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Multi-Time Scale Operation and Simulation Strategy of the Park Based on Model Predictive Control
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作者 Jun Zhao Chaoying Yang +1 位作者 Ran Li Jinge Song 《Energy Engineering》 EI 2024年第3期747-767,共21页
Due to the impact of source-load prediction power errors and uncertainties,the actual operation of the park will have a wide range of fluctuations compared with the expected state,resulting in its inability to achieve... Due to the impact of source-load prediction power errors and uncertainties,the actual operation of the park will have a wide range of fluctuations compared with the expected state,resulting in its inability to achieve the expected economy.This paper constructs an operating simulation model of the park power grid operation considering demand response and proposes a multi-time scale operating simulation method that combines day-ahead optimization and model predictive control(MPC).In the day-ahead stage,an operating simulation plan that comprehensively considers the user’s side comfort and operating costs is proposed with a long-term time scale of 15 min.In order to cope with power fluctuations of photovoltaic,wind turbine and conventional load,MPC is used to track and roll correct the day-ahead operating simulation plan in the intra-day stage to meet the actual operating operation status of the park.Finally,the validity and economy of the operating simulation strategy are verified through the analysis of arithmetic examples. 展开更多
关键词 Demand response model predictive control multiple time scales operating simulation
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The Impact of Optimizing Details in the Operating Room on the Level of Knowledge, Attitude, and Practice of Hospital Infection Prevention and Control by Surgeons, as Well as the Effectiveness of Infection Control
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作者 Yuanyuan Zhang 《Surgical Science》 2024年第7期421-429,共9页
Objective: This paper aims to explore the impact of optimizing details in the operating room on the level of knowledge, attitude, and practice of hospital infection prevention and control by surgeons, as well as the e... Objective: This paper aims to explore the impact of optimizing details in the operating room on the level of knowledge, attitude, and practice of hospital infection prevention and control by surgeons, as well as the effectiveness of infection control. Methods: From January 2022 to June 2023, a total of 120 patients were screened and randomly divided into a control group (routine care and hospital infection management) and a study group (optimizing details in the operating room). Results: Significant differences were found between the two groups in the data of surgeons’ level of knowledge, attitude, and practice in hospital infection prevention and control, infection rates, and nursing satisfaction, with the study group showing better results (P Conclusion: The use of optimizing details in the operating room among surgeons can effectively improve surgeons’ level of knowledge, attitude, and practice in hospital infection prevention and control, reduce infection occurrence, and is worth promoting. 展开更多
关键词 Optimizing Details in the operating Room Infection Level of Knowledge ATTITUDE and Practice Infection control
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Application of Energy-Saving Materials in Architectural Design
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作者 Yajuan Liu 《Journal of World Architecture》 2024年第3期72-77,共6页
The conventional process of building construction is associated with issues such as the waste of construction materials and environmental pollution.Sustainable development highlights the importance of energy conservat... The conventional process of building construction is associated with issues such as the waste of construction materials and environmental pollution.Sustainable development highlights the importance of energy conservation and eco-friendly practices.It is essential to use energy-efficient and green materials in building designs to ensure the healthy growth of construction companies.This article discusses the advantages and principles of incorporating energy-saving materials in architectural design.It examines the strategies and critical control points for using energy-saving materials in architectural design,offering guidance for the sustainable development of the construction industry. 展开更多
关键词 energy-saving materials Architectural design Advantages control strategy
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Application of Specialized Group Management in the Quality Control of Perioperative Nursing
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作者 Cong Fu Xuefei Li +4 位作者 Li Wang Yuanyuan Jiang Xinrong Qi Chen Ding Shanshan Tang 《Journal of Clinical and Nursing Research》 2024年第2期70-75,共6页
