226 research outputs found
ANCILLARY SERVICE REQUIREMENT BASED AUTOMATIC GENERATION CONTROL ASSESSMENT IN A DEREGULATED POWER SYSTEM WITH HES AND IPFC UNITS
This paper intends the evaluation measures for obtaining the Ancillary ServicesRequirement (ASR) indices stand on Automatic Generation Control (AGC) in a deregulated power system.Ancillary services are vital to support the transmission of electric power from vendor to user with the responsibility of control areas and transmitting utilities within those control areas to maintain steadfast operations of the interconnected power system under deregulated environment. In this swot, Proportional Integral Derivative with derivative Filter (PIDF) is projected for the AGC loop of a two-area thermal power system with reheat bicycle mix condensation turbine. The control constraints of the PIDF controller are optimized using the Big Bang Big Crunch (BBBC) algorithm.ASR keys are computed stranded on the dynamic response of the control input deviations and the mechanical power generation deviations of each area for dissimilar nature of possible transactions. These indices designate the ancillary service requirements and are required to improve the competence of the physical operation of the power system with the augmented transmission capacity in the network. An advanced application of Hydrogen Energy Storage (HES), when coordinated with the Interline Power Flow Controller (IPFC) for the development of AGC loop of a two-area thermal power system is also painstaking. Simulation reveals that the proposed PIDF controller tuned with BBBC algorithm perk up the dynamic output response of the test system. Moreover, it can also be pragmatic that the ASR Indices are computed for a two-area thermal power system with HES and IPFC units indicates that the new advanced control for a better restoration of the power system output responses and ensure enhanced ASR indices in order to afford the superior margin of steadiness
Impact of coordination of intertie transformer tap changers on active power losses assessed by Big Bang Big Crunch algorithm
Abstract: Power utilities worldwide face significant technical power losses. There are two categories of power losses: technical and non-technical losses. Technical losses occur on the transmission and distribution lines, transformer windings, and capacitors. These include active power losses which are caused by resistive components and reactive power losses which are caused by reactive components. Transformer tap changers play a key role in the minimization of power losses. Many researchers have already investigated the effect of transformer tap changers on power systems. However, none of their publications have assessed the impact of transformer tap changers on power flows in the context of interties to minimize active power losses using BBBC algorithm. The aim of this study is to assess the impact of intertie transformer tap changers on active power losses using BBBC algorithm...M.Phil. (Electrical Engineering in Power and Energy Systems
A Fuzzy Logic-Based System for Soccer Video Scenes Classification
Massive global video surveillance worldwide captures data but lacks detailed activity information to flag events of interest, while the human burden of monitoring video footage is untenable. Artificial intelligence (AI) can be applied to raw video footage to identify and extract required information and summarize it in linguistic formats. Video summarization automation usually involves text-based data such as subtitles, segmenting text and semantics, with little attention to video summarization in the processing of video footage only. Classification problems in recorded videos are often very complex and uncertain due to the dynamic nature of the video sequence and light conditions, background, camera angle, occlusions, indistinguishable scene features, etc.
Video scene classification forms the basis of linguistic video summarization, an open research problem with major commercial importance. Soccer video scenes present added challenges due to specific objects and events with similar features (e.g. βpeopleβ include audiences, coaches, and players), as well as being constituted from a series of quickly changing and dynamic frames with small inter-frame variations. There is an added difficulty associated with the need to have light weight video classification systems working in real time with massive data sizes.
In this thesis, we introduce a novel system based on Interval Type-2 Fuzzy Logic Classification Systems (IT2FLCS) whose parameters are optimized by the Big BangβBig Crunch (BB-BC) algorithm, which allows for the automatic scenes classification using optimized rules in broadcasted soccer matches video. The type-2 fuzzy logic systems would be unequivocal to present a highly interpretable and transparent model which is very suitable for the handling the encountered uncertainties in video footages and converting the accumulated data to linguistic formats which can be easily stored and analysed. Meanwhile the traditional black box techniques, such as support vector machines (SVMs) and neural networks, do not provide models which could be easily analysed and understood by human users. The BB-BC optimization is a heuristic, population-based evolutionary approach which is characterized by the ease of implementation, fast convergence and low computational cost. We employed the BB-BC to optimize our system parameters of fuzzy logic membership functions and fuzzy rules. Using the BB-BC we are able to balance the system transparency (through generating a small rule set) together with increasing the accuracy of scene classification. Thus, the proposed fuzzy-based system allows achieving relatively high classification accuracy with a small number of rules thus increasing the system interpretability and allowing its real-time processing. The type-2 Fuzzy Logic Classification System (T2FLCS) obtained 87.57% prediction accuracy in the scene classification of our testing group data which is better than the type-1 fuzzy classification system and neural networks counterparts. The BB-BC optimization algorithms decrease the size of rule bases both in T1FLCS and T2FLCS; the T2FLCS finally got 85.716% with reduce rules, outperforming the T1FLCS and neural network counterparts, especially in the βout-of-range dataβ which validates the T2FLCSs capability to handle the high level of faced uncertainties.
