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Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable 被引量:4
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作者 Shaoxia Feng Juan Wang Jun Zhao 《IEEE/CAA Journal of Automatica Sinica》 EI CSCD 2019年第1期167-176,共10页
This paper is concerned with the stability and robust stability of switched positive linear systems(SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretiz... This paper is concerned with the stability and robust stability of switched positive linear systems(SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions, some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases, respectively. The copositive Lyapunov functions constructed in this paper are timevarying during the dwell time and time-invariant afterwards. In addition, the above approach is extended to the switched interval positive systems. A numerical example is proposed to illustrate our approach. 展开更多
关键词 Discretized co-positive Lyapunov functions mode-dependent DWELL time robust STABILITY SWITCHED positive linear systems (SPLSs) UNSTABLE subsystem
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Adaptive Backstepping Slide Mode Control of Pneumatic Position Servo System 被引量:12
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作者 REN Haipeng FAN Juntao 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2016年第5期1003-1009,共7页
With the price decreasing of the pneumatic proportional valve and the high performance micro controller, the simple structure and high tracking performance pneumatic servo system demonstrates more application potentia... With the price decreasing of the pneumatic proportional valve and the high performance micro controller, the simple structure and high tracking performance pneumatic servo system demonstrates more application potential in many fields. However, most existing control methods with high tracking performance need to know the model information and to use pressure sensor. This limits the application of the pneumatic servo system. An adaptive backstepping slide mode control method is proposed for pneumatic position servo system. The proposed method designs adaptive slide mode controller using backstepping design technique. The controller parameter adaptive law is derived from Lyapunov analysis to guarantee the stability of the system. A theorem is testified to show that the state of closed-loop system is uniformly bounded, and the closed-loop system is stable. The advantages of the proposed method include that system dynamic model parameters are not required for the controller design, uncertain parameters bounds are not need, and the bulk and expensive pressure sensor is not needed as well. Experimental performance, as compared with some existing methods. results show that the designed controller can achieve better tracking 展开更多
关键词 pneumatic position servo system adaptive backstepping design slide mode control uncertain parameter tracking accuracy
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Analysis and Comparison of Range-Range Positioning Mode and Hyperbolic Positioning Mode 被引量:4
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作者 Shi-ru Chen Ding-jie Xu Yao Sun 《Journal of Marine Science and Application》 2002年第1期60-64,共5页
Three key factors are discussed, which affect positioning accuracy of range-range positioning mode and hyperbolicpositioning mode.Based on the error elliptical theory, the expressions of positioning error and of posit... Three key factors are discussed, which affect positioning accuracy of range-range positioning mode and hyperbolicpositioning mode.Based on the error elliptical theory, the expressions of positioning error and of positioning geometric factor ofrange-range positioning mode and hyperbolic positioning mode are derived, and the positioning error and the blind positioningarea of two different positioning modes are analyzed. According to the requirement of navigation area, an optimum 展开更多
关键词 RADIO NAVIGATION range- RANGE positIONING mode HYPERBOLIC positIONING mode
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Improved estimation of rotor position for sensorless control of a PMSM based on a sliding mode observer 被引量:8
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作者 Wahyu Kunto Wibowo Seok-Kwon Jeong 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第7期1643-1656,共14页