Objective:To explore the role of specialized group management in the quality control of perioperative nursing.Methods:45 surgical nurses from our hospital were selected as the research subjects.Traditional operating r... Objective:To explore the role of specialized group management in the quality control of perioperative nursing.Methods:45 surgical nurses from our hospital were selected as the research subjects.Traditional operating room management was adopted from July 2019 to June 2020,and specialized group management was adopted from July 2020 to June 2021.The surgeon’s satisfaction,surgical nurses’core professional competence,and surgical patients’satisfaction were obtained through surveys and the results were analyzed.Results:Surgeon satisfaction before the implementation of specialized group management was significantly lower than after its implementation(P<0.05).Besides,surgical nurses’core professional competency scores before the implementation of specialized group management were significantly lower than after its implementation(P<0.05).Lastly,surgical patients’satisfaction before the implementation of specialized group management was significantly lower than after its implementation(P<0.05).Conclusion:Specialized group management helps to improve the quality of perioperative care and should be applied in clinical practice. 展开更多
关键词 Specialized group management operating room Quality of care control
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An Intelligent Control Method for the Low-Carbon Operation of Energy-Intensive Equipment
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作者 Tianyou Chai Mingyu Li +3 位作者 Zheng Zhou Siyu Cheng Yao Jia Zhiwei Wu 《Engineering》 SCIE EI CAS CSCD 2023年第8期84-95,共12页
Based on an analysis of the operational control behavior of operation experts on energy-intensive equipment,this paper proposes an intelligent control method for low-carbon operation by combining mechanism analysis wi... Based on an analysis of the operational control behavior of operation experts on energy-intensive equipment,this paper proposes an intelligent control method for low-carbon operation by combining mechanism analysis with deep learning,linking control and optimization with prediction,and integrating decision-making with control.This method,which consists of setpoint control,self-optimized tuning,and tracking control,ensures that the energy consumption per tonne is as low as possible,while remaining within the target range.An intelligent control system for low-carbon operation is developed by adopting the end-edge-cloud collaboration technology of the Industrial Internet.The system is successfully applied to a fused magnesium furnace and achieves remarkable results in reducing carbon emissions. 展开更多
关键词 Energy-intensive equipment Low-carbon operation Intelligent control End-edge-cloud collaboration technology
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Design of Diversified Intelligent Control System for Energy-saving Optimization of Solar Greenhouse in North China
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作者 Yanmeng HE Baohui MA 《Asian Agricultural Research》 2023年第7期45-50,53,共7页
Intelligent greenhouse can promote the development of modern agriculture, realize the high quality and high yield of crops, and also bring greater economic benefits. In accordance with the climate conditions in northw... Intelligent greenhouse can promote the development of modern agriculture, realize the high quality and high yield of crops, and also bring greater economic benefits. In accordance with the climate conditions in northwest China, a set of intelligent control system for diversified environment of solar greenhouse was designed. The system divides the annual greenhouse control into six stages according to the optimal energy saving. It uses modern detection technology to collect the greenhouse environmental temperature, environmental humidity, soil humidity, CO_(2) concentration and illumination parameters under different working modes. It uses programmable logic control technology to realize the data processing of various parameters and the action control of rolling film, wet curtain fan and other actuators. It uses KingView monitoring software to realize the monitoring and manual control of greenhouse environment parameters. The operation results indicate that the control system runs stably and basically meets the control requirements. 展开更多
关键词 Solar greenhouse energy-saving optimization Diversified control Intelligent control
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Operation Control Method of Relay Protection in Flexible DC Distribution Network Compatible with Distributed Power Supply
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作者 Zihan Qi 《Energy Engineering》 EI 2023年第11期2547-2563,共17页