We also presented a novel approach based on the scenes classification system combined with the dynamic time warping algorithm to implement the video events detection for real world processing. The proposed system could run on recorded or live video clips and output a label to describe the event in order to provide the high level summarization of the videos to the user
Investigations on performance enhancement measures of the bidirectional converter in PVβwind interconnected microgrid system
This is the final version. Available from MDPI via the DOI in this record.β―In this work, a hybrid microgrid framework was created with the assistance of a photovoltaic (PV) and wind turbine (WT) generator. Additionally, bidirectional control mechanisms were implemented where an AC system was integrated with permanent magnet synchronous generator (PMSG)-based WT and a DC system was integrated with a sliding mode algorithm controlled maximum power point tracker (MPPT)-integrated PV system. The wind and PV interconnected microgrid system was mathematically modeled for steady-state conditions. This hybrid microgrid model was simulated using the MATLAB/SIMULINK platform. Optimal load management strategy was performed on a chosen hybrid microgrid system. Various case studies pertaining to connection and disconnection of sources and loads were performed on the test system. The outcomes establish that the system can be kept up in a steady-state condition under the recommended control plans when the network is changed, starting with one working condition then onto the next
Optimum design of steel building structures using migration-based vibrating particles system
Acknowledgment This research is supported by a research grant of the University of Tabriz (Number: 1615). We sincerely express our gratitude to Assoc. Prof. Saeid Kazemzadeh Azad for providing the required data for the design examples.Peer reviewedPostprin
Optimization-Based Evolutionary Data Mining Techniques for Structural Health Monitoring
In recent years, data mining technology has been employed to solve various Structural Health Monitoring (SHM) problems as a comprehensive strategy because of its computational capability. Optimization is one the most important functions in Data mining. In an engineering optimization problem, it is not easy to find an exact solution. In this regard, evolutionary techniques have been applied as a part of procedure of achieving the exact solution. Therefore, various metaheuristic algorithms have been developed to solve a variety of engineering optimization problems in SHM. This study presents the most applicable as well as effective evolutionary techniques used in structural damage identification. To this end, a brief overview of metaheuristic techniques is discussed in this paper. Then the most applicable optimization-based algorithms in structural damage identification are presented, i.e. Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Imperialist Competitive Algorithm (ICA) and Ant Colony Optimization (ACO). Some related examples are also detailed in order to indicate the efficiency of these algorithms
