To explore the green development of automobile enterprises and promote the achievement of the“dual carbon”target,based on the bounded rationality assumptions,this study constructed a tripartite evolutionary game mod...To explore the green development of automobile enterprises and promote the achievement of the“dual carbon”target,based on the bounded rationality assumptions,this study constructed a tripartite evolutionary game model of gov-ernment,commercial banks,and automobile enterprises;introduced a dynamic reward and punishment mechanism;and analyzed the development process of the three parties’strategic behavior under the static and dynamic reward and punish-ment mechanism.Vensim PLE was used for numerical simulation analysis.Our results indicate that the system could not reach a stable state under the static reward and punishment mechanism.A dynamic reward and punishment mechanism can effectively improve the system stability and better fit real situations.Under the dynamic reward and punishment mechan-ism,an increase in the initial probabilities of the three parties can promote the system stability,and the government can im-plement effective supervision by adjusting the upper limit of the reward and punishment intensity.Finally,the implementa-tion of green credit by commercial banks plays a significant role in promoting the green development of automobile enter-prises.展开更多
The human-induced vertical vibration serviceability of low-frequency and lightweight footbridges is studied based on the moving mass-spring-damper(MMSD) biodynamic model, and the mass damper(TMD) with different op...The human-induced vertical vibration serviceability of low-frequency and lightweight footbridges is studied based on the moving mass-spring-damper(MMSD) biodynamic model, and the mass damper(TMD) with different optimal model parameters being used to control the vertical vibration.First, the MMSD biodynamic model is employed to simulate the pedestrians, and the time-varying control equations of the vertical dynamic coupling system of the pedestrian-bridgeTMD are established with the consideration of pedestrianbridge dynamic interaction; and the equations are solved by using the Runge-Kutta-Felhberg integral method with variable step size. Secondly, the footbridge dynamic response is calculated under the model of pedestrian-structure dynamic interaction and the model of moving load when the pedestrian pace frequency is consistent with the natural frequency of footbridge. Finally, a comparative study and analysis are made on the control effects of the vertical dynamic coupling system in different optimal models of the TMD. The calculation results show that the pedestrian-bridge dynamic interaction cannot be ignored when the vertical human-induced vibration serviceability of low-frequency and light-weight footbridge is evaluated. The TMD can effectively reduce the vibration under the resonance of pedestrian-bridge, and TMD parameters are recommended for the determination by the Warburton optimization model.展开更多
Aim To analyse stability of the three-dimensional rotational movements of a human torso system under perturbations using anatomical data of muscles (McGill, 1992). Methods To use the linearized analysis methods and a ...Aim To analyse stability of the three-dimensional rotational movements of a human torso system under perturbations using anatomical data of muscles (McGill, 1992). Methods To use the linearized analysis methods and a special model in which the effect of ligamentous and passive resitance by discs and fibers is included. Results The model is capable of predicting the muscle forces,and joint reaction forces at the L5/Sl which are the biomechani- cal factors used to asses the risk of the discs and annulus fibers. Conclusions It can also be used to analyze and neural excitation levels for a diverse Set of trunk movement.展开更多
Abstract--This paper conducts a survey on iterative learn- ing control (ILC) with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, includ...Abstract--This paper conducts a survey on iterative learn- ing control (ILC) with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, including passive and active types, can cause data loss or fragment due to various factors. Passive incomplete information refers to incomplete data and information caused by practical system limitations during data collection, storage, transmission, and processing, such as data dropouts, delays, disordering, and limited transmission bandwidth. Active incomplete information refers to incomplete data and information caused by man-made reduction of data quantity and quality on the premise that the given objective is satisfied, such as sampling and quantization. This survey emphasizes two aspects: the first one is how to guarantee good learning performance and tracking performance with passive incomplete data, and the second is how to balance the control performance index and data demand by active means. The promising research directions along this topic are also addressed, where data robustness is highly emphasized. This survey is expected to improve understanding of the restrictive relationship and trade-off between incomplete data and tracking performance, quantitatively, and promote further developments of ILC theory. Index Terms--Data dropout, data robustness, incomplete in- formation, iterative learning controi(ILC), quantized control, sampled control, varying lengths.展开更多