A novel operation control method for relay protection in flexible DC distribution networks with distributed power supply is proposed to address the issue of inaccurate fault location during relay protection,leading to... A novel operation control method for relay protection in flexible DC distribution networks with distributed power supply is proposed to address the issue of inaccurate fault location during relay protection,leading to poor performance.The method combines a fault-tolerant fault location method based on long-term and short-term memory networks to accurately locate the fault section.Then,an operation control method for relay protection based on adaptive weight and whale optimization algorithm(WOA)is used to construct an objective function considering the shortest relay protection action time and the smallest impulse current.The adaptive weight and WOA are employed to obtain the optimal strategy for relay protection operation control,reducing the action time and impulse current.Experimental results demonstrate the effectiveness of the proposed method in accurately locating faults and improving relay protection performance.The longest operation time is reduced by 4.7023 s,and the maximum impulse current is limited to 0.3 A,effectively controlling the impact of large impulse currents and enhancing control efficiency. 展开更多
关键词 Compatible distributed power supply FLEXIBILITY DC distribution network relay protection operation control
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Application Strategy of PLC Technology in Energy-Saving Control of Tunnel Lighting
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作者 Yuling Zhang 《Journal of Electronic Research and Application》 2023年第3期7-12,共6页
In this study,we investigated on the application of planar lightwave circuit(PLC)technology in energy-saving control of tunnel lighting.The application status of PLC in the field of energy saving followed by the neces... In this study,we investigated on the application of planar lightwave circuit(PLC)technology in energy-saving control of tunnel lighting.The application status of PLC in the field of energy saving followed by the necessity of energy saving in tunnel lighting was analyzed.Finally,the application of PLC in tunnel lighting energy-saving control around the three dimensions of system overall architecture design,control scheme,and program control process was investigated.The results showed that the system meets the requirements of control effect,robustness,and visual effect after trial operation,and is suitable for practical applications. 展开更多
关键词 energy-saving tunnel lighting PLC technology control scheme Program control
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Incentive operation characteristics and influence feedback of existing building energy-saving renovation market development
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作者 WANG Feng-hui GUO Han-ding WANG Xing 《Ecological Economy》 2021年第3期186-207,共22页
The quality of the existing building energy-saving renovation market determines the inherent inevitability of incentive,while unique requirements for the incentive should be satisfied by stage characteristics and indi... The quality of the existing building energy-saving renovation market determines the inherent inevitability of incentive,while unique requirements for the incentive should be satisfied by stage characteristics and individualization of the three entities of the existing building energy-saving renovation market development.Firstly,the analysis of internal and external factors’composition and system influencing the existing construction market development incentive structure was performed.Then,system dynamics was implemented to build the feedback model of incentive effects of market development of existing buildings energy-saving reconstruction.Discussions on the realization path of the incentive for the development of the existing energy-saving building market were also pointed out.Finally,this paper conducted the analysis of the dynamic feedback characteristics and key incentive factors of the incentive for the development of the existing building energy-saving renovation market.Based on the analyses and discussions above,this paper provides methodological guidance and implementation approach for the incentive path selection and policy-making of the existing building energy-saving transformation market,trying to help improve the incentive effectiveness of the market,and also promote healthy and sustainable development of the existing building energy-saving renovation market. 展开更多
关键词 existing building energy-saving renovation market development incentive operation influencing factor dynamic feedback
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Fuzzy self-tuning PID control of the operation temperatures in a two-staged membrane separation process 被引量:8
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作者 Lei Wang Wencai Du +1 位作者 Hai Wang Hong Wu 《Journal of Natural Gas Chemistry》 EI CAS CSCD 2008年第4期409-414,共6页
A two-staged membrane separation process for hydrogen recovery from refinery gases is introduced. The principle of the gas membrane separation process and the influence of the operation temperatures are analyzed. As t... A two-staged membrane separation process for hydrogen recovery from refinery gases is introduced. The principle of the gas membrane separation process and the influence of the operation temperatures are analyzed. As the conventional PID controller is difficult to make the operation temperatures steady, a fuzzy self-tuning PID control algorithm is proposed. The application shows that the algorithm is effective, the operation temperatures of both stages can be controlled steadily, and the operation flexibility and adaptability of the hydrogen recovery unit are enhanced with safety. This study lays a foundation to optimize the control of the membrane separation process and thus ensure the membrane performance. 展开更多