Load frequency control scheme for a microgrid system with the application of hTLO-DE algorithm
Load frequency control (LFC) is a crucial feature of electric power systems to maintain a balance between power supply and load demand, thus avoiding a deviation of the grid frequency. The present work aims to implement an effective LFC scheme for a microgrid system consisting of a diesel generator (DEG), a wind turbine generator (WTG) and a battery storage system. Proportional-integral-double-derivative (PIDD) controllers are used to implement the proposed LFC scheme. The controller parameters are computed using an innovative hybrid teaching-learning-optimization differential-evaluation (hTLO-DE) algorithm. The main scope of the work lies in application of hTLO-DE optimized PIDD controllers in DEG-WTG-battery storage based MG system. The results obtained with PIDD controllers are compared with those obtained with the traditional PI and PID controllers. A critical analysis shows that the PIDD controller can provide better dynamic responses in terms of settling time and magnitude of oscillations compared to PI and PID controllers. The frequency responses of the system are studied under different scenarios of generation and load variations, which establishes the robustness of the proposed PIDD-based LFC scheme
Load frequency control of multi area interconnected power system using differential evolution algorithm
In this paper, Proportional Integral Derivative (PID) controller is designed using Differential Evolution (DE) algorithm to Load Frequency Control (LFC) in three areas of an interconnected power system. The proposed controller has appropriate dynamic response, so it increases damping in transient state in unhealthy conditions. Different generators have been used in three areas. Area 1 includes thermal non-reheat generator and two thermal reheat generators; area 2 includes hydro and thermal non-reheat generators, and area 3 includes hydro and thermal reheat generators. In order to evaluate the performance of the controller, Sim/Matlab software is used. Simulation results show that the controller designed using DE algorithm is not affected by load changes, disturbance, or system parameters changes. Comparing the results of proposed algorithm with other load frequency control algorithms, such as PSO and GA, it has been found that this method has a more appropriate response and satisfactory performance
Reactive power control in micro-grid networks using adaptive control
