studies the recyclable nature of RLVs by presenting a solution method for determining minimum-fuel optimal trajectories using principles from optimal control theory and particle swarm optimization (PSO). This problem is formulated as a minimum-landing error powered descent problem where it is desired to move the RLV from a fixed set of initial conditions to three different sets of terminal conditions. However, unlike other powered descent studies, this paper considers the highly nonlinear effects caused by atmospheric drag, which are often ignored for studies on the Moon or on Mars. Rather than optimizing the controls directly, the throttle control is assumed to be bang-off-bang with a predetermined thrust direction for each phase of flight. The PSO method is verified in a one-dimensional comparison study, and it is then applied to the two-dimensional cases, the results of which are illustrated.

Keywords: minimum-fuel optimal trajectory, particle swarm optimization, reusable rocket, SpaceX

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Authors: Abdelkader Merah, Kada Hartani

Abstract:

A reference model based control approach for improving behavior following car is proposed in this paper. The reference model is nonlinear and provides dynamic solutions consistent with safety constraints and comfort specifications. a robust fuzzy logic based control strategy is further proposed in this paper. A set of simulation results showing the suitability of the proposed technique for various demanding cenarios is also included in this paper.

Keywords: reference model, longitudinal control, fuzzy logic, design of car

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Authors: Som Pal Baliyan

Abstract:

Dairy enterprise has been a major source of employment and income generation in most of the economies worldwide. Botswana government has also identified dairy as one of the agricultural sectors towards diversification of the mineral dependent economy of the country. The huge gap between local demand and supply of milk and milk products indicated that there are not only constraints but also; opportunities exist in this sub sector of agriculture. Therefore, this study was an attempt to identify constraints and opportunities in dairy production industry in Botswana. The possible ways to mitigate the constraints were also identified. The findings should assist the stakeholders especially, policy makers in the formulation of effective policies for the growth of dairy sector in the country. This quantitative study adopted a survey research design. A final survey followed by a pilot survey was conducted for data collection. The purpose of the pilot survey was to collect basic information on the nature and extent of the constraints, opportunities and ways to mitigate the constraints in dairy production. Based on the information from pilot survey, a four point Likert’s scale type questionnaire was constructed, validated and tested for its reliability. The data for the final survey were collected from purposively selected twenty five dairy farms. The descriptive statistical tools were employed to analyze data. Among the twelve constraints identified; high feed costs, feed shortage and availability, lack of technical support, lack of skilled manpower, high prevalence of pests and diseases and, lack of dairy related technologies were the six major constraints in dairy production. Grain feed production, roughage feed production, manufacturing of dairy feed, establishment of milk processing industry and, development of transportation systems were the five major opportunities among the eight opportunities identified. Increasing production of animal feed locally, increasing roughage feed production locally, provision of subsidy on animal feed, easy access to sufficient financial support, training of the farmers and, effective control of pests and diseases were identified as the six major ways to mitigate the constraints. It was recommended that the identified constraints and opportunities as well as the ways to mitigate the constraints need to be carefully considered by the stakeholders especially, policy makers during the formulation and implementation of the policies for the development of dairy sector in Botswana.

Keywords: dairy enterprise, milk production, opportunities, production constraints

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Authors: Zongjie Wang, Zhizhong Guo

Abstract:

While the regular optimal power flow model focuses on a single time scan, the optimization of power systems is typically intended for a time duration with respect to a desired objective function. In this paper, a temporal optimal power flow model for a time period is proposed. To reduce the computation burden needed for calculating temporal optimal power flow, a characteristic optimal power flow model is proposed, which employs different characteristic load patterns to represent the objective function and security constraints. A numerical method based on the interior point method is also proposed for solving the characteristic optimal power flow model. Both the temporal optimal power flow model and characteristic optimal power flow model can improve the systems’ desired objective function for the entire time period. Numerical studies are conducted on the IEEE 14 and 118-bus test systems to demonstrate the effectiveness of the proposed characteristic optimal power flow model.

Keywords: optimal power flow, time period, security, economy

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Authors: Ebrahim H. Kapeel, Ahmed M. Kamel, Hossam Hendy, Yehia Z. Elhalwagy

Abstract:

Interest in autopilot design has been raised intensely as a result of recent advancements in Unmanned Aerial vehicles (UAVs). Due to the enormous number of applications that UAVs can achieve, the number of applied control theories used for them has increased in recent years. These small fixed-wing UAVs are suffering high non-linearity, sensitivity to disturbances, and coupling effects between their channels. In this work, the nonlinear dynamic inversion (NDI) control law is designed for a nonlinear small fixed-wing UAV model. The NDI is preferable for varied operating conditions, there is no need for a scheduling controller. Moreover, it’s applicable for high angles of attack. For the designed flight controller validation, a nonlinear Modified PI-D controller is performed with our model. A comparative study between both controllers is achieved to evaluate the NDI performance. Simulation results and analysis are proposed to illustrate the effectiveness of the designed controller based on NDI.