关键词 membrane separation hydrogen recovery operation temperature fuzzy self-tuning PID control
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High-Speed Trains Automatic Operation with Protection Constraints: A Resilient Nonlinear Gain-based Feedback Control Approach 被引量:2
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作者 Shigen Gao Yuhan Hou +2 位作者 Hairong Dong Sebastian Stichel Bin Ning 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2019年第4期992-999,共8页
This paper addresses the control design for automatic train operation of high-speed trains with protection constraints.A new resilient nonlinear gain-based feedback control approach is proposed,which is capable of gua... This paper addresses the control design for automatic train operation of high-speed trains with protection constraints.A new resilient nonlinear gain-based feedback control approach is proposed,which is capable of guaranteeing,under some proper non-restrictive initial conditions,the protection constraints control raised by the distance-to-go(moving authority)curve and automatic train protection in practice.A new hyperbolic tangent function-based model is presented to mimic the whole operation process of high-speed trains.The proposed feedback control methods are easily implementable and computationally inexpensive because the presence of only two feedback gains guarantee satisfactory tracking performance and closed-loop stability,no adaptations of unknown parameters,function approximation of unknown nonlinearities,and attenuation of external disturbances in the proposed control strategies.Finally,rigorous proofs and comparative simulation results are given to demonstrate the effectiveness of the proposed approaches. 展开更多
关键词 AUTOMATIC TRAIN operation high-speed TRAIN nonlinear GAIN feedback PROTECTION CONSTRAINT resilient control
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Control of seismic and operational vibrations of rotating machines using semi-active mounts 被引量:1
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作者 R.Rana T.T.Soong 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2004年第1期85-100,共16页
A dual isolation problem for rotating machines consists of isolation of housing structures from the machine vibrations and protection of machines during an earthquake to maintain their functionality. Desirable charact... A dual isolation problem for rotating machines consists of isolation of housing structures from the machine vibrations and protection of machines during an earthquake to maintain their functionality. Desirable characteristics of machine mounts for the above two purposes can differ significantly due to difference in nature of the excitation and performance criteria in the two situations. In this paper, relevant response quantities are identified that may be used to quantify performance and simplified models of rotating machines are presented using which these relevant response quantities may be calculated. Using random vibration approach with a stationary excitation, it is shown that significant improvement in seismic performance is achievable by proper mount design. Results of shaking table experiments performed with a realistic setup using a centrifugal pump are presented. It is concluded that a solution to this dual isolation problem lies in a semi-active mount capable switching its properties from ‘operation-optimum’ to ‘seismic-optimum’ at the onset of a seismic event. 展开更多
关键词 rotating machines simple modeling seismic control operational control semi-active control
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Operation Efficiency Optimisation Modelling and Application of Model Predictive Control 被引量:2
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作者 Xiaohua Xia Jiangfeng Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI 2015年第2期166-172,共7页
The efficiency of any energy system can be charaterised by the relevant efficiency components in terms of performance, operation, equipment and technology(POET). The overall energy efficiency of the system can be opti... The efficiency of any energy system can be charaterised by the relevant efficiency components in terms of performance, operation, equipment and technology(POET). The overall energy efficiency of the system can be optimised by studying the POET energy efficiency components. For an existing energy system, the improvement of operation efficiency will usually be a quick win for energy efficiency. Therefore, operation efficiency improvement will be the main purpose of this paper. General procedures to establish operation efficiency optimisation models are presented. Model predictive control, a popular technique in modern control theory, is applied to solve the obtained energy models. From the case studies in water pumping systems, model predictive control will have a prosperous application in more energy efficiency problems. 展开更多