The performance of Smith prediction monitoring automatic gauge control(AGC) system is influenced by model mismatching greatly in strip rolling process. Aiming at this problem, a feedback-assisted iterative learning co...The performance of Smith prediction monitoring automatic gauge control(AGC) system is influenced by model mismatching greatly in strip rolling process. Aiming at this problem, a feedback-assisted iterative learning control strategy, which learned unknown modeling error by using previous control information repeatedly, was introduced into Smith prediction monitoring AGC system. Firstly, conventional Smith predictor and improved Smith predictor with PI-P controller were analyzed. Secondly, on the basis of establishing of feedback-assisted iterative learning control strategy for improved Smith predictor, process control signal update law and control error were deduced, then convergence condition of this strategy was put forward and proved. Finally, after modeling the automatic position control system, the PI-P Smith prediction monitoring AGC system with feedback-assisted iterative learning control was researched through simulation. Simulation results indicate that this system remains stable during model mismatching. The robustness and response of monitoring AGC is improved by development of feedback-assisted iterative learning control strategy for PI-P Smith predictor.展开更多
A dynamic thermal transfer model of a proton exchange membrane fuel cell (PEMFC) stack is developed based on energy conservation in order to reach better temperature control of PEMFC stack. Considering its uncertain p...A dynamic thermal transfer model of a proton exchange membrane fuel cell (PEMFC) stack is developed based on energy conservation in order to reach better temperature control of PEMFC stack. Considering its uncertain parameters and disturbance, we propose a robust adaptive controller based on backstepping algorithm of Lyaponov function. Numerical simulations indicate the validity of the proposed controller.展开更多
A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Base...A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.展开更多
A quarter-automobile active suspension model was proposed. High speed on/off solenoid valves were used as control valves and fuzzy control was chosen as control method . Based on force analyses of system parts, a math...A quarter-automobile active suspension model was proposed. High speed on/off solenoid valves were used as control valves and fuzzy control was chosen as control method . Based on force analyses of system parts, a mathematical model of the active suspension system was established and simplified by linearization method. Simulation study was conducted with Matlab and three scale coefficients of fuzzy controller (ke, kec, ku) were acquired. And an experimental device was designed and produced. The results indicate that the active suspension system can achieve better vibration isolation performance than passive suspension system, the displacement amplitude of automobile body can be reduced to 55%. Fuzzy control is an effective control method for active suspension system.展开更多
Aluminum matrix composites reinforced by in situ Al2O3 and Al3Zr particles are fabricated from A356-Zr(CO3)2 system via magnetochemistry reaction,and the morphologies,sizes and distributions of the in situ particles a...Aluminum matrix composites reinforced by in situ Al2O3 and Al3Zr particles are fabricated from A356-Zr(CO3)2 system via magnetochemistry reaction,and the morphologies,sizes and distributions of the in situ particles as well as the microstructures,mechanical mechanisms of the composites are investigated by XRD,SEM,TEM and in situ tensile tests.The results indicate that with the pulsed magnetic field assistance,the morphologies of the in situ particles are mainly with ball-shape,the sizes are in nanometer scale and the distributions in the matrix are uniform.The interfaces between the in situ particles and the aluminum matrix are net and no interfacial outgrowth is observed.These are due to the strong vibration induced by the applied magnetic field in the aluminum melt,which in turn,accelerates the melt reactions.The effects of the magnetic field on the above contributions are discussed in detail.展开更多
Lyapunov exponents can act as the judgment rule whether the systems is chaotic or not.We propose an approach to control chaotic systems by varying the Lyapunov exponents of the system. At last we use this method to co...Lyapunov exponents can act as the judgment rule whether the systems is chaotic or not.We propose an approach to control chaotic systems by varying the Lyapunov exponents of the system. At last we use this method to control a chemical system. Both the theoretical analysis and the simulation results prove that this method can quickly and effectively stabilize the chaotic systems to the desire points.展开更多
Separation-recycle system is an important part in chemical process, and its optimization is a multiobjective problem. In this paper the process optimization procedure is proposed. The fuzzy optimization algorithm with...Separation-recycle system is an important part in chemical process, and its optimization is a multiobjective problem. In this paper the process optimization procedure is proposed. The fuzzy optimization algorithm with the concept of relative importance degree (RID) is utilized to transfer multi-objective optimization (MO-O) model into a single-objective optimization (SO-O) framework. The treatment of process condensate in synthesisa mmonia plant is taken as example to illustrate the optimization procedure, and the satisfactory result demonstrates feasibility and effectiveness of the suggested method.展开更多
