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Proposed Entanglement Swapping in Continuous Variable Systems via Braiding
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作者 苏洪轶 陈景灵 +1 位作者 邓东灵 吴春凤 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第12期981-984,共4页
We study entanglement swapping in continuous variable systems by using braiding transformations.It isfound that entanglement swapping in two-mode squeezed vacuum states and squeezed coherent states can be realizedbase... We study entanglement swapping in continuous variable systems by using braiding transformations.It isfound that entanglement swapping in two-mode squeezed vacuum states and squeezed coherent states can be realizedbased on the braiding operators. 展开更多
关键词 entanglement swapping continuous variable systems BRAIDING
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Observation and Measures of Robust Correlations for Continuous Variable System
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作者 Tesfay Gebremariam 曾业雄 +1 位作者 陈歆宇 李崇 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第11期661-666,共6页
In this work, we examine the robust continuous variable quantum correlation by analyzing two coupled optomechanical systems. Under the linearization approximation, the steady state correlation is quantified through co... In this work, we examine the robust continuous variable quantum correlation by analyzing two coupled optomechanical systems. Under the linearization approximation, the steady state correlation is quantified through correlation function of two non-Hermitian operators and we find that quantum correlation is always existence between two optical fields, two-oscillators and optical field-oscillator. Unlike the discrete variable system, we show quantum correlation in our model seems to be independent without any close transfer relationship. We further emphasize the influence of cavity-cavity coupling parameter on the amount of quantum correlations. 展开更多
关键词 steady state correlations quantum measurement continuous variable systems
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A Harmonic Disturbance Suppression Method For Frequency Time-variable Systems
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作者 ZHOU Xinxiu FANG Jiancheng +1 位作者 LIU Gang ZHANG Ran 《中国电机工程学报》 EI CSCD 北大核心 2011年第36期I0012-I0012,247,共1页
The problem of complete rejection of external inaccessible disturbances plays an important role in the modem control theory.Analysis and design of a control system with harmonic disturbances are challenging.This paper... The problem of complete rejection of external inaccessible disturbances plays an important role in the modem control theory.Analysis and design of a control system with harmonic disturbances are challenging.This paper present both linear and nonlinear harm onics observers for systems with harm onic disturbances. 展开更多
关键词 harmonic disturbance linear matrix inequality nonlinear disturbance observer variable structure control magnetically suspended
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Soliton Interactions and Collision Dynamics in a Variable-Coefficient Coupled Nonlocal Nonlinear Schrödinger Systems
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作者 Xinnan Cui Zhiyang Zhang +2 位作者 Muwei Liu Fenghua Qi Wenjun Liu 《Chinese Physics Letters》 2025年第10期68-74,共7页
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ... The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems. 展开更多
关键词 two soliton solutions soliton interactions assigning different functions collision dynamics nonstandard hirota bilinear methodthe nonstandard hirota bilinear method variable coefficient coupled nonlocal nonlinear schr dinger systems coupled nonlocal nonlinear schr dinger equations variable coefficients
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Multi-agent System Cooperative Control of Autonomous Vehicle Chassis Based on Scenario-driven Hybrid-DMPC with Variable Topology
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作者 Yuxing Li Yingfeng Cai +2 位作者 Yubo Lian Xiaoqiang Sun Long Chen 《Chinese Journal of Mechanical Engineering》 2025年第5期156-175,共20页
The development of chassis active safety control technology has improved vehicle stability under extreme conditions.However,its cross-system and multi-functional characteristics make the controller difficult to achiev... The development of chassis active safety control technology has improved vehicle stability under extreme conditions.However,its cross-system and multi-functional characteristics make the controller difficult to achieve cooperative goals.In addition,the chassis system,which has high complexity,numerous subsystems,and strong coupling,will also lead to low computing efficiency and poor control effect of the controller.Therefore,this paper proposes a scenario-driven hybrid distributed model predictive control algorithm with variable control topology.This algorithm divides multiple stability regions based on the vehicle’s β−γ phase plane,forming a mapping relationship between the control structure and the vehicle’s state.A control input fusion mechanism within the transition domain is designed to mitigate the problems of system state oscillation and control input jitter caused by switching control structures.Then,a distributed state-space equation with state coupling and input coupling characteristics is constructed,and a weighted local agent cost function in quadratic programming is derived.Through cost coupling,local agents can coordinate global performance goals.Finally,through Simulink/CarSim joint simulation and hardware-in-the-loop(HIL)test,the proposed algorithm is validated to improve vehicle stability while ensuring trajectory tracking accuracy and has good applicability for multi-objective coordinated control.This paper combines the advantages of distributed MPC and decentralized MPC,achieving a balance between approximating the global optimal results and the solution’s efficiency. 展开更多
关键词 Autonomous vehicle Distributed control Multi-agent system Hybrid-DMPC variable topology
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Strong Laws of Large Numbers for Sequences of Blockwise m-Dependent and Sub-Orthogonal Random Variables under Sublinear Expectations 被引量:1
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作者 Jialiang FU 《Journal of Mathematical Research with Applications》 2026年第1期103-118,共16页
In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random vari... In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random variables,and another is for sub-orthogonal random variables.Both extend the strong law of large numbers for independent random variables under sublinear expectations to the non-independent case. 展开更多
关键词 sublinear expectations strong law of large numbers blockwise m-dependent suborthogonal random variables
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Design and experiment of the variable rate fertilization system for soybeanand maize strip compound planting
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作者 Li Ding Kaixuan Wang +6 位作者 Yechao Yuan Yuanyuan Li Huanhuan Chen Zheng Zhang Qianyi Wang Changchang Yu He Li 《International Journal of Agricultural and Biological Engineering》 2025年第6期122-134,共13页
In view of the existing composite planting cannot do independent control of fertilizer rate for each row,and fertilizer is easy to moisture solidification caking and rely on a single way to measure the speed of inaccu... In view of the existing composite planting cannot do independent control of fertilizer rate for each row,and fertilizer is easy to moisture solidification caking and rely on a single way to measure the speed of inaccurate problems,a split-drive variable fertilizer application system was designed for soybean and maize strip cropping composites.It includes roller crushing bi-directional spiral fertilizer discharger,split-drive variable fertilizer application system and‘GNSS+encoder’dual speed measurement system.By modeling agglomerated fertilizer particles,discrete element simulation was carried out to analyze the crushing effect.The speed measurement error variation folds of both GNSS and encoder under different speed conditions were obtained through field speed measurement tests.Finally,4.5 km/h was identified as the switching point between the two speed measurements.Through bench testing,a mathematical relationship model was developed for the soybean and maize belts in terms of‘Fertilizer Application Rate-Operating Travel Speed-Metering Mechanism Rotor Speed’,and the results are presented in the table below.Fertilizer discharge consistency was verified for fertilizer dischargers.Field trials were conducted,and the results show:The soybean belt had a maximum error of 4.81%at a fertilizer application rate of 150 kg/hm2 and an operating speed of 5 km/h;the maximum error in the corn belt was 4.67%at a fertilizer application rate of 600 kg/hm2 and operating speed of 4 km/h.Both have a maximum error of less than 5%,which meets the requirements for variable fertilizer application. 展开更多
关键词 variable fertilization EDEM simulation soybean corn compound planting spiral fertilizer apparatus
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Intermediate-variable-based adaptive extended Kalman filter for nonlinear non-Gaussian cyber-physical systems with unknown inputs
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作者 MIAO Kelei YAN Zejun +2 位作者 ZHANG Xudong CHEN Yourong REN Hongliang 《High Technology Letters》 2025年第4期329-337,共9页
This article proposes an adaptive extended Kalman filter(EKF)for nonlinear cyber-physical systems(CPSs)under unknown inputs and non-Gaussian noises.It is known that the traditional extended Kalman filter is applicable... This article proposes an adaptive extended Kalman filter(EKF)for nonlinear cyber-physical systems(CPSs)under unknown inputs and non-Gaussian noises.It is known that the traditional extended Kalman filter is applicable to nonlinear systems with Gaussian white noise.The system is reformulated with intermediate variables to expand the application of nonlinear systems under unknown inputs and non-Gaussian noises,which help decompose unknown input estimation into residual tracking and state observation subproblems.By introducing the orthogonal principle of innovation and attenuation factor,the intermediate variables-based filter can improve the estimation performance under non-Gaussian noises and unknown inputs.Simulation results validate the effectiveness of the proposed method. 展开更多
关键词 nonlinear non-Gaussian system intermediate variable adaptive extended Kalman filter
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Influence of ambient geochemical and microbiological variables on the bacterial diversity in a cold seep ecosystem in North Indian Ocean
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作者 Delcy R.Nazareth Maria Judith Gonsalves Nitisha Sangodkar 《Geoscience Frontiers》 2025年第3期153-163,共11页
Cold seeps are oases for biological communities on the sea floor around hydrocarbon emission pathways.Microbial utilization of methane and other hydrocarbons yield products that fuel rich chemosynthetic communities at... Cold seeps are oases for biological communities on the sea floor around hydrocarbon emission pathways.Microbial utilization of methane and other hydrocarbons yield products that fuel rich chemosynthetic communities at these sites.One such site in the cold seep ecosystem of Krishna-Godavari basin(K-G basin)along the east coast of India,discovered in Feb 2018 at a depth of 1800 m was assessed for its bacterial diversity.The seep bacterial communities were dominated by phylum Proteobacteria(57%),Firmicutes(16%)and unclassified species belonging to the family Helicobacteriaceae.The surface sediments of the seep had maximum OTUs(operational taxonomic units)(2.27×10^(3))with a Shannon alpha diversity index of 8.06.In general,environmental parameters like total organic carbon(p<0.01),sulfate(p<0.001),sulfide(p<0.05)and methane(p<0.01)were responsible for shaping the bacterial community of the cold seep ecosystem in the K-G Basin.Environmental parameters play a significant role in changing the bacterial diversity richness between different cold seep environments in the oceans. 展开更多
关键词 SEDIMENTS Environmental variables PROTEOBACTERIA Cold seep ecosystem Organic matter
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Global Existence and Blow-up of Solutions for Fourth-order Parabolic Equation with p(x)-Laplacian and Variable Exponents
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作者 YANG Chunxiao YU Lifei DUAN Chenyan 《数学进展》 北大核心 2026年第1期221-239,共19页
In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence... In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0. 展开更多
关键词 fourth-order parabolic equation variable exponent source global existence asymptotic behavior BLOW-UP
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Thermo-mechanical damage behavior of the interface between hybrid alkali-resistant glass fiber-reinforced concrete and rock under high and variable temperature conditions
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作者 Cong Zhang Zhen Xu +4 位作者 Shanyong Wang Chong Shi Hui Wang Yonggang Zhang Guoqing Chen 《International Journal of Mining Science and Technology》 2026年第2期399-421,共23页
Thermal-mechanical damage and deformation at the interface between shotcrete linings and the surrounding rock of tunnels under high-temperature and variable-temperature conditions are critical to the safe construction... Thermal-mechanical damage and deformation at the interface between shotcrete linings and the surrounding rock of tunnels under high-temperature and variable-temperature conditions are critical to the safe construction and operation of tunnel engineering.This study investigated the thermo-mechanical damage behavior of the composite interface between alkali-resistant glass fiber-reinforced concrete(ARGFRC)and granite,focusing on a plateau railway tunnel.Laboratory triaxial tests,laser scanning,XRD analysis,numerical simulations,and theoretical analyses were employed to investigate how different initial curing temperatures and joint roughness coefficient(JRC)influence interfacial damage behavior.The results indicate that an increase in interface roughness exacerbates the structural damage at the interface.At a JRC of 19.9 and a temperature of 70℃,crack initiation in granite was notably restrained when the confining pressure rose from 7 MPa to 10 MPa.Roughness-induced stress distribution at the interface was notably altered,although this effect became less pronounced under high confining pressure conditions.Additionally,during high-temperature curing,thermal stress concentration at the tips of micro-convex protrusions on the granite surface induced microcracks in the adjacent ARGFRC matrix,followed by deformation.These findings provide practical guidelines for designing concrete support systems to ensure tunnel structural safety in high-altitude regions with harsh thermal environments. 展开更多
关键词 High and variable temperature ARGFRC-granite INTERFACE Thermo-mechanical coupling Damage evolution
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A data-and expert-driven framework for establishing land cover-related essential variables for SDG monitoring and assessment
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作者 Hao Wu Ping Zhang +6 位作者 Jun Chen Songnian Li Jing Li Shu Peng Dongyang Hou Jun Zhang Hao Chen 《Geography and Sustainability》 2026年第1期236-246,共11页
Sustained and spatially explicit monitoring of the United Nations 2030 Agenda for Sustainable Development is critical for effectively tracking progress toward the global Sustainable Development Goals(SDGs).Although la... Sustained and spatially explicit monitoring of the United Nations 2030 Agenda for Sustainable Development is critical for effectively tracking progress toward the global Sustainable Development Goals(SDGs).Although land cover information has long been recognized as an essential component for monitoring SDGs,a standardized scientific framework for identifying and prioritizing land cover related essential variables does not exist.Therefore,we propose a novel expert-and data-driven framework for identifying,refining,and selecting a priority list of Essential Land cover-related Variables for SDGs(ELcV4SDGs).This framework integrates methods including expert knowledge-based analysis,clustering of variables with similar attributes,and quantified index calculation to establish the priority list.Applying the framework to 15 specific SDG indicators,we found that the ELcV4SDGs priority list comprises three main categories,type and structure,pattern and intensity,and process and evolution of land cover,which are further divided into 19 subcategories and ultimately encompass 50 general variables.The ELcV4SDGs will support detailed spatial monitoring and enhance their scientific applications for SDG monitoring and assessment,thereby guiding future SDG priority actions and informing decision-making to advance the 2030 SDGs agenda at local,national,and global levels. 展开更多
关键词 Essential variable Land cover SDG Spatial monitoring and assessment Interactive analysis Refinement and selection
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A TimeXer-Based Numerical Forecast Correction Model Optimized by an Exogenous-Variable Attention Mechanism
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作者 Yongmei Zhang Tianxin Zhang Linghua Tian 《Computers, Materials & Continua》 2026年第3期1770-1785,共16页
Marine forecasting is critical for navigation safety and disaster prevention.However,traditional ocean numerical forecasting models are often limited by substantial errors and inadequate capture of temporal-spatial fe... Marine forecasting is critical for navigation safety and disaster prevention.However,traditional ocean numerical forecasting models are often limited by substantial errors and inadequate capture of temporal-spatial features.To address the limitations,the paper proposes a TimeXer-based numerical forecast correction model optimized by an exogenous-variable attention mechanism.The model treats target forecast values as internal variables,and incorporates historical temporal-spatial data and seven-day numerical forecast results from traditional models as external variables based on the embedding strategy of TimeXer.Using a self-attention structure,the model captures correlations between exogenous variables and target sequences,explores intrinsic multi-dimensional relationships,and subsequently corrects endogenous variables with the mined exogenous features.The model’s performance is evaluated using metrics including MSE(Mean Squared Error),MAE(Mean Absolute Error),RMSE(Root Mean Square Error),MAPE(Mean Absolute Percentage Error),MSPE(Mean Square Percentage Error),and computational time,with TimeXer and PatchTST models serving as benchmarks.Experiment results show that the proposed model achieves lower errors and higher correction accuracy for both one-day and seven-day forecasts. 展开更多
关键词 TimeXer model exogenous variable attention mechanism sea surface temperature temporal-spatial features forecast correction
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OptimizationDesign and Numerical Simulation of Variable Tube Diameter Heat Exchanger for Split Air Conditioning Indoor Unit
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作者 Zheming Cheng Xinping Ou Yang +2 位作者 Leren Tao Zihao Wang Ke Sun 《Frontiers in Heat and Mass Transfer》 2026年第1期288-313,共26页
Energy shortage has become one of themost concerning issues in the world today,and improving energy utilization efficiency is a key area of research for experts and scholars worldwide.Small-diameter heat exchangers of... Energy shortage has become one of themost concerning issues in the world today,and improving energy utilization efficiency is a key area of research for experts and scholars worldwide.Small-diameter heat exchangers offer advantages such as reduced material usage,lower refrigerant charge,and compact structure.However,they also face challenges,including increased refrigerant pressure drop and smaller heat transfer area inside the tubes.This paper combines the advantages and disadvantages of both small and large-diameter tubes and proposes a combined-diameter heat exchanger,consisting of large and small diameters,for use in the indoor units of split-type air conditioners.There are relatively few studies in this area.In this paper,A theoretical and numerical computation method is employed to establish a theoretical-numerical calculation model,and its reliability is verified through experiments.Using this model,the optimal combined diameters and flow path design for a combined-diameter heat exchanger using R32 as the working fluid are derived.The results show that the heat transfer performance of all combined diameter configurations improves by 2.79%to 8.26%compared to the baseline design,with the coefficient of performance(COP)increasing from 4.15 to 4.27~4.5.These designs can save copper material,but at the cost of an increase in pressure drop by 66.86%to 131.84%.The scheme IIIH,using R32,is the optimal combined-diameter and flow path configuration that balances both heat transfer performance and economic cost. 展开更多
关键词 Split air condition variable tube diameter enhanced heat transfer numerical simulation structural design optimization
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Variable universe fuzzy expert system for aluminum electrolysis 被引量:3
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作者 曹丹阳 曾水平 李晋宏 《Transactions of Nonferrous Metals Society of China》 SCIE EI CAS CSCD 2011年第2期429-436,共8页
In aluminum electrolytic process, the variables affect the current efficiency and the stability of electrolysis cells. AIF3 addition and aluminum tapping volume are two important factors that affect economic benefits ... In aluminum electrolytic process, the variables affect the current efficiency and the stability of electrolysis cells. AIF3 addition and aluminum tapping volume are two important factors that affect economic benefits of aluminum electrolytic production. Fuzzy logic provides a suitable mechanism to describe the relationship between the process variables and the current efficiency. Fuzzy expert system based on Mamdani fuzzy inference process for aluminum electrolysis was adopted to adjust A1F3 addition and aluminum tapping volume. A novel variable universe approach was applied in the system to solve the problem that different electrolysis cells have different universes of variables. The system was applied to 300 kA aluminum electrolysis cells in a aluminum plant. Experimental results showed that the electrolyte temperature was kept stably between 945 and 955℃, the current efficiency reached 93.5%, and the DC power consumption was 13 000 kW.h per ton aluminum. 展开更多
关键词 variable universe fuzzy expert system aluminum electrolysis
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Instantaneous rotation speed measurement and error analysis for variable speed hydraulic system 被引量:1
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作者 杨彬 谷立臣 +1 位作者 刘永 王平 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2015年第4期315-321,共7页
In order to monitor the working state of piston motor and measure its instantaneous rotation speed accurately, the measuring principle and method of instantaneous rotation speed based on industrial personal computer a... In order to monitor the working state of piston motor and measure its instantaneous rotation speed accurately, the measuring principle and method of instantaneous rotation speed based on industrial personal computer and data acquisition card are introduced, and the major error source, influence mechanism and processing method of data quantization error are dis- cussed. By means of hybrid programming approach of LabVIEW and MATLAB, the instantaneous rotation speed measurement system for the piston motor in variable speed hydraulic system is designed. The simulation and experimental results show that the designed instantaneous speed measurement system is feasible. Furthermore, the sampling frequency has an important influ- ence on the instantaneous rotation speed measurement of piston motor and higher sampling frequency can lower quantization er- ror and improve measurement accuracy. 展开更多
关键词 variable speed hydraulic system instantaneous rotation speed measurement error analysis hybrid programming
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On the Motion of Controllable Mechanical Systems Having Variable Mass 被引量:1
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作者 朱海平 吴惠彬 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 1994年第2期122-130,共9页
The differential equations of motion of a comtlaint system with parameters and variable mass, of a system with variable mass and servo constraints and those for the control problem on the forced motion of constraint s... The differential equations of motion of a comtlaint system with parameters and variable mass, of a system with variable mass and servo constraints and those for the control problem on the forced motion of constraint systems with variable mass are given respectively. Finally, an example is presented. 展开更多
关键词 variable mass systems/controllable mechanical system servo constraint forced motion
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ROBUST STABILIZATING FOR A OLASS OF UNOERTAIN NONLINEAR INTEROONNECTED SYSTEMS USING VARIABLE STRUCTURE CONTROL
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作者 姜斌 万健如 王先来 《Transactions of Tianjin University》 EI CAS 1999年第1期42-46,共5页
The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (... The robust stabilizating control problem for a class of uncertain nonlinear large-scale systems is discussed. Based on the theory of both input/output (I/O) linearization and decentralized variable structure control (VSC),two-level and decentralized variable structure control laws for this kind of systems are presented respectively,which achieve asymptotically stabilization despite the uncertainties and disturbances. At last,sirnulation of the disturbed two-pendulum system is given to illustrate the feasibility of proposed technique. 展开更多
关键词 nonlinear interconnected systems UNCERTAINTY STABILIZATION variable structure control input/output linearization
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Application of water loop variable refrigerant flow air-conditioning system in large-scale buildings in northern China
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作者 孙婷婷 倪龙 +1 位作者 姚杨 马最良 《Journal of Southeast University(English Edition)》 EI CAS 2010年第2期197-200,共4页
A water loop variable refrigerant flow(WLVRF)air-conditioning system is designed to be applied in large-scale buildings in northern China.The system is energy saving and it is an integrated system consisting of a va... A water loop variable refrigerant flow(WLVRF)air-conditioning system is designed to be applied in large-scale buildings in northern China.The system is energy saving and it is an integrated system consisting of a variable refrigerant flow(VRF)air-conditioning unit,a water loop and an air source heat pump.The water loop transports energy among different regions in the buildings instead of refrigerant pipes,decreasing the scale of the VRF air-conditioning unit and improving the performance.Previous models for refrigerants and building loads are cited in this investigation.Mathematical models of major equipment and other elements of the system are established using the lumped parameter method based on the DATAFIT software and the MATLAB software.The performance of the WLVRF system is simulated.The initial investments and the running costs are calculated based on the results of market research.Finally,a contrast is carried out between the WLVRF system and the traditional VRF system.The results show that the WLVRF system has a better working condition and lower running costs than the traditional VRF system. 展开更多
关键词 variable refrigerant flow air-conditioning system water loop large-scale building
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Exact Invariants and Adiabatic Invariants of Nonholonomic Variable Mass Systems
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作者 陈向炜 梅凤翔 《Journal of Beijing Institute of Technology》 EI CAS 2001年第2期131-137,共7页
By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variab... By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variable mass systems under small excitation is discussed. The concept of high order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied. 展开更多
关键词 analytical mechanics variable mass PERTURBATION adiabatic invariant
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