关键词 Model predictive control(MPC) operation efficiency energy efficiency
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Optimization of Control Loops and Operating Parameters for Three-Phase Separators Used in Oilfield Central Processing Facilities
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作者 Zhenfeng Li Yaqiao Li Guangjun Wei 《Fluid Dynamics & Materials Processing》 EI 2023年第3期635-649,共15页
In this study,the Stokes formula is used to analyze the separation effect of three-phase separators used in a Oilfield Central Processing Facility.The considered main influencing factors include(but are not limited to... In this study,the Stokes formula is used to analyze the separation effect of three-phase separators used in a Oilfield Central Processing Facility.The considered main influencing factors include(but are not limited to)the typical size of oil and water droplets,the residence time and temperature of fluid and the dosage of demulsifier.Using the“Specification for Oil and Gas Separators”as a basis,the control loops and operating parameters of each separator are optimized Considering the Halfaya Oilfield as a testbed,it is shown that the proposed approach can lead to good results in the production stage. 展开更多
关键词 Distributed control system(DCS) three-phase separator control loop operating parameter
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Active Compliance Control of a Position‑Controlled Industrial Robot for Simulating Space Operations 被引量:2
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作者 Jun He Mingjin Shen +1 位作者 Feng Gao Haibo Zhang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2022年第6期63-75,共13页
An industrial robot with a six-axis force/torque sensor is usually used to produce a zero-gravity environment for testing space robotic operations.However,using traditional force control methods,such as admittance con... An industrial robot with a six-axis force/torque sensor is usually used to produce a zero-gravity environment for testing space robotic operations.However,using traditional force control methods,such as admittance control,causes position-controlled industrial robots to undergo from force divergence owing to intrinsic time delay.In this paper,a new force control method is proposed to eliminate the force divergence.A hardware-in-the-loop(HIL)simulator with an industrial robot is first presented.The free-floating satellite dynamics and the motion mapping from the satellites to simulator are both established.Thus,the effects of measurement delay and dynamic response delay on contact velocity and force are investigated.After that,a real-time estimation method for contact stiffness and damping is proposed based on the adaptive Kalman filter.The measurement delay is compensated by a phase lead model.Moreover,the identified contact parameters are adopted to modify contact forces,and thus the dynamics response delay can be compensated for.Finally,a co-simulation and experiments were conducted to verify the force control method.The results show that contact stiffness and damping could be identified exactly and that the simulation divergence could be prevented.This paper proposes an active compliance control method that can deal with force constrained tasks of a position-controlled robot in unknown environments. 展开更多
关键词 Contact stiffness Parameter estimation Force control Space operation
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Controlled remote implementation of quantum operations with high-dimensional systems 被引量:1
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作者 詹佑邦 李晓薇 +1 位作者 马鹏程 施锦 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第4期118-123,共6页
We present two protocols for the controlled remote implementation of quantum operations between three-party high-dimensional systems. Firstly, the controlled teleportation of an arbitrary unitary operation by bidirect... We present two protocols for the controlled remote implementation of quantum operations between three-party high-dimensional systems. Firstly, the controlled teleportation of an arbitrary unitary operation by bidirectional quantum state teleportaion (BQST) with high-dimensional systems is considered. Then, instead of using the BQST method, a protocol for controlled remote implementation of partially unknown operations belonging to some restricted sets in high-dimensional systems is proposed. It is shown that, in these protocols, if and only if the controller would like to help the sender with the remote operations, the controlled remote implementation of quantum operations for high-dimensional systems can be completed. 展开更多
关键词 controlled remote implementation quantum operation TELEPORTATION high-dimensional entangled state
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A mathematical model for optimized operation and controlin a CDQ-Boiler system 被引量:1
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作者 De Wang Tao Yang +4 位作者 Zhi Wen Junxiao Feng Ning Kong Qin Wang Weimin Wang 《Journal of University of Science and Technology Beijing》 CSCD 2005年第5期390-393,共4页