Given the actual working of a fully mechanized plough at a mining face, we have proposed a formula for running constraints between powered supports and a coal plough under assumed geological conditions of the coal fac...Given the actual working of a fully mechanized plough at a mining face, we have proposed a formula for running constraints between powered supports and a coal plough under assumed geological conditions of the coal face and, on this basis, established an automatic control model of powered supports for the coal plough face. We introduced the working principle of the powered support control system of the plough at the mining face. We established three advanced characteristics of this control system: response speed, reliability and easy maintenance of the system. As well, we briefly introduced, the principal function of primary and subordinate controllers and the realization of the communication system by a Single Bus. Ten controllers were constructed and tested in our laboratorium. The results show that the control model is practical and meets actual conditions. It provides a theoretical basis for designing a comouter control system for a oowered support system of a plough at a mining face.展开更多
Based on frequency response and convex optimization,a novel optimal control system was developed for chemical processes.The feedforward control is designed to improve the tracking performance of closed loop chemical s...Based on frequency response and convex optimization,a novel optimal control system was developed for chemical processes.The feedforward control is designed to improve the tracking performance of closed loop chemical systems.The parametric model is not required because the system directly utilizes the frequency response of the loop transfer function,which can be measured accurately.In particular,the extremal values of magnitude and phase can be solved according to constrained quadratic programming optimizer and convex optimization.Simulation examples show the effectiveness of the method.The design method is simple and easily adopted in chemical industry.展开更多
With a comprehensive consideration of multiple product types, past-sequence-dependent ( p-s-d ) setup times, and deterioration effects constraints in processes of wafer fabrication systems, a novel scheduling model ...With a comprehensive consideration of multiple product types, past-sequence-dependent ( p-s-d ) setup times, and deterioration effects constraints in processes of wafer fabrication systems, a novel scheduling model of multiple orders per job(MOJ) on identical parallel machines was developed and an immune genetic algorithm(IGA) was applied to solving the scheduling problem. A scheduling problem domain was described. A non-linear mathematical programming model was also set up with an objective function of minimizing total weighted earliness-tardlness penalties of the system. On the basis of the mathematical model, IGA was put forward. Based on the genetic algorithm (GA), the proposed algorithm (IGA) can generate feasible solutions and ensure the diversity of antibodies. In the process of immunization programming, to guarantee the algorithm's convergence performance, the modified rule of apparent tardiness cost with setups (ATCS) was presented. Finally, simulation experiments were designed, and the results indicated that the algorithm had good adaptability when the values of the constraints' characteristic parameters were changed and it verified the validity of the algorithm.展开更多
In studying the diffusion-controlled adsorption kinetics of aqueous surfactant solutions at the air/solution surface by means of the maximal bubble pressure method, Fick's diffusion equation for a sphere should be...In studying the diffusion-controlled adsorption kinetics of aqueous surfactant solutions at the air/solution surface by means of the maximal bubble pressure method, Fick's diffusion equation for a sphere should be used. In this paper the equation was solved by means of Laplace transformation under different initial and boundary conditions. The dynamic surface adsorption F(t) for a surfactant solution, which was used to describe the diffusion-controlled adsorption kinetics at the solution surface, was derived. Different from the planar surface adsorption, the dynamic surface adsorption F(t) for the short time consists of two terms: one is the same as Ward-Tordai equation and the other reflects the geometric effect caused by the spherical bubble surface. This effect should not be neglected for the very small radius of the capillary. The equilibrium surface tension γeq and the dynamic surface tension γ(t) of aqueous C10E6 [CH3(CH2)9(OCH2CH2)6OH] solution at temperature 25℃ were measuredby means of Wilhelmy plate method and maximal bubble pressure method respectively. As t→ 0, the theoreticalanalysis is in good agreement with experimental results and the dependence of γ(t) on is linear.展开更多
基金supported by the National Natural Science Foundation of China(71973001).