This work proposes a new strategy to improve the rotor position estimation of a permanent magnet synchronous motor(PMSM) over wide speed range. Rotor position estimation of a PMSM is performed by using sliding mode ob... This work proposes a new strategy to improve the rotor position estimation of a permanent magnet synchronous motor(PMSM) over wide speed range. Rotor position estimation of a PMSM is performed by using sliding mode observer(SMO). An adaptive observer gain was designed based on Lyapunov function and applied to solve the chattering problem caused by the discontinuous function of the SMO in the wide speed range. The cascade low-pass filter(LPF) with variable cut-off frequency was proposed to reduce the chattering problem and to attenuate the filtering capability of the SMO. In addition, the phase shift caused by the filter was counterbalanced by applying the variable phase delay compensation for the whole speed area. High accuracy estimation result of the rotor position was obtained in the experiment by applying the proposed estimation strategy. 展开更多
关键词 rotor position estimation permanent magnet synchronous motor sliding mode observer adaptive observer gain cascadelow-pass filter variable cut-off frequency variable phase delay compensation
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Position Control of a Series Elastic Actuator Based on Global Sliding Mode Controller Design 被引量:1
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作者 Wei Yin Lei Sun +1 位作者 Meng Wang Jingtai Liu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2019年第3期850-858,共9页
A series elastic actuator(SEA) is a powerful device in the area of human-machine integration, but it still suffers from difficult position control issues. Therefore, in this paper,an efficient approach is proposed to ... A series elastic actuator(SEA) is a powerful device in the area of human-machine integration, but it still suffers from difficult position control issues. Therefore, in this paper,an efficient approach is proposed to solve this problem. The approach design is divided into two steps: feedback linearization(FL) and global sliding mode(GSM) controller design. The bounded analysis is presented and global asymptotic convergence is analytically proven. Simulation and experiment results illustrate the effectiveness of the proposed scheme. 展开更多
关键词 Feedback LINEARIZATION (FL) global SLIDING mode (GSM) position control SERIES ELASTIC ACTUATOR (SEA)
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Position Sensorless Control for Permanent Magnet Synchronous Motor Using Sliding Mode Observer 被引量:2
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作者 陈益广 傅涛 李响 《Transactions of Tianjin University》 EI CAS 2005年第5期338-342,共5页
An approach of position sensorless control for permanent magnet synchronous motor ( PMSM ) is put forward based on a sliding mode observer. The mathematical model of PMSM in a stationary αβ reference frame is adop... An approach of position sensorless control for permanent magnet synchronous motor ( PMSM ) is put forward based on a sliding mode observer. The mathematical model of PMSM in a stationary αβ reference frame is adopted, and the system is controlled by the digital signal processor ( DSP; TMS320LF2407 according to the control achieve closed loop operation of the motor, the stator theory of sliding mode observer. In order to magnetic field should be vertical with the rotor magnetic field and be synchronous with rotor rotating, so the position and speed of PMSM is estimated in real time and the estimated position is modified continuously. The simulation results indicate that the proposed observer has high precision is more robust to the parametric variation and load in estimation of PMSM position and speed, and torque disturbance. 展开更多
关键词 permanent magnet synchronous motor position sensorless control sliding mode observer digital signal processor
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Cone beam computed tomography-guided differences among registration methods for lung cancer and the effects of tumor position,treatment model,and tumor size on positioning errors 被引量:1
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作者 Jiayu Du Jie Tang +1 位作者 Qian Zhang Xiaojie Ma 《Oncology and Translational Medicine》 CAS 2021年第5期203-208,共6页
Objective To explore the differences in three different registration methods of cone beam computed tomography(CBCT)-guided down-regulated intense radiation therapy for lung cancer as well as the effects of tumor locat... Objective To explore the differences in three different registration methods of cone beam computed tomography(CBCT)-guided down-regulated intense radiation therapy for lung cancer as well as the effects of tumor location,treatment mode,and tumor size on registration.Methods This retrospective analysis included 80 lung cancer patients undergoing radiotherapy in our hospital from November 2017 to October 2019 and compared automatic bone registration,automatic grayscale(t+r)registration,and automatic grayscale(t)positioning error on the X-,Y-,and Z-axes under three types of registration methods.The patients were also grouped according to tumor position,treatment mode,and tumor size to compare positioning errors.Results On the X-,Y-,and Z-axes,automatic grayscale(t+r)and automatic grayscale(t)registration showed a better trend.Analysis of the different treatment modes showed