Search results for: optimal homotopy perturbation method.

Authors: Marwan Abukhaled, Ibrahim Sadek

Abstract:

This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a distributed piezoelectric actuators. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations.

Keywords: Optimal control, Thermoelastic beam, variational approach, modal expansion approach

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Authors: Tomoaki Hashimoto

Abstract:

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

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

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Authors: Sana Testouri, Karim Saadaoui, Mohamed Benrejeb

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This paper presents a Particle Swarm Optimization (PSO) method for determining the optimal parameters of a first-order controller for TCP/AQM system. The model TCP/AQM is described by a second-order system with time delay. First, the analytical approach, based on the D-decomposition method and Lemma of Kharitonov, is used to determine the stabilizing regions of a firstorder controller. Second, the optimal parameters of the controller are obtained by the PSO algorithm. Finally, the proposed method is implemented in the Network Simulator NS-2 and compared with the PI controller.

Keywords: AQM, first-order controller, time delay, stability, PSO.

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Authors: Aniruddha Bhattacharya, Pranab Kumar Chattopadhyay

Abstract:

Optimal reactive power flow is an optimization problem with one or more objective of minimizing the active power losses for fixed generation schedule. The control variables are generator bus voltages, transformer tap settings and reactive power output of the compensating devices placed on different bus bars. Biogeography- Based Optimization (BBO) technique has been applied to solve different kinds of optimal reactive power flow problems subject to operational constraints like power balance constraint, line flow and bus voltages limits etc. BBO searches for the global optimum mainly through two steps: Migration and Mutation. In the present work, BBO has been applied to solve the optimal reactive power flow problems on IEEE 30-bus and standard IEEE 57-bus power systems for minimization of active power loss. The superiority of the proposed method has been demonstrated. Considering the quality of the solution obtained, the proposed method seems to be a promising one for solving these problems.

Keywords: Active Power Loss, Biogeography-Based Optimization, Migration, Mutation, Optimal Reactive Power Flow.

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Authors: R. Srinivasa Rao

Abstract:

This paper presents a new and efficient approach for capacitor placement in radial distribution systems that determine the optimal locations and size of capacitor with an objective of improving the voltage profile and reduction of power loss. The solution methodology has two parts: in part one the loss sensitivity factors are used to select the candidate locations for the capacitor placement and in part two a new algorithm that employs Plant growth Simulation Algorithm (PGSA) is used to estimate the optimal size of capacitors at the optimal buses determined in part one. The main advantage of the proposed method is that it does not require any external control parameters. The other advantage is that it handles the objective function and the constraints separately, avoiding the trouble to determine the barrier factors. The proposed method is applied to 9 and 34 bus radial distribution systems. The solutions obtained by the proposed method are compared with other methods. The proposed method has outperformed the other methods in terms of the quality of solution.

Keywords: Distribution systems, Capacitor allocation, Loss reduction, Fuzzy, PGSA.

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Authors: R. Srinivasa Rao, S. V. L. Narasimham

Abstract:

This paper presents a new and efficient approach for capacitor placement in radial distribution systems that determine the optimal locations and size of capacitor with an objective of improving the voltage profile and reduction of power loss. The solution methodology has two parts: in part one the loss sensitivity factors are used to select the candidate locations for the capacitor placement and in part two a new algorithm that employs Plant growth Simulation Algorithm (PGSA) is used to estimate the optimal size of capacitors at the optimal buses determined in part one. The main advantage of the proposed method is that it does not require any external control parameters. The other advantage is that it handles the objective function and the constraints separately, avoiding the trouble to determine the barrier factors. The proposed method is applied to 9, 34, and 85-bus radial distribution systems. The solutions obtained by the proposed method are compared with other methods. The proposed method has outperformed the other methods in terms of the quality of solution.

Keywords: Distribution systems, Capacitor placement, loss reduction, Loss sensitivity factors, PGSA.

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Authors: Y. Wang

Abstract:

Traveling salesman problem (TSP) is hard to resolve when the number of cities and routes become large. The frequency graph is constructed to tackle the problem. A frequency graph maintains the topological relationships of the original weighted graph. The numbers on the edges are the frequencies of the edges emulated from the local optimal Hamiltonian paths. The simplest kind of local optimal Hamiltonian paths are computed based on the four vertices and three lines inequality. The search algorithm is given to find the optimal Hamiltonian circuit based on the frequency graph. The experiments show that the method can find the optimal Hamiltonian circuit within several trials.

Keywords: Traveling salesman problem, frequency graph, local optimal Hamiltonian path, four vertices and three lines inequality.