Based on analyzing the thermal process of a CDQ (coke dry quenching)-Boiler system, the mathematical model for opti-mized operation and control in the CDQ-Boiler system was developed. It includes a mathematical mode... Based on analyzing the thermal process of a CDQ (coke dry quenching)-Boiler system, the mathematical model for opti-mized operation and control in the CDQ-Boiler system was developed. It includes a mathematical model for heat transferring process in the CDQ unit, a mathematical model for heat transferring process in the boiler and a combustion model for circulating gas in the CDQ-Boiler system. The model was verified by field data, then a series of simulations under several typical operating conditions of CDQ-Boiler were carried on, and in turn, the online relation formulas between the productivity and the optimal circulating gas, and the one between the productivity and the optimal second air, were achieved respectively. These relation equations have been success- fully used in a CDQ-Boiler computer control system in the Baosteel, to realize online optimized guide and control, and meanwhile high efficiency in the CDQ-Boiler system has been achieved. 展开更多
关键词 coke dry quenching-boiler system optimized operation and control mathematical model
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Research on the cooperative train control method in the metro system for energy saving
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作者 Siyao Li Bo Yuan +1 位作者 Yun Bai Jianfeng Liu 《Railway Sciences》 2023年第3期371-394,共24页
Purpose–To address the problem that the current train operation mode that train selects one of several offline pre-generated control schemes before the departure and operates following the scheme after the departure,... Purpose–To address the problem that the current train operation mode that train selects one of several offline pre-generated control schemes before the departure and operates following the scheme after the departure,energy-saving performance of the whole metro system cannot be guaranteed.Design/methodology/approach–A cooperative train control framework is formulated to regulate a novel train operation mode.The classic train four-phase control strategy is improved for generating specific energy-efficient control schemes for each train.An improved brute force(BF)algorithm with a two-layer searching idea is designed to solve the optimisation model of energy-efficient train control schemes.Findings–Case studies on the actual metro line in Guangzhou,China verify the effectiveness of the proposed train control methods compared with four-phase control strategy under different kinds of train operation scenarios and calculation parameters.The verification on the computation efficiency as well as accuracy of the proposed algorithm indicates that it meets the requirement of online optimisation.Originality/value–Most existing studies optimised energy-efficient train timetable or train control strategies through an offline process,which has a defect in coping with the disturbance or delays effectively and promptly during real-time train operation.This paper studies an online optimisation of cooperative train control based on the rolling optimisation idea,where energy-efficient train operation can be realised once train running time is determined,thus mitigating the impact of unpredictable operation situations on the energy-saving performance of trains. 展开更多
关键词 Train operation scheme Energy saving Cooperative control Metro system
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Management System Activities of the Operation and Utilization of GHARR-1
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作者 Edward Shitsi Henry Cecil Odoi +10 位作者 Kwame Gyamfi Philip Dordoh-Gasu Isaac Kwasi Baidoo Edward Oscar Amponsah-Abu Emmanuel Kwesi Boafo Samuel Yao Ganyaglo Samuel Boakye Dampare Henry Kwame Obeng William Osei-Mensah Wilfred Sedofia Massiasta Robert Ekow Quagraine 《World Journal of Engineering and Technology》 2023年第4期807-826,共20页
The Ghana Research Reactor-1 (GHARR-1) is a 34 kW low enriched uranium (LEU) Miniature Neutron Source Reactor (MNSR), tank-in-pool type and cooled by natural circulation under atmospheric pressure operating conditions... The Ghana Research Reactor-1 (GHARR-1) is a 34 kW low enriched uranium (LEU) Miniature Neutron Source Reactor (MNSR), tank-in-pool type and cooled by natural circulation under atmospheric pressure operating conditions. GHARR-1 is owned by Ghana Atomic Energy Commission (GAEC) and operated by National Nuclear Research Institute (NNRI), one of the institutes of GAEC. GHARR-1 is housed by Nuclear Reactors Research Centre (NRRC), one of the Centres of NNRI. Management/Administration, Radiation protection, Reactor operation and maintenance, Reactor utilization and Physical protection are the various systems/units that integrate to manage the activities of operation and utilization of GHARR-1 in addition to the quality assurance and quality control management system of the research reactor facility. The GHARR-1 which is currently in operation follows a robust maintenance culture adopted by the management system and this has made it possible to keep the reactor in operation with minimal interruption. The management