Keywords: attitude control, nonlinear PID, dynamic inversion

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Authors: Sandeep Singh

Abstract:

In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: Adel Sabry Eesa, Adnan Mohsin Abdulazeez Brifcani, Zeynep Orman

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This paper presents a new meta-heuristic bio-inspired optimization algorithm which is called Cuttlefish Algorithm (CFA). The algorithm mimics the mechanism of color changing behavior of the cuttlefish to solve numerical global optimization problems. The colors and patterns of the cuttlefish are produced by reflected light from three different layers of cells. The proposed algorithm considers mainly two processes: reflection and visibility. Reflection process simulates light reflection mechanism used by these layers, while visibility process simulates visibility of matching patterns of the cuttlefish. To show the effectiveness of the algorithm, it is tested with some other popular bio-inspired optimization algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Bees Algorithm (BA) that have been previously proposed in the literature. Simulations and obtained results indicate that the proposed CFA is superior when compared with these algorithms.

Keywords: Cuttlefish Algorithm, bio-inspired algorithms, optimization, global optimization problems

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Authors: Safa Adi

Abstract:

This paper will consider the problem of sequential mining patterns embedded in a database by handling the time constraints as defined in the GSP algorithm (level wise algorithms). We will compare two previous approaches GTC and PSP, that resumes the general principles of GSP. Furthermore this paper will discuss PG-hybrid algorithm, that using PSP and GTC. The results show that PSP and GTC are more efficient than GSP. On the other hand, the GTC algorithm performs better than PSP. The PG-hybrid algorithm use PSP algorithm for the two first passes on the database, and GTC approach for the following scans. Experiments show that the hybrid approach is very efficient for short, frequent sequences.

Keywords: database, GTC algorithm, PSP algorithm, sequential patterns, time constraints

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Authors: Meraj Ali Khan, Falleh R. Al-Solamy

Abstract:

In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature.

Keywords: duality, multiobjective programming, univex functions, univex

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Authors: Hamid Nikzad, Shinta Yoshitomi

Abstract:

In this paper, nonlinear static pushover analysis is performed on 15 storied RC building structure with a shear wall to evaluate the seismic performance of the building. Section sizes of the members are obtained based on structural optimization method utilizing MATLAB frame optimizer, then the structure is simulated and designed in ETABS program conforming ACI 318-14 design code. The pushover curve has been generated by pushing the top node of the structure to the limited target displacement. Members failure due to the formation of plastic hinges, considering shear wall-frame structure was observed and the result of this study is presented based on current regulation of FEMA356, ASCE7-10, and ACI 318-14 design criteria

Keywords: structural optimization, linear static analysis, ETABS, MATLAB, RC moment frame, RC shear wall structures

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Authors: Pedro F. Albuquerque, Pedro V. Gamboa, Miguel A. Silvestre

Abstract:

The present work describes the implementation of the Enhanced Collaborative Optimization (ECO) multilevel architecture with a gradient-based optimization algorithm with the aim of performing a multidisciplinary design optimization of a generic unmanned aerial vehicle with morphing technologies. The concepts of weighting coefficient and a dynamic compatibility parameter are presented for the ECO architecture. A routine that calculates the aircraft performance for the user defined mission profile and vehicle’s performance requirements has been implemented using low fidelity models for the aerodynamics, stability, propulsion, weight, balance and flight performance. A benchmarking case study for evaluating the advantage of using a variable span wing within the optimization methodology developed is presented.

Keywords: multidisciplinary, multilevel, morphing, enhanced collaborative optimization

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Authors: Jaroslav Masek, Juraj Camaj, Eva Nedeliakova

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The aim of optimization of store management is not only designing the situation of store management itself including its equipment, technology and operation. In optimization of store management we need to consider also synchronizing of technological, transport, store and service operations throughout the whole process of logistic chain in such a way that a natural flow of material from provider to consumer will be achieved the shortest possible way, in the shortest possible time in requested quality and quantity and with minimum costs. The paper deals with the application of the queuing theory for optimization of warehouse processes. The first part refers to common information about the problematic of warehousing and using mathematical methods for logistics chains optimization. The second part refers to preparing a model of a warehouse within queuing theory. The conclusion of the paper includes two examples of using queuing theory in praxis.

Keywords: queuing theory, logistics system, mathematical methods, warehouse optimization

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Authors: Babar Sultan, Kiran Sultan, Waseem Khan, Ijaz Mansoor Qureshi

Abstract:

In this paper, a novel idea for the performance enhancement of secondary network is proposed for Underlay Cognitive Radio Networks (CRNs). In Underlay CRNs, primary users (PUs) impose strict interference constraints on the secondary users (SUs). The proposed scheme is based on Artificial Bee Colony (ABC) optimization for relay selection and power allocation to handle the highlighted primary challenge of Underlay CRNs. ABC is a simple, population-based optimization algorithm which attains global optimum solution by combining local search methods (Employed and Onlooker Bees) and global search methods (Scout Bees). The proposed two-phase relay selection and power allocation algorithm aims to maximize the signal-to-noise ratio (SNR) at the destination while operating in an underlying mode. The proposed algorithm has less computational complexity and its performance is verified through simulation results for a different number of potential relays, different interference threshold levels and different transmit power thresholds for the selected relays.

