Vessels with semi-closed tanks(i.e.,well docks)are widely applied in the military operation and maritime engineer-ing.The water is bound by the semi-closed floating tank and forced by both the incident waves and ship...Vessels with semi-closed tanks(i.e.,well docks)are widely applied in the military operation and maritime engineer-ing.The water is bound by the semi-closed floating tank and forced by both the incident waves and ship’s motions.The free surface oscillations inside the flooded well dock is thus distinctive and very complicated.So far,the natural modes of semi-closed floating tanks have not yet been studied.This paper investigates the characteristics of natural modes of a floating semi-closed tank by combining a mode-resolving model based on mild-slope equations and a hydrodynamic model based on computational fluid dynamics.Results show that the first three natural periods(i.e.,74,23.6,and 14 s)of the tank fall into the band of swell and infragravity waves and they could be triggered under certain circumstance.Multi-period free surface oscillations are observed inside the tank,including the longest natural period(i.e.,74 s),though the incident waves are monochromatic.A possible generation mechanism for the long-period mode is explained on the basis of liquid sloshing and harbor oscillations.Moreover,a long-period component with a period close to the natural mode of well dock is observed in the ship motions,which is generated by the interaction between the waves and ship.展开更多
We have numerically and experimentally investigated the flow modes of Taylor-Couette system consisting of coaxial two cylinders with vertical axes. The inner cylinder rotates and the outer cylinder and the bottom end ...We have numerically and experimentally investigated the flow modes of Taylor-Couette system consisting of coaxial two cylinders with vertical axes. The inner cylinder rotates and the outer