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Authors: R.Narmatha Banu, D.Devaraj

Abstract:

This paper presents a genetic algorithm based approach for solving security constrained optimal power flow problem (SCOPF) including FACTS devices. The optimal location of FACTS devices are identified using an index called overload index and the optimal values are obtained using an enhanced genetic algorithm. The optimal allocation by the proposed method optimizes the investment, taking into account its effects on security in terms of the alleviation of line overloads. The proposed approach has been tested on IEEE-30 bus system to show the effectiveness of the proposed algorithm for solving the SCOPF problem.

Keywords: Optimal Power Flow, Genetic Algorithm, FlexibleAC transmission system (FACTS) devices, Severity Index (SI), Security Enhancement, Thyristor controlled series capacitor (TCSC).

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Authors: M. Mohebbi, K. Shakeri

Abstract:

Since the actuator capacity is limited, in the real application of active control systems under sever earthquakes it is conceivable that the actuators saturate, hence the actuator saturation should be considered as a constraint in design of optimal controllers. In this paper optimal design of active controllers for nonlinear structures by considering actuator saturation, has been studied. The proposed method for designing optimal controllers is based on defining an optimization problem which the objective has been to minimize the maximum displacement of structure when a limited capacity for actuator has been used. To this end a single degree of freedom (SDF) structure with a bilinear hysteretic behavior has been simulated under a white noise ground acceleration of different amplitudes. Active tendon control mechanism, comprised of prestressed tendons and an actuator, and extended nonlinear Newmark method based instantaneous optimal control algorithm have been used. To achieve the best results, the weights corresponding to displacement, velocity, acceleration and control force in the performance index have been optimized by the Distributed Genetic Algorithm (DGA). Results show the effectiveness of the proposed method in considering actuator saturation. Also based on the numerical simulations it can be concluded that the actuator capacity and the average value of required control force are two important factors in designing nonlinear controllers which consider the actuator saturation.

Keywords: Active control, Actuator Saturation, Distributedgeneticalgorithms, Nonlinear.

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Authors: Hitoshi Takata, Tomohiro Hachino, Masaki Horai, Kazuo Komatsu

Abstract:

In this paper, we are concerned with the design and its simulation studies of a modified extremum seeking control for nonlinear systems. A standard extremum seeking control has a simple structure, but it takes a long time to reach an optimal operating point. We consider a modification of the standard extremum seeking control which is aimed to reach the optimal operating point more speedily than the standard one. In the modification, PD acceleration term is added before an integrator making a principal control, so that it enables the objects to be regulated to the optimal point smoothly. This proposed method is applied to Monod and Williams-Otto models to investigate its effectiveness. Numerical simulation results show that this modified method can improve the time response to the optimal operating point more speedily than the standard one.

Keywords: Extremum seeking control, Monod model, Williams- Otto model, PD acceleration term, Optimal operating point.

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Authors: Christian Rathgeber, Franz Winkler, Xiaoyu Kang, Steffen Müller

Abstract:

In this contribution two approaches for calculating optimal trajectories for highly automated vehicles are presented and compared. The first one is based on a non-linear vehicle model, used for evaluation. The second one is based on a simplified model and can be implemented on a current ECU. In usual driving situations both approaches show very similar results.

Keywords: Trajectory planning, direct method, indirect method, highly automated driving.

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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Authors: Sorawit Stapornchaisit, Sidshchadhaa Aumted, Hiroshi Takami

Abstract:

In this paper, we propose a novel adaptive voltage control strategy for boost converter via Inverse LQ Servo-Control. Our presented strategy is based on an analytical formula of Inverse Linear Quadratic (ILQ) design method, which is not necessary to solve Riccati’s equation directly. The optimal and adaptive controller of the voltage control system is designed. The stability and the robust control are analyzed. Whereas, we can get the analytical solution for the optimal and robust voltage control is achieved through the natural angular velocity within a single parameter and we can change the responses easily via the ILQ control theory. Our method provides effective results as the stable responses and the response times are not drifted even if the condition is changed widely.

Keywords: Boost converter, optimal voltage control, inverse LQ design method, type-1 servo-system, adaptive control.

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Authors: Zia R. Tahir, P. Mandal

Abstract:

A numerical study is presented on buckling and post buckling behaviour of laminated carbon fiber reinforced plastic (CFRP) thin-walled cylindrical shells under axial compression using asymmetric meshing technique (AMT). Asymmetric meshing technique is a perturbation technique to introduce disturbance without changing geometry, boundary conditions or loading conditions. Asymmetric meshing affects predicted buckling load, buckling mode shape and post-buckling behaviour. Linear (eigenvalue) and nonlinear (Riks) analyses have been performed to study the effect of asymmetric meshing in the form of a patch on buckling behaviour. The reduction in the buckling load using Asymmetric meshing technique was observed to be about 15%. An isolated dimple formed near the bifurcation point and the size of which increased to reach a stable state in the post-buckling region. The load-displacement curve behaviour applying asymmetric meshing is quite similar to the curve obtained using initial geometric imperfection in the shell model.