Keywords: artificial bee colony, underlay spectrum sharing, cognitive radio networks, amplify-and-forward

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

Abstract:

The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: Basil Manos, Parthena Chatzinikolaou, Fedra Kiomourtzi

Abstract:

This paper presents a Multicriteria Mathematical Programming model for farm planning and sustainable optimization of agricultural production. The model can be used as a tool for the analysis and simulation of agricultural production plans, as well as for the study of impacts of various measures of Common Agriculture Policy in the member states of European Union. The model can achieve the optimum production plan of a farm or an agricultural region combining in one utility function different conflicting criteria as the maximization of gross margin and the minimization of fertilizers used, under a set of constraints for land, labor, available capital, Common Agricultural Policy etc. The proposed model was applied to the region of Larisa in central Greece. The optimum production plan achieves a greater gross return, a less fertilizers use, and a less irrigated water use than the existent production plan.

Keywords: sustainable optimization, multicriteria analysis, agricultural production, farm planning

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Authors: Giselle Maggie-Fer Castañeda Lozano

Abstract:

The main objective of this research was to explore the role of neural network architectures in simulating behavioral phenomena as a potential explanation for selective associations, specifically related to biological constraints on learning. Biological constraints on learning refer to the limitations observed in conditioning procedures, where learning is expected to occur. The study involved simulations of five different experiments exploring various phenomena and sources of biological constraints in learning. These simulations included the interaction between response and reinforcer, stimulus and reinforcer, specificity of stimulus-reinforcer associations, species differences, neuroanatomical constraints, and learning in uncontrolled conditions. The overall results demonstrated that by manipulating neural network architectures, conditions can be created to model and explain diverse biological constraints frequently reported in comparative psychology literature as learning typicities. Additionally, the simulations offer predictive content worthy of experimental testing in the pursuit of new discoveries regarding the specificity of learning. The implications and limitations of these findings are discussed. Finally, it is suggested that this research could inaugurate a line of inquiry involving the use of neural networks to study biological factors in behavior, fostering the development of more ethical and precise research practices.

Keywords: comparative psychology, connectionism, conditioning, experimental analysis of behavior, neural networks

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Authors: Nabil Mezhoud

Abstract:

The economic operation of electric energy generating systems is one of the predominant problems in energy systems. Due to the need for better reliability, high energy quality, lower losses, lower cost and a clean environment, the application of renewable and sustainable energy sources, such as wind energy, solar energy, etc., in recent years has become more widespread. In this work, one of a bio-inspired meta-heuristic algorithm inspired by the flashing behavior of fireflies at night called the Firefly Algorithm (FFA) is applied to solve the Optimal Energy Management (OEM) and the environmental index (EI) problems of a micro-grid (MG) operating by Renewable and Sustainable Generation Systems (RSGS). Our main goal is to minimize the nonlinear objective function of an electrical microgrid, taking into account equality and inequality constraints. The FFA approach was examined and tested on a standard MG system composed of different types of RSGS, such as wind turbines (WT), photovoltaic systems (PV), and non-renewable energy, such as fuel cells (FC), micro turbine (MT), diesel generator (DEG) and loads with energy storage systems (ESS). The results are promising and show the effectiveness and robustness of the proposed approach to solve the OEM and the EI problems. The results of the proposed method have been compared and validated with those known references published recently.

Keywords: renewable energy sources, energy management, distributed generator, micro-grids, firefly algorithm

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Authors: Ayad Al-Mahturi, Herman Wahid

Abstract:

This paper presents an optimal state feedback controller based on Linear Quadratic Regulator (LQR) for a two-rotor aero-dynamical system (TRAS). TRAS is a highly nonlinear multi-input multi-output (MIMO) system with two degrees of freedom and cross coupling. There are two parameters that define the behavior of LQR controller: state weighting matrix and control weighting matrix. The two parameters influence the performance of LQR. Particle Swarm Optimization (PSO) is proposed to optimally tune weighting matrices of LQR. The major concern of using LQR controller is to stabilize the TRAS by making the beam move quickly and accurately for tracking a trajectory or to reach a desired altitude. The simulation results were carried out in MATLAB/Simulink. The system is decoupled into two single-input single-output (SISO) systems. Comparing the performance of the optimized proportional, integral and derivative (PID) controller provided by INTECO, results depict that LQR controller gives a better performance in terms of both transient and steady state responses when PSO is performed.

Keywords: LQR controller, optimal control, particle swarm optimization (PSO), two rotor aero-dynamical system (TRAS)

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