Purpose. Despite their economic and environmental benefits, distributed products in power systems have caused problems in power systems. One of the most important issues in this regard is voltage fluctuations and frequencies in Micro-grids, which depends on several factors, such as variable consumption load and errors in powersystems. One of the main challenges associated with the use of Micro-grids is power management among distributed generation sources. Power management plays a pivotal role in numerous Micro-grids and may ensure the stable and improved performance of Micro-grids in the permanent status of the system. The present study aimed to examine the power control in Micro-grids by proposing an adaptive control method along with the PID controller for power management and coordination in Micro-grids. This coordination system operates between production sources and controlling the voltage and frequency levels against the possible disturbances occurring anywhere in the system loop. The results of the simulation of the proposed algorithm in MATLAB software environment exhibited a high success rate (i.e., proper response to the fluctuations in the Micro-grid) and extremely low error rate (i.e., proper reactive power in the grid).Π¦Π΅Π»Ρ. ΠΠ΅ΡΠΌΠΎΡΡΡ Π½Π° ΠΈΡ
ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈ ΡΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΡΠ΅ΠΈΠΌΡΡΠ΅ΡΡΠ²Π°, ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠ΅ ΠΏΡΠΎΠ΄ΡΠΊΡΡ Π² ΡΠ½Π΅ΡΠ³ΠΎΡΠΈΡΡΠ΅ΠΌΠ°Ρ
ΠΏΡΠΈΠ²ΠΎΠ΄ΡΡ ΠΊ Π²ΠΎΠ·Π½ΠΈΠΊΠ½ΠΎΠ²Π΅Π½ΠΈΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌ Π² ΠΏΠΎΡΠ»Π΅Π΄Π½ΠΈΡ
. ΠΠ΄Π½ΠΈΠΌ ΠΈΠ· Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ Π²Π°ΠΆΠ½ΡΡ
Π²ΠΎΠΏΡΠΎΡΠΎΠ² Π² ΡΡΠΎΠΉ ΡΠ²ΡΠ·ΠΈ ΡΠ²Π»ΡΡΡΡΡ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΡ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΡ ΠΈ ΡΠ°ΡΡΠΎΡΡ Π² ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΡΡ
, ΠΊΠΎΡΠΎΡΡΠ΅ Π·Π°Π²ΠΈΡΡΡ ΠΎΡ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΈΡ
ΡΠ°ΠΊΡΠΎΡΠΎΠ², ΡΠ°ΠΊΠΈΡ
ΠΊΠ°ΠΊ ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½Π°Ρ Π½Π°Π³ΡΡΠ·ΠΊΠ° ΠΏΠΎΡΡΠ΅Π±Π»Π΅Π½ΠΈΡ ΠΈ ΠΎΡΠΈΠ±ΠΊΠΈ Π² ΡΠ½Π΅ΡΠ³ΠΎΡΠΈΡΡΠ΅ΠΌΠ°Ρ
. ΠΠ΄Π½ΠΎΠΉ ΠΈΠ· ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΠΏΡΠΎΠ±Π»Π΅ΠΌ, ΡΠ²ΡΠ·Π°Π½Π½ΡΡ
Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΠ΅ΠΉ, ΡΠ²Π»ΡΠ΅ΡΡΡ ΡΠ½Π΅ΡΠ³ΠΎ-ΠΌΠ΅Π½Π΅Π΄ΠΆΠΌΠ΅Π½Ρ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠΎΠ² ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΠΉ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ. ΠΠ½Π΅ΡΠ³ΠΎ-ΠΌΠ΅Π½Π΅Π΄ΠΆΠΌΠ΅Π½Ρ ΠΈΠ³ΡΠ°Π΅Ρ ΠΊΠ»ΡΡΠ΅Π²ΡΡ ΡΠΎΠ»Ρ Π²ΠΎ ΠΌΠ½ΠΎΠ³ΠΈΡ
ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΡΡ
ΠΈ ΠΌΠΎΠΆΠ΅Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΡΡ ΡΡΠ°Π±ΠΈΠ»ΡΠ½ΡΡ ΠΈ ΡΠ»ΡΡΡΠ΅Π½Π½ΡΡ ΡΠ°Π±ΠΎΡΡ ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΠ΅ΠΉ ΠΏΡΠΈ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠΌ ΡΠΎΡΡΠΎΡΠ½ΠΈΠΈ ΡΠΈΡΡΠ΅ΠΌΡ. ΠΠ°ΡΡΠΎΡΡΠ΅Π΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΎ Π½Π° ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ½Π΅ΡΠ³ΠΎ-ΠΌΠ΅Π½Π΅Π΄ΠΆΠΌΠ΅Π½ΡΠ° Π² ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΡΡ
ΠΏΡΡΠ΅ΠΌ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΈΡ Π°Π΄Π°ΠΏΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π²ΠΌΠ΅ΡΡΠ΅ Ρ ΠΠΠ-ΠΊΠΎΠ½ΡΡΠΎΠ»Π»Π΅ΡΠΎΠΌ Π΄Π»Ρ ΡΠ½Π΅ΡΠ³ΠΎ-ΠΌΠ΅Π½Π΅Π΄ΠΆΠΌΠ΅Π½ΡΠ° ΠΈ ΠΊΠΎΠΎΡΠ΄ΠΈΠ½Π°ΡΠΈΠΈ Π² ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΡΡ
. ΠΡΠ° ΡΠΈΡΡΠ΅ΠΌΠ° ΠΊΠΎΠΎΡΠ΄ΠΈΠ½Π°ΡΠΈΠΈ ΡΡΠ½ΠΊΡΠΈΠΎΠ½ΠΈΡΡΠ΅Ρ ΠΌΠ΅ΠΆΠ΄Ρ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ°ΠΌΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΠΌΠΎΠΉ ΡΠ½Π΅ΡΠ³ΠΈΠΈ ΠΈ ΠΊΠΎΠ½ΡΡΠΎΠ»ΠΈΡΡΠ΅Ρ ΡΡΠΎΠ²Π½ΠΈ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΡ ΠΈ ΡΠ°ΡΡΠΎΡΡ Π² ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠΈ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΠΏΠΎΠΌΠ΅Ρ
, Π²ΠΎΠ·Π½ΠΈΠΊΠ°ΡΡΠΈΡ
Π² Π»ΡΠ±ΠΎΠΌ ΠΌΠ΅ΡΡΠ΅ ΠΊΠΎΠ½ΡΡΡΠ° ΡΠΈΡΡΠ΅ΠΌΡ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅ MATLAB ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ Π²ΡΡΠΎΠΊΡΡ ΡΡΠ΅ΠΏΠ΅Π½Ρ ΡΡΠΏΠ΅Ρ
Π°(ΡΠΎ Π΅ΡΡΡ ΠΏΡΠ°Π²ΠΈΠ»ΡΠ½ΡΡ ΡΠ΅Π°ΠΊΡΠΈΡ Π½Π° ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΡ Π² ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΠΈ) ΠΈ ΡΡΠ΅Π·Π²ΡΡΠ°ΠΉΠ½ΠΎ Π½ΠΈΠ·ΠΊΡΡ ΡΠ°ΡΡΠΎΡΡ ΠΎΡΠΈΠ±ΠΎΠΊ(ΡΠΎ Π΅ΡΡΡ Π½Π°Π΄Π»Π΅ΠΆΠ°ΡΡΡ ΡΠ΅Π°ΠΊΡΠΈΠ²Π½ΡΡ ΠΌΠΎΡΠ½ΠΎΡΡΡ Π² ΡΠ΅ΡΠΈ)
REACTIVE POWER CONTROL IN MICRO-GRID NETWORKS USING ADAPTIVE CONTROL
Purpose. Despite their economic and environmental benefits, distributed products in power systems have caused problems in power systems. One of the most important issues in this regard is voltage fluctuations and frequencies in Micro-grids, which depends on several factors, such as variable consumption load and errors in power systems. One of the main challenges associated with the use of Micro-grids is power management among distributed generation sources. Power management plays a pivotal role in numerous Micro-grids and may ensure the stable and improved performance of Micro-grids in the permanent status of the system. The present study aimed to examine the power control in Micro-grids by proposing an adaptive control method along with the PID controller for power management and coordination in Micro-grids. This coordination system operates between production sources and controlling the voltage and frequency levels against the possible disturbances occurring anywhere in the system loop. The results of the simulation of the proposed algorithm in MATLAB software environment exhibited a high success rate (i.e., proper response to the fluctuations in the Micro-grid) and extremely low error rate (i.e., proper reactive power in the grid).Π¦Π΅Π»Ρ. ΠΠ΅ΡΠΌΠΎΡΡΡ Π½Π° ΠΈΡ
ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈ ΡΠΊΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΏΡΠ΅ΠΈΠΌΡΡΠ΅ΡΡΠ²Π°, ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠ΅ ΠΏΡΠΎΠ΄ΡΠΊΡΡ Π² ΡΠ½Π΅ΡΠ³ΠΎΡΠΈΡΡΠ΅ΠΌΠ°Ρ