文摘To explore the green development of automobile enterprises and promote the achievement of the“dual carbon”target,based on the bounded rationality assumptions,this study constructed a tripartite evolutionary game model of gov-ernment,commercial banks,and automobile enterprises;introduced a dynamic reward and punishment mechanism;and analyzed the development process of the three parties’strategic behavior under the static and dynamic reward and punish-ment mechanism.Vensim PLE was used for numerical simulation analysis.Our results indicate that the system could not reach a stable state under the static reward and punishment mechanism.A dynamic reward and punishment mechanism can effectively improve the system stability and better fit real situations.Under the dynamic reward and punishment mechan-ism,an increase in the initial probabilities of the three parties can promote the system stability,and the government can im-plement effective supervision by adjusting the upper limit of the reward and punishment intensity.Finally,the implementa-tion of green credit by commercial banks plays a significant role in promoting the green development of automobile enter-prises.
基金The National Natural Science Foundation of China(No.51508257,51668042,51578274)the Yangtze River Scholar and the Innovation Team of M inistry of Education(No.IRT13068)the Scientific Research Project of Gansu Higher Education(No.2015B-34)
文摘The human-induced vertical vibration serviceability of low-frequency and lightweight footbridges is studied based on the moving mass-spring-damper(MMSD) biodynamic model, and the mass damper(TMD) with different optimal model parameters being used to control the vertical vibration.First, the MMSD biodynamic model is employed to simulate the pedestrians, and the time-varying control equations of the vertical dynamic coupling system of the pedestrian-bridgeTMD are established with the consideration of pedestrianbridge dynamic interaction; and the equations are solved by using the Runge-Kutta-Felhberg integral method with variable step size. Secondly, the footbridge dynamic response is calculated under the model of pedestrian-structure dynamic interaction and the model of moving load when the pedestrian pace frequency is consistent with the natural frequency of footbridge. Finally, a comparative study and analysis are made on the control effects of the vertical dynamic coupling system in different optimal models of the TMD. The calculation results show that the pedestrian-bridge dynamic interaction cannot be ignored when the vertical human-induced vibration serviceability of low-frequency and light-weight footbridge is evaluated. The TMD can effectively reduce the vibration under the resonance of pedestrian-bridge, and TMD parameters are recommended for the determination by the Warburton optimization model.
文摘Aim To analyse stability of the three-dimensional rotational movements of a human torso system under perturbations using anatomical data of muscles (McGill, 1992). Methods To use the linearized analysis methods and a special model in which the effect of ligamentous and passive resitance by discs and fibers is included. Results The model is capable of predicting the muscle forces,and joint reaction forces at the L5/Sl which are the biomechani- cal factors used to asses the risk of the discs and annulus fibers. Conclusions It can also be used to analyze and neural excitation levels for a diverse Set of trunk movement.
基金supported by the National Natural Science Foundation of China(61673045)Beijing Natural Science Foundation(4152040)
文摘Abstract--This paper conducts a survey on iterative learn- ing control (ILC) with incomplete information and associated control system design, which is a frontier of the ILC field. The incomplete information, including passive and active types, can cause data loss or fragment due to various factors. Passive incomplete information refers to incomplete data and information caused by practical system limitations during data collection, storage, transmission, and processing, such as data dropouts, delays, disordering, and limited transmission bandwidth. Active incomplete information refers to incomplete data and information caused by man-made reduction of data quantity and quality on the premise that the given objective is satisfied, such as sampling and quantization. This survey emphasizes two aspects: the first one is how to guarantee good learning performance and tracking performance with passive incomplete data, and the second is how to balance the control performance index and data demand by active means. The promising research directions along this topic are also addressed, where data robustness is highly emphasized. This survey is expected to improve understanding of the restrictive relationship and trade-off between incomplete data and tracking performance, quantitatively, and promote further developments of ILC theory. Index Terms--Data dropout, data robustness, incomplete in- formation, iterative learning controi(ILC), quantized control, sampled control, varying lengths.