Keywords: CFRP Composite Cylindrical Shell, Finite Element Analysis, Perturbation Technique, Asymmetric Meshing Technique, Linear Eigenvalue analysis, Non-linear Riks Analysis

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Authors: Peter Benneth, Tsaroh N. Theophilus, Prince Benjamin

Abstract:

This research work aims at studying the application of Legendre Transformation Method (LTM) to Hamilton Jacobi Bellman (HJB) equation which is an example of optimal control problem. We discuss the steps involved in modelling the HJB equation as it relates to mathematical finance by applying the Ito’s lemma and maximum principle theorem. By applying the LTM and dual theory, the resultant HJB equation is transformed to a linear Partial Differential Equation (PDE). Also, the Optimal Investment Strategy (OIS) and the optimal value function were obtained under the exponential utility function. Furthermore, some numerical results were also presented with observations that the OIS under exponential utility is directly proportional to the appreciation rate of the risky asset and inversely proportional to the instantaneous volatility, predetermined interest rate, risk averse coefficient. Finally, it was observed that the optimal fund size is an increasing function of the risk free interest rate. This result is consistent with some existing results.

Keywords: Legendre transformation method, Optimal investment strategy, Ito’s lemma, Hamilton Jacobi Bellman equation, Geometric Brownian motion, financial market.

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Authors: Siliang Wang, Minghui Wang, Jun Hu

Abstract:

A novel path planning approach is presented to solve optimal path in stochastic, time-varying networks under priori traffic information. Most existing studies make use of dynamic programming to find optimal path. However, those methods are proved to be unable to obtain global optimal value, moreover, how to design efficient algorithms is also another challenge. This paper employs a decision theoretic framework for defining optimal path: for a given source S and destination D in urban transit network, we seek an S - D path of lowest expected travel time where its link travel times are discrete random variables. To solve deficiency caused by the methods of dynamic programming, such as curse of dimensionality and violation of optimal principle, an integer programming model is built to realize assignment of discrete travel time variables to arcs. Simultaneously, pruning techniques are also applied to reduce computation complexity in the algorithm. The final experiments show the feasibility of the novel approach.

Keywords: pruning method, stochastic, time-varying networks, optimal path planning.

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Authors: K. Varesi

Abstract:

This paper proposes a Particle Swarm Optimization (PSO) based technique for the optimal allocation of Distributed Generation (DG) units in the power systems. In this paper our aim is to decide optimal number, type, size and location of DG units for voltage profile improvement and power loss reduction in distribution network. Two types of DGs are considered and the distribution load flow is used to calculate exact loss. Load flow algorithm is combined appropriately with PSO till access to acceptable results of this operation. The suggested method is programmed under MATLAB software. Test results indicate that PSO method can obtain better results than the simple heuristic search method on the 30-bus and 33- bus radial distribution systems. It can obtain maximum loss reduction for each of two types of optimally placed multi-DGs. Moreover, voltage profile improvement is achieved.

Keywords: Distributed Generation (DG), Optimal Allocation, Particle Swarm Optimization (PSO), Power Loss Minimization, Voltage Profile Improvement.

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Authors: K. Balamurugan, R. Muralisachithanandam, V. Dharmalingam, R. Srikanth

Abstract:

This paper deals with the optimal choice and allocation of multi FACTS devices in Deregulated power system using Evolutionary Programming method. The objective is to achieve the power system economic generation allocation and dispatch in deregulated electricity market. Using the proposed method, the locations of the FACTS devices, their types and ratings are optimized simultaneously. Different kinds of FACTS devices are simulated in this study such as UPFC, TCSC, TCPST, and SVC. Simulation results validate the capability of this new approach in minimizing the overall system cost function, which includes the investment costs of the FACTS devices and the bid offers of the market participants. The proposed algorithm is an effective and practical method for the choice and allocation of FACTS devices in deregulated electricity market environment. The standard data of IEEE 14 Bus systems has been taken into account and simulated with aid of MAT-lab software and results were obtained.

Keywords: FACTS devices, Optimal allocation, Deregulated electricity market, Evolutionary programming, Mat Lab.