ΠΏΡΠΈΠ²ΠΎΠ΄ΡΡ ΠΊ Π²ΠΎΠ·Π½ΠΈΠΊΠ½ΠΎΠ²Π΅Π½ΠΈΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌ Π² ΠΏΠΎΡΠ»Π΅Π΄Π½ΠΈΡ
. ΠΠ΄Π½ΠΈΠΌ ΠΈΠ· Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ Π²Π°ΠΆΠ½ΡΡ
Π²ΠΎΠΏΡΠΎΡΠΎΠ² Π² ΡΡΠΎΠΉ ΡΠ²ΡΠ·ΠΈ ΡΠ²Π»ΡΡΡΡΡ ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΡ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΡ ΠΈ ΡΠ°ΡΡΠΎΡΡ Π² ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΡΡ
, ΠΊΠΎΡΠΎΡΡΠ΅ Π·Π°Π²ΠΈΡΡΡ ΠΎΡ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΈΡ
ΡΠ°ΠΊΡΠΎΡΠΎΠ², ΡΠ°ΠΊΠΈΡ
ΠΊΠ°ΠΊ ΠΏΠ΅ΡΠ΅ΠΌΠ΅Π½Π½Π°Ρ Π½Π°Π³ΡΡΠ·ΠΊΠ° ΠΏΠΎΡΡΠ΅Π±Π»Π΅Π½ΠΈΡ ΠΈ ΠΎΡΠΈΠ±ΠΊΠΈ Π² ΡΠ½Π΅ΡΠ³ΠΎΡΠΈΡΡΠ΅ΠΌΠ°Ρ
. ΠΠ΄Π½ΠΎΠΉ ΠΈΠ· ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΠΏΡΠΎΠ±Π»Π΅ΠΌ, ΡΠ²ΡΠ·Π°Π½Π½ΡΡ
Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΠ΅ΠΉ, ΡΠ²Π»ΡΠ΅ΡΡΡ ΡΠ½Π΅ΡΠ³ΠΎΠΌΠ΅Π½Π΅Π΄ΠΆΠΌΠ΅Π½Ρ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠΎΠ² ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΠΉ Π³Π΅Π½Π΅ΡΠ°ΡΠΈΠΈ. ΠΠ½Π΅ΡΠ³ΠΎΠΌΠ΅Π½Π΅Π΄ΠΆΠΌΠ΅Π½Ρ ΠΈΠ³ΡΠ°Π΅Ρ ΠΊΠ»ΡΡΠ΅Π²ΡΡ ΡΠΎΠ»Ρ Π²ΠΎ ΠΌΠ½ΠΎΠ³ΠΈΡ
ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΡΡ
ΠΈ ΠΌΠΎΠΆΠ΅Ρ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠΈΡΡ ΡΡΠ°Π±ΠΈΠ»ΡΠ½ΡΡ ΠΈ ΡΠ»ΡΡΡΠ΅Π½Π½ΡΡ ΡΠ°Π±ΠΎΡΡ ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΠ΅ΠΉ ΠΏΡΠΈ ΠΏΠΎΡΡΠΎΡΠ½Π½ΠΎΠΌ ΡΠΎΡΡΠΎΡΠ½ΠΈΠΈ ΡΠΈΡΡΠ΅ΠΌΡ. ΠΠ°ΡΡΠΎΡΡΠ΅Π΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΎ Π½Π° ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ½Π΅ΡΠ³ΠΎΠΌΠ΅Π½Π΅Π΄ΠΆΠΌΠ΅Π½ΡΠ° Π² ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΡΡ
ΠΏΡΡΠ΅ΠΌ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΈΡ Π°Π΄Π°ΠΏΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π²ΠΌΠ΅ΡΡΠ΅ Ρ ΠΠΠ-ΠΊΠΎΠ½ΡΡΠΎΠ»Π»Π΅ΡΠΎΠΌ Π΄Π»Ρ ΡΠ½Π΅ΡΠ³ΠΎΠΌΠ΅Π½Π΅Π΄ΠΆΠΌΠ΅Π½ΡΠ° ΠΈ ΠΊΠΎΠΎΡΠ΄ΠΈΠ½Π°ΡΠΈΠΈ Π² ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΡΡ
. ΠΡΠ° ΡΠΈΡΡΠ΅ΠΌΠ° ΠΊΠΎΠΎΡΠ΄ΠΈΠ½Π°ΡΠΈΠΈ ΡΡΠ½ΠΊΡΠΈΠΎΠ½ΠΈΡΡΠ΅Ρ ΠΌΠ΅ΠΆΠ΄Ρ ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠ°ΠΌΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΠΈΠΌΠΎΠΉΒ ΡΠ½Π΅ΡΠ³ΠΈΠΈ ΠΈ ΠΊΠΎΠ½ΡΡΠΎΠ»ΠΈΡΡΠ΅Ρ ΡΡΠΎΠ²Π½ΠΈ Π½Π°ΠΏΡΡΠΆΠ΅Π½ΠΈΡ ΠΈ ΡΠ°ΡΡΠΎΡΡ Π² ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠΈ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΡΡ
ΠΏΠΎΠΌΠ΅Ρ
, Π²ΠΎΠ·Π½ΠΈΠΊΠ°ΡΡΠΈΡ
Π² Π»ΡΠ±ΠΎΠΌ ΠΌΠ΅ΡΡΠ΅ ΠΊΠΎΠ½ΡΡΡΠ° ΡΠΈΡΡΠ΅ΠΌΡ. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΠΎΠ³ΠΎ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° Π² ΠΏΡΠΎΠ³ΡΠ°ΠΌΠΌΠ½ΠΎΠΉ ΡΡΠ΅Π΄Π΅ MATLAB ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ Π²ΡΡΠΎΠΊΡΡ ΡΡΠ΅ΠΏΠ΅Π½Ρ ΡΡΠΏΠ΅Ρ
Π° (ΡΠΎ Π΅ΡΡΡ ΠΏΡΠ°Π²ΠΈΠ»ΡΠ½ΡΡ ΡΠ΅Π°ΠΊΡΠΈΡ Π½Π° ΠΊΠΎΠ»Π΅Π±Π°Π½ΠΈΡ Π² ΠΌΠΈΠΊΡΠΎΡΠ΅ΡΠΈ) ΠΈ ΡΡΠ΅Π·Π²ΡΡΠ°ΠΉΠ½ΠΎ Π½ΠΈΠ·ΠΊΡΡ ΡΠ°ΡΡΠΎΡΡ ΠΎΡΠΈΠ±ΠΎΠΊ (ΡΠΎ Π΅ΡΡΡ Π½Π°Π΄Π»Π΅ΠΆΠ°ΡΡΡ ΡΠ΅Π°ΠΊΡΠΈΠ²Π½ΡΡ ΠΌΠΎΡΠ½ΠΎΡΡΡ Π² ΡΠ΅ΡΠΈ)
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