differences in the three registration methods;however,these were not statistically significant.Analysis according to tumor sizes showed significant differences between the three registration methods(P<0.05).Analysis according to tumor positions showed differences in the X-and Y-axes that were not significant(P>0.05),while the autopsy registration in the Z-axis showed the largest difference in the mediastinal and hilar lymph nodes(P<0.05).Conclusion The treatment mode was not the main factor affecting registration error in lung cancer.Three registration methods are available for tumors in the upper and lower lungs measuring<3 cm;among these,automatic gray registration is recommended,while any gray registration method is recommended for tumors located in the mediastinal hilar site measuring<3 cm and in the upper and lower lungs≥3 cm. 展开更多
关键词 lung cancer IMRT positioning error registration method CBCT different tumor locations different treatment modes tumor size
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Effect of loading point position on fracture mode of rock
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作者 饶秋华 孙宗颀 +2 位作者 徐继成 王桂尧 张静宜 《中国有色金属学会会刊:英文版》 CSCD 2001年第5期764-767,共4页
Anti symmetric four point bending specimen with different loading point positions was used to study effect of loading point position on fracture mode of rock in order to explore a feasible method for achieving Mode Ⅱ... Anti symmetric four point bending specimen with different loading point positions was used to study effect of loading point position on fracture mode of rock in order to explore a feasible method for achieving Mode Ⅱ fracture and determining Mode Ⅱ fracture toughness of rock, K ⅡC . Numerical and experimental results show that the distance between the inner and outer loading points, L 1+ L 2, has a great influence on stresses at notch tip and fracture mode. When L 1+ L 2>0.5 L or 0.1 L < L 1+ L 2<0.5 L , maximum principal stress σ 1 exceeds the tensile strength σ t. The ratio of τ max / σ 1 is relatively low or high and thus Mode Ⅰ or mixed mode fracture occurs. When L 1+ L 2< 0.1 L , σ 1 is smaller than σ t and the ratio of τ max / σ 1 is much higher, which facilitates the occurrence of Mode Ⅱ fracture. 展开更多
关键词 fracture mode loading point position stress analysis ROCK
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Two-mode intelligent coordinating control of position for the welding positioner 被引量:2
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作者 樊丁 周万坤 谭伟明 《China Welding》 EI CAS 1998年第1期50-55,共6页
A new intelligent control method for welding positioner is proposed. Applying an improved fuzzy controller and a variable PID controller, a two-mode intelligent coordinating controller ( TMICC ) is designed on basis o... A new intelligent control method for welding positioner is proposed. Applying an improved fuzzy controller and a variable PID controller, a two-mode intelligent coordinating controller ( TMICC ) is designed on basis of fuzzy logic and rules. The simulation and experimental results show that this control system can obtain better dynamic and static characteristics. 展开更多
关键词 AC servo position control two-mode coordinating controller fuzzy control welding positioner
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Positioning Error of Optoelectronic Telescope Compensated by Bipolar PWM Driving Mode
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作者 LIXiao-yan ZHOUHui +1 位作者 FUHong HOUYun-hai 《Semiconductor Photonics and Technology》 CAS 2005年第2期139-141,共3页
The optoelectronic telescope has two sets of control systems: azimuth one and elevation one, and both are driven by PWM power amplifier with high efficiency and wide speed regulation range. The diagram of the azimuth ... The optoelectronic telescope has two sets of control systems: azimuth one and elevation one, and both are driven by PWM power amplifier with high efficiency and wide speed regulation range. The diagram of the azimuth control system is demonstrated, the nonlinear factors is analyzed at low speed, and some related experiments are carried out. The results show that the positioning error with unipolar is 86 codes(106.21″), while 18 codes (22.23″) is with bipolar PWM driver. 展开更多
关键词 TELESCOPE TRACKING positIONING PWM driving mode
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USING TLS ALGORITHM TO IMPROVE GPS POSITIONING PRECISION WITH ALTITUDE HOLD MODE
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作者 Liu Lichuan Tian Zengshan Huang Shunji(Dept of Electrical Engineering, UESTC, Chengdu 610054) 《Journal of Electronics(China)》 2002年第2期120-124,共5页