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Authors: Satyendra Pratap Singh, S. P. Singh

Abstract:

This paper presents a methodology using Gravitational Search Algorithm for optimal placement of Phasor Measurement Units (PMUs) in order to achieve complete observability of the power system. The objective of proposed algorithm is to minimize the total number of PMUs at the power system buses, which in turn minimize installation cost of the PMUs. In this algorithm, the searcher agents are collection of masses which interact with each other using Newton’s laws of gravity and motion. This new Gravitational Search Algorithm based method has been applied to the IEEE 14-bus, IEEE 30-bus and IEEE 118-bus test systems. Case studies reveal optimal number of PMUs with better observability by proposed method.

Keywords: Gravitational Search Algorithm (GSA), Law of Motion, Law of Gravity, Observability, Phasor Measurement Unit.

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Authors: R. Oloomi, M. A. Sadrnia

Abstract:

This paper proposes a new optimal feedback controller for voltage source converters VSC's, for current regulated voltage source converters, which allows compensate the harmonics of current produced by nonlinear loads and load reactive power. The aim of the present paper is to describe a novel switching signal generation technique called optimal controller which guarantees that the injected currents follow the reference currents determined by the compensation strategy, with the smallest possible tracking error and fixed switching frequency. It is compared with well-known hysteresis current controller HCC. The validity of presented method and its comparison with HCC is studied through simulation results.

Keywords: Hysteresis Current Controller, Optimal Controller, Switching pattern, Voltage Source Converter.

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Authors: Jin-O Kim, Hyun-Il Son

Abstract:

As the electrical power industry is restructured, the electrical power exchange is becoming extended. One of the key information used to determine how much power can be transferred through the network is known as available transfer capability (ATC). To calculate ATC, traditional deterministic approach is based on the severest case, but the approach has the complexity of procedure. Therefore, novel approach for ATC calculation is proposed using cost-optimization method in this paper, and is compared with well-being method and risk-benefit method. This paper proposes the optimal transfer capability of HVDC system between mainland and a separated island in Korea through these three methods. These methods will consider production cost, wheeling charge through HVDC system and outage cost with one depth (N-1 contingency)

Keywords: ATC, power system interconnection, well-being method, cost-optimization method, risk-benefit analysis, outage cost.

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Authors: Gayadhar Panda, Sidhartha Panda, C. Ardil

Abstract:

A modified Genetic Algorithm (GA) based optimal selection of parameters for Automatic Generation Control (AGC) of multi-area electric energy systems is proposed in this paper. Simulations on multi-area reheat thermal system with and without consideration of nonlinearity like governor dead band followed by 1% step load perturbation is performed to exemplify the optimum parameter search. In this proposed method, a modified Genetic Algorithm is proposed where one point crossover with modification is employed. Positional dependency in respect of crossing site helps to maintain diversity of search point as well as exploitation of already known optimum value. This makes a trade-off between exploration and exploitation of search space to find global optimum in less number of generations. The proposed GA along with decomposition technique as developed has been used to obtain the optimum megawatt frequency control of multi-area electric energy systems. Time-domain simulations are conducted with trapezoidal integration along with decomposition technique. The superiority of the proposed method over existing one is verified from simulations and comparisons.

Keywords: Automatic Generation Control (AGC), Reheat, Proportional Integral (PI) controller, Dead Band, Genetic Algorithm(GA).

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Authors: A. Puras Trueba, J. R. Llata García

Abstract:

A nonlinear optimal controller with a fuzzy gain scheduler has been designed and applied to a Line-Of-Sight (LOS) stabilization system. Use of Linear Quadratic Regulator (LQR) theory is an optimal and simple manner of solving many control engineering problems. However, this method cannot be utilized directly for multigimbal LOS systems since they are nonlinear in nature. To adapt LQ controllers to nonlinear systems at least a linearization of the model plant is required. When the linearized model is only valid within the vicinity of an operating point a gain scheduler is required. Therefore, a Takagi-Sugeno Fuzzy Inference System gain scheduler has been implemented, which keeps the asymptotic stability performance provided by the optimal feedback gain approach. The simulation results illustrate that the proposed controller is capable of overcoming disturbances and maintaining a satisfactory tracking performance.

Keywords: Fuzzy Gain-Scheduling, Gimbal, Line-Of-SightStabilization, LQR, Optimal Control

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Authors: Aiman Elragig, Hanan Dreiwi, Dung Ly, Idriss Elmabrook

Abstract:

This paper highlights a new approach to look at online principle components analysis (OPCA). Given a data matrix X ∈ R,^m x n we characterise the online updates of its covariance as a matrix perturbation problem. Up to the principle components, it turns out that online updates of the batch PCA can be captured by symmetric matrix perturbation of the batch covariance matrix. We have shown that as n→ n0 >> 1, the batch covariance and its update become almost similar. Finally, utilize our new setup of online updates to find a bound on the angle distance of the principle components of X and its update.