基金Project(51074051)supported by the National Natural Science Foundation of China
文摘The performance of Smith prediction monitoring automatic gauge control(AGC) system is influenced by model mismatching greatly in strip rolling process. Aiming at this problem, a feedback-assisted iterative learning control strategy, which learned unknown modeling error by using previous control information repeatedly, was introduced into Smith prediction monitoring AGC system. Firstly, conventional Smith predictor and improved Smith predictor with PI-P controller were analyzed. Secondly, on the basis of establishing of feedback-assisted iterative learning control strategy for improved Smith predictor, process control signal update law and control error were deduced, then convergence condition of this strategy was put forward and proved. Finally, after modeling the automatic position control system, the PI-P Smith prediction monitoring AGC system with feedback-assisted iterative learning control was researched through simulation. Simulation results indicate that this system remains stable during model mismatching. The robustness and response of monitoring AGC is improved by development of feedback-assisted iterative learning control strategy for PI-P Smith predictor.
文摘A dynamic thermal transfer model of a proton exchange membrane fuel cell (PEMFC) stack is developed based on energy conservation in order to reach better temperature control of PEMFC stack. Considering its uncertain parameters and disturbance, we propose a robust adaptive controller based on backstepping algorithm of Lyaponov function. Numerical simulations indicate the validity of the proposed controller.
基金Preject 50225519 supported by the National Outstanding Youth Science Foundation of China
文摘A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.
文摘A quarter-automobile active suspension model was proposed. High speed on/off solenoid valves were used as control valves and fuzzy control was chosen as control method . Based on force analyses of system parts, a mathematical model of the active suspension system was established and simplified by linearization method. Simulation study was conducted with Matlab and three scale coefficients of fuzzy controller (ke, kec, ku) were acquired. And an experimental device was designed and produced. The results indicate that the active suspension system can achieve better vibration isolation performance than passive suspension system, the displacement amplitude of automobile body can be reduced to 55%. Fuzzy control is an effective control method for active suspension system.
基金Project(2007AA03Z548) supported by High-Tech Research and Development Program of ChinaProject(50971066) supported by the National Natural Science Foundation of ChinaProject(1283000349) supported by the Jiangsu University Research Fund for Advanced Scholars,China
文摘Aluminum matrix composites reinforced by in situ Al2O3 and Al3Zr particles are fabricated from A356-Zr(CO3)2 system via magnetochemistry reaction,and the morphologies,sizes and distributions of the in situ particles as well as the microstructures,mechanical mechanisms of the composites are investigated by XRD,SEM,TEM and in situ tensile tests.The results indicate that with the pulsed magnetic field assistance,the morphologies of the in situ particles are mainly with ball-shape,the sizes are in nanometer scale and the distributions in the matrix are uniform.The interfaces between the in situ particles and the aluminum matrix are net and no interfacial outgrowth is observed.These are due to the strong vibration induced by the applied magnetic field in the aluminum melt,which in turn,accelerates the melt reactions.The effects of the magnetic field on the above contributions are discussed in detail.
文摘Lyapunov exponents can act as the judgment rule whether the systems is chaotic or not.We propose an approach to control chaotic systems by varying the Lyapunov exponents of the system. At last we use this method to control a chemical system. Both the theoretical analysis and the simulation results prove that this method can quickly and effectively stabilize the chaotic systems to the desire points.