This paper presents a new method of improving Global Positioning System(GPS)positioning precision. Based on the altitude hold mode, the method does not need any other equipment. Under this constraint condition, the To... This paper presents a new method of improving Global Positioning System(GPS)positioning precision. Based on the altitude hold mode, the method does not need any other equipment. Under this constraint condition, the Total Least Squares(TLS) algorithm is used to prove that the method is effective. Theoretical analysis shows that the algorithm can significantly improve the GPS positioning precision. 展开更多
关键词 GPS positioning precision: Altitude hold mode Total Least Squares(TLS) algorithm
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Effect of toroidal mode coupling on explosive dynamics of m/n=3/1 double tearing mode
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作者 Xingqiang LU Ge GAO +2 位作者 Zhiwei MA Wei GUO Xin LI 《Plasma Science and Technology》 SCIE EI CAS CSCD 2024年第10期8-16,共9页
The CLT code was used to quantitatively study the impact of toroidal mode coupling on the explosive dynamics of the m/n=3/1 double tearing mode.The focus of this study was on explosive reconnection processes,in which ... The CLT code was used to quantitatively study the impact of toroidal mode coupling on the explosive dynamics of the m/n=3/1 double tearing mode.The focus of this study was on explosive reconnection processes,in which the energy bursts and the main mode no longer dominates when the separation between two rational surfaces is relatively large in the medium range.The development of higher m and n modes is facilitated by a relatively large separation between two rational surfaces,a small q_(min)(the minimum value of the safety factor),or low resistivity.The relationships between the higher m and n mode development,explosive reconnection rate,and position exchange of 3/1 islands are summarized for the first time.Separation plays a more important role than q_(min)in enhancing the development of higher m and n modes.At a relatively large separation,the good development of higher m and n modes greatly reduces the reconnection rate and suppresses the development of the main mode,resulting in the main mode not being able to develop sufficiently large to generate the position changes of 3/1 islands. 展开更多
关键词 toroidal mode coupling higher m and n modes explosive growth reconnection rate position change
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基于级联惯性负载转矩观测器的永磁伺服电机复合抗扰控制
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作者 彭诚 王兵 +1 位作者 易志萱 李赐图 《湖南工业大学学报》 2025年第1期26-34,共9页
针对永磁伺服电机在运行时位置跟踪精度差和抗干扰性能弱等问题,提出一种模型预测位置控制与非奇异快速终端滑模速度控制相结合的复合模型预测控制策略。该控制策略采用非奇异快速终端滑模设计速度控制器,以有效提高响应速度及系统鲁棒... 针对永磁伺服电机在运行时位置跟踪精度差和抗干扰性能弱等问题,提出一种模型预测位置控制与非奇异快速终端滑模速度控制相结合的复合模型预测控制策略。该控制策略采用非奇异快速终端滑模设计速度控制器,以有效提高响应速度及系统鲁棒性;采用模型预测位置控制提高位置跟踪精度;同时,采用基于转动惯量观测和负载转矩观测器相结合的级联惯性负载转矩观测器观测负载转矩并进行前馈补偿,进一步提高系统的抗干扰性能。通过仿真和实验结果可得,所提复合模型预测控制可有效提高永磁伺服电机的动态响应速度和抗负载扰动能力。 展开更多
关键词 永磁伺服电机 模型预测位置控制 滑模控制 负载转矩观测器 转动惯量辨识
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Automatically positioning microseismic sources in mining by the stereo tomographic method using full wavefields 被引量:3
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作者 缪华祥 姜福兴 +3 位作者 宋雪娟 宋建勇 杨淑华 焦俊如 《Applied Geophysics》 SCIE CSCD 2012年第2期168-176,234,235,共11页
For microseisimic monitoring it is difficult to determine wave modes and their propagation velocity. In this paper, we propose a new method for automatically inverting in real time the source characteristics of micros... For microseisimic monitoring it is difficult to determine wave modes and their propagation velocity. In this paper, we propose a new method for automatically inverting in real time the source characteristics of microseismic events in mine engineering without wave mode identification and velocities. Based on the wave equation in a spherical coordinate system, we derive a tomographic imaging equation and formulate a scanning parameter selection criterion by which the microseisimic event maximum energy and corresponding parameters can be determined. By determining the maximum energy positions inside a given risk district, we can indentify microseismic events inside or outside the risk districts. The synthetic and field examples demonstrate that the proposed tomographic imaging method can automatically position microseismic events by only knowing the risk district dimensions and range of velocities without identifying the wavefield modes and accurate velocities. Therefore, the new method utilizes the full wavefields to automatically monitor microseismic events. 展开更多
关键词 microseismic full wavefields wavefield mode identification tomographic image source parameters automatic positioning
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Geochemical Characteristics and Significance of Major Elements, Trace Elements and REE in Mineralized Altered Rocks of Large-Scale Tsagaan Suvarga Cu-Mo Porphyry Deposit in Mongolia 被引量:3
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作者 方维萱 杨社锋 +2 位作者 刘正桃 韦星林 张宝琛 《Journal of Rare Earths》 SCIE EI CAS CSCD 2007年第6期759-769,共11页