system activities adopted at the Centre to ensure safety of the workers, public and the research reactor facility include authorization of the operation of the reactor for any experiments/modifications;providing material and financial resources for maintaining the research reactor facility;following standard procedures while carrying out Neutron Activation Analysis;participation in IAEA proficiency test;irradiation sites/positions characterization;following standard procedures while carrying out reactor operation and maintenance including reactor and pool water purification and other related activities;monitoring radiation levels in the controlled, supervised and uncontrolled areas of the research reactor facility as well as during reactor operation and maintenance;controlling the physical entry of the workers and public into the research reactor facility;and ensuring that the security structures provided to protect the reactor facility are functioning properly. The thorough knowledge on the functions of the various components that make up the electrical/electronic and control systems of the reactor has been observed to be important for continuous successful maintenance of the research reactor to keep the reactor in operation. This work provides some management system activities adopted to monitor the activities of the research reactor operation and utilization to guarantee safety of workers, public and the environment as well as to safeguard a continuous operation of the research reactor. These management system activities adopted among others, are in the form of Monitoring Forms provided for monitoring the activities of the research reactor operation and utilization in order to ensure standard procedures and specifications are followed and quality services are rendered to the public. 展开更多
关键词 Management Systems Quality Assurance and Quality control Research Re-actor operation and Utilization Monitoring Forms Ghana Research Reactor-1 (GHARR-1)
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From Control Theory to Gravitational Waves
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作者 Jean-Francois Pommaret 《Advances in Pure Mathematics》 2024年第2期49-100,共52页
When D:ξ→η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D<sub>1:</su... When D:ξ→η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D<sub>1:</sub>η→ξ such that Dξ = η implies D<sub>1</sub>η = 0. When D is involutive, the procedure provides successive first-order involutive operators D<sub>1</sub>,...,D<sub>n </sub>when the ground manifold has dimension n. Conversely, when D<sub>1</sub> is given, a much more difficult “inverse problem” is to look for an operator D:ξ→η having the generating CC D<sub>1</sub>η = 0. If this is possible, that is when the differential module defined by D<sub>1</sub> is “torsion-free”, that is when there does not exist any observable quantity which is a sum of derivatives of η that could be a solution of an autonomous OD or PD equation for itself, one shall say that the operator D<sub>1</sub> is parametrized by D. The parametrization is said to be “minimum” if the differential module defined by D does not contain a free differential submodule. The systematic use of the adjoint of a differential operator provides a constructive test with five steps using double differential duality. We prove and illustrate through many explicit examples the fact that a control system is controllable if and only if it can be parametrized. Accordingly, the controllability of any OD or PD control system is a “built in” property not depending on the choice of the input and output variables among the system variables. In the OD case and when D<sub>1</sub> is formally surjective, controllability just amounts to the formal injectivity of ad(D<sub>1</sub>), even in the variable coefficients case, a result still not acknowledged by the control community. Among other applications, the parametrization of the Cauchy stress operator in arbitrary dimension n has attracted many famous scientists (G. B. Airy in 1863 for n = 2, J. C. Maxwell in 1870, E. Beltrami in 1892 for n = 3, and A. Einstein in 1915 for n = 4). We prove that all these works are already explicitly using the self-adjoint Einstein operator, which cannot be parametrized and the comparison needs no comment. As a byproduct, they are all based on a confusion between the so-called div operator D<sub>2</sub> induced from the Bianchi operator and the Cauchy operator, adjoint of the Killing operator D which is parametrizing the Riemann operator D<sub>1</sub> for an arbitrary n. This purely mathematical result deeply questions the origin and existence of gravitational waves, both with the mathematical foundations of general relativity. As a matter of fact, this new framework provides a totally open domain of applications for computer algebra as the quoted test can be studied by means of Pommaret bases and related recent packages. 展开更多
关键词 Differential operator Differential Sequence Killing operator Riemann operator Bianchi operator Cauchy operator control Theory controllability Elasticity General Relativity
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