Keywords: Online data updates, covariance matrix, online principle component analysis (OPCA), matrix perturbation.

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Authors: H. Shayeghi, B. Mohamadi

Abstract:

This paper presents a possibilistic (fuzzy) model in optimal siting and sizing of Distributed Generation (DG) for loss reduction and improve voltage profile in power distribution system. Multi-objective problem is developed in two phases. In the first one, the set of non-dominated planning solutions is obtained (with respect to the objective functions of fuzzy economic cost, and exposure) using genetic algorithm. In the second phase, one solution of the set of non-dominated solutions is selected as optimal solution, using a suitable max-min approach. This method can be determined operation-mode (PV or PQ) of DG. Because of considering load uncertainty in this paper, it can be obtained realistic results. The whole process of this method has been implemented in the MATLAB7 environment with technical and economic consideration for loss reduction and voltage profile improvement. Through numerical example the validity of the proposed method is verified.

Keywords: Fuzzy Power Flow, DG siting and sizing, LoadUncertainty, Multi-objective Possibilistic Model.

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Authors: S. Swain, P. S. Khuntia

Abstract:

In this paper an optimal convex controller is designed to control the angle of attack of a FOXTROT aircraft. Then the order of the system model is reduced to a low-dimensional state space by using Balanced Truncation Model Reduction Technique and finally the robust stability of the reduced model of the system is tested graphically by using Kharitonov rectangle and Zero Exclusion Principle for a particular range of perturbation value. The same robust stability is tested theoretically by using Frequency Sweeping Function for robust stability.

Keywords: Convex Optimization, Kharitonov Stability Criterion, Model Reduction, Robust Stability.

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Authors: Yohei Saika, Hiroki Sakaematsu, Shota Akiyama

Abstract:

We investigated statistical performance of Bayesian inference using maximum entropy and MAP estimation for several models which approximated wave-fronts in remote sensing using SAR interferometry. Using Monte Carlo simulation for a set of wave-fronts generated by assumed true prior, we found that the method of maximum entropy realized the optimal performance around the Bayes-optimal conditions by using model of the true prior and the likelihood representing optical measurement due to the interferometer. Also, we found that the MAP estimation regarded as a deterministic limit of maximum entropy almost achieved the same performance as the Bayes-optimal solution for the set of wave-fronts. Then, we clarified that the MAP estimation perfectly carried out phase unwrapping without using prior information, and also that the MAP estimation realized accurate phase unwrapping using conjugate gradient (CG) method, if we assumed the model of the true prior appropriately.

Keywords: Bayesian inference using maximum entropy, MAP estimation using conjugate gradient method, SAR interferometry.

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Authors: S. Sadallah

Abstract:

In this paper, dynamic programming is used to determine the optimal management of financial resources in company. Solution of the problem by consider into simpler substructures is constructed. The optimal management of internal capital of company are simulated. The tools applied in this development are based on graph theory. The software of given problems is built by using greedy algorithm. The obtained model and program maintenance enable us to define the optimal version of management of proper financial flows by using visual diagram on each level of investment.

Keywords: Management, software, optimal, greedy algorithm, graph-diagram.

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Authors: Amit Kumar, Manjot Kaur

Abstract:

In this paper, the fuzzy linear programming formulation of fuzzy maximal flow problems are proposed and on the basis of the proposed formulation a method is proposed to find the fuzzy optimal solution of fuzzy maximal flow problems. In the proposed method all the parameters are represented by triangular fuzzy numbers. By using the proposed method the fuzzy optimal solution of fuzzy maximal flow problems can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed.

Keywords: Fuzzy linear programming, Fuzzy maximal flow problem, Ranking function, Triangular fuzzy number

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Authors: Yongxin Yuan, Jiashang Jiang

Abstract:

A new numerical method for simultaneously updating mass and stiffness matrices based on incomplete modal measured data is presented. By using the Kronecker product, all the variables that are to be modified can be found out and then can be updated directly. The optimal approximation mass matrix and stiffness matrix which satisfy the required eigenvalue equation and orthogonality condition are found under the Frobenius norm sense. The physical configuration of the analytical model is preserved and the updated model will exactly reproduce the modal measured data. The numerical example seems to indicate that the method is quite accurate and efficient.

Keywords: Finite element model, model updating, modal data, optimal approximation.

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