The alteration types of the large-scale Tsagaan Suvarga Cu-Mo porphyry deposit mostly comprise stockwork silicification, argillization, quartz-sericite alteration, K-silicate alteration, and propylitization. The miner... The alteration types of the large-scale Tsagaan Suvarga Cu-Mo porphyry deposit mostly comprise stockwork silicification, argillization, quartz-sericite alteration, K-silicate alteration, and propylitization. The mineralized and altered zones from hydrothermal metallogenic center to the outside successively are Cu-bearing stockwork silicification zone, Cu-beating argillized zone, Cu-Mo-bearing quartz-sericite alteration zone, Cu-Mo-bearing K-silicate alteration zone, and pro- pylitization zone. The K-silicate alteration occurred in the early phase, quartz-sericite alteration in the medium phase, and argillization and carbonatization (calcite) in the later phase. Ore-bearing-altered rocks are significantly controlled by the structure and fissure zones of different scales, and NE- and NW-trending fissure zones could probably be the migration pathways of the porphyry hydrothermal system. Results in this study indicated that the less the concentrations of REE, LREE, and HREE and the more the extensive fractionation between LREE and HREE, the closer it is to the center circulatory hydrothermal ore-forming and the more extensive silicification. The exponential relationship between the fractionation of LREE and HREE and the intensity of silicification and K-silicate alteration was found in the Cu-Mo deposit studied. The negative Eu anomaly, normal Eu, positive Eu anomaly and obviously positive Eu anomaly are coincident with the enhancement of Na2O and K2O concentrations gradually, which indicated that Eu anomaly would be significantly controlled by the alkaline metasomatism of the circulatory hydrothermal ore-forming system. Therefore, such characteristics as the positive Eu anomaly, the obvious fractionation between LREE and HREE and their related special alteration lithofacies are suggested to be metallogenic prognostic and exploration indications for Tsagaan Suvarga-style porphyry Cu-Mo deposits in Mongolia and China. 展开更多
关键词 mongolia tsagaan suvarga porphyry Cu-Mo deposit wall rock alteration fractionation mode positive Eu anomaly rare earths
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Research on a combinatorial control method for coaxial rotor aircraft based on sliding mode 被引量:5
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作者 Yi-ran Wei Hong-bin Deng +2 位作者 Zhen-hua Pan Ke-wei Li Han Chen 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2022年第2期280-292,共13页
Aiming at the position and attitude tracking of coaxial rotor aircraft(CRA),this paper proposes a combinatorial control method of sliding mode control(SMC)coupled with proportional-integralderivative control(PIDC).Con... Aiming at the position and attitude tracking of coaxial rotor aircraft(CRA),this paper proposes a combinatorial control method of sliding mode control(SMC)coupled with proportional-integralderivative control(PIDC).Considering the complete description of flight dynamics,aerodynamics and airflow interference,the dynamical model of CRA is established.The dynamical model is simplified according to the actual flight,then the simplified dynamical model is divided into two subsystems:a fully-actuated subsystem and an under-actuated subsystem.The controller of the fully-actuated subsystem consists of a SMC controller coupled with a rate bounded PIDC controller,while the controller of the under-actuated subsystem is composed of a SMC controller.The sliding manifold is defined by combining the position and velocity tracking errors of the state variables for each subsystem.Lyapunov stability theory is used to verify the stability of the sliding mode controller,which ensures that all state trajectories of the system can reach and stay on the sliding mode surface,the uncertainty and external interference of the model are compensated.Simulation and experiment compared with the conventional PIDC are carried out,the results demonstrate the effectiveness and the robustness of the proposed control method of this paper. 展开更多
关键词 Coaxial rotor aircraft Sliding mode control position and attitude tracking Simulation Experiment
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Operation of Kerr-lens mode-locked Ti:sapphire laser in the non-soliton regime 被引量:2
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作者 刘华刚 胡明列 +3 位作者 宋有建 栗岩峰 柴路 王清月 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第1期372-377,共6页