文摘Separation-recycle system is an important part in chemical process, and its optimization is a multiobjective problem. In this paper the process optimization procedure is proposed. The fuzzy optimization algorithm with the concept of relative importance degree (RID) is utilized to transfer multi-objective optimization (MO-O) model into a single-objective optimization (SO-O) framework. The treatment of process condensate in synthesisa mmonia plant is taken as example to illustrate the optimization procedure, and the satisfactory result demonstrates feasibility and effectiveness of the suggested method.
基金Project 104030 supported by the Ministry of Education of the People’s Republic of China
文摘Given the actual working of a fully mechanized plough at a mining face, we have proposed a formula for running constraints between powered supports and a coal plough under assumed geological conditions of the coal face and, on this basis, established an automatic control model of powered supports for the coal plough face. We introduced the working principle of the powered support control system of the plough at the mining face. We established three advanced characteristics of this control system: response speed, reliability and easy maintenance of the system. As well, we briefly introduced, the principal function of primary and subordinate controllers and the realization of the communication system by a Single Bus. Ten controllers were constructed and tested in our laboratorium. The results show that the control model is practical and meets actual conditions. It provides a theoretical basis for designing a comouter control system for a oowered support system of a plough at a mining face.
基金Supported by the National Natural Science Foundation of China(51205133) Natural Science Foundation of Shanghai(11ZR1409000) Ph.D.Programs Foundation of Ministry of Education of China(20110074120007)
文摘Based on frequency response and convex optimization,a novel optimal control system was developed for chemical processes.The feedforward control is designed to improve the tracking performance of closed loop chemical systems.The parametric model is not required because the system directly utilizes the frequency response of the loop transfer function,which can be measured accurately.In particular,the extremal values of magnitude and phase can be solved according to constrained quadratic programming optimizer and convex optimization.Simulation examples show the effectiveness of the method.The design method is simple and easily adopted in chemical industry.
基金National Natural Science Foundations of China(No.61273035,No.71071115)
文摘With a comprehensive consideration of multiple product types, past-sequence-dependent ( p-s-d ) setup times, and deterioration effects constraints in processes of wafer fabrication systems, a novel scheduling model of multiple orders per job(MOJ) on identical parallel machines was developed and an immune genetic algorithm(IGA) was applied to solving the scheduling problem. A scheduling problem domain was described. A non-linear mathematical programming model was also set up with an objective function of minimizing total weighted earliness-tardlness penalties of the system. On the basis of the mathematical model, IGA was put forward. Based on the genetic algorithm (GA), the proposed algorithm (IGA) can generate feasible solutions and ensure the diversity of antibodies. In the process of immunization programming, to guarantee the algorithm's convergence performance, the modified rule of apparent tardiness cost with setups (ATCS) was presented. Finally, simulation experiments were designed, and the results indicated that the algorithm had good adaptability when the values of the constraints' characteristic parameters were changed and it verified the validity of the algorithm.
基金Supported by the Scientific Research Foundation of the State Education Ministry for the Returned Overseas Chinese Scholars (D4200111).
文摘In studying the diffusion-controlled adsorption kinetics of aqueous surfactant solutions at the air/solution surface by means of the maximal bubble pressure method, Fick's diffusion equation for a sphere should be used. In this paper the equation was solved by means of Laplace transformation under different initial and boundary conditions. The dynamic surface adsorption F(t) for a surfactant solution, which was used to describe the diffusion-controlled adsorption kinetics at the solution surface, was derived. Different from the planar surface adsorption, the dynamic surface adsorption F(t) for the short time consists of two terms: one is the same as Ward-Tordai equation and the other reflects the geometric effect caused by the spherical bubble surface. This effect should not be neglected for the very small radius of the capillary. The equilibrium surface tension γeq and the dynamic surface tension γ(t) of aqueous C10E6 [CH3(CH2)9(OCH2CH2)6OH] solution at temperature 25℃ were measuredby means of Wilhelmy plate method and maximal bubble pressure method respectively. As t→ 0, the theoreticalanalysis is in good agreement with experimental results and the dependence of γ(t) on is linear.