A Kerr-lens mode-locked Ti:sapphire laser operating in a non-soliton regime is demonstrated. Dispersive wave generation is observed as a result of third order dispersion in the vicinity of zero dispersion. The charac... A Kerr-lens mode-locked Ti:sapphire laser operating in a non-soliton regime is demonstrated. Dispersive wave generation is observed as a result of third order dispersion in the vicinity of zero dispersion. The characteristics of the Ti:sapphire l^ser operating in a positive dispersion regime are presented, where the oscillator directly generates pulses with duration continuously tunable from 0.37 ps to 2.11 ps, and 36 fs pulses are achieved atter extracavity compression. The oscillation is numerically simulated with an extended nonlinear Schr6dinger equation, and the simulation results are in good agreement with the experimental results. 展开更多
关键词 Kerr-lens mode locking dispersive wave generation positive dispersion regime Ti:sapphire laser
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Data-processing induced GPS-positioning error 被引量:3
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作者 Tian Yunfeng 《Geodesy and Geodynamics》 2012年第3期51-56,共6页
Global Positioning System data processing is affected by many non-tectonic factors, including the common-mode errors (CME) in station-position time series. The characteristics and origins of CME are still not clear,... Global Positioning System data processing is affected by many non-tectonic factors, including the common-mode errors (CME) in station-position time series. The characteristics and origins of CME are still not clear, due to uneven distribution of global GPS networks and the lack of reliable data of the position time series. In this work, data from 241 continuous GPS stations were reprocessed in a consistent way and the results were compared with those generated at Jet Propulsion Laboratory (JPL). Improvements of residual positions were obtained for many low-quality stations, especially those located in Asia and Australia. 展开更多
关键词 GPS position time series REPROCESSING non-tectonic common-mode error
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Damage Position of Concrete Beam Based on Test of Even Change Point
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作者 张开鹏 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2004年第3期72-73,共2页
The quantitative analysis of damage position of concrete beam is established.The method of damage position free of models used in this paper is based on the variations of strain mode and test of even change point.The ... The quantitative analysis of damage position of concrete beam is established.The method of damage position free of models used in this paper is based on the variations of strain mode and test of even change point.The discrete model and the position criterion are presented.Numerical example is conducted,the result demonstrates that the method of damage position is correct and effective. 展开更多
关键词 test of even change point strain mode damage position
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Dynamic modeling and simulation for the rigid flexible coupling system with a non-tip mass
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作者 李崔春 孟秀云 刘藻珍 《Journal of Beijing Institute of Technology》 EI CAS 2015年第4期432-440,共9页
The rigid flexible coupling system with a mass at non-tip position of the flexible beam is studied in this paper. Using the theory about mechanics problems in a non-inertial coordinate sys- tem, the dynamic equations ... The rigid flexible coupling system with a mass at non-tip position of the flexible beam is studied in this paper. Using the theory about mechanics problems in a non-inertial coordinate sys- tem, the dynamic equations of the rigid flexible coupling system with dynamic stiffening are estab- lished. It is clearly elucidated for the first time that, dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beam and the transverse vibration deformation of the beam. The modeling approach in this paper successfully solves problems of popular modeling methods nowadays: the derivation process is too complex by using only one dynamic principle; a clearly theoretical mechanism for dynamic stiffening can' t be offered. First, the mass at non-tip po- sition is incorporated into the continuous dynamic equations of the system by use of the Dirac lunch tion and the Heaviside function. Then, based on the conclusions of orthogonalization about the nor- mal constrained modes, the finite dimensional state space equations suitable for controller design are obtained. The numerical simulation results show that: dynamic stiffening is included in the first-or- der model established in this paper, which indicates the dynamic responses of the rigid flexible cou- pling system with large overall motion accurately. The results also show that the mass has a soften- ing effect on the dynamic behavior of the flexible beam, and the effect would be more obvious when the mass has a larger mass, or lies closer to the tip of the beam. 展开更多
关键词 non-inertial coordinate system rigid flexible coupling dynamic stiffening mass at non-tip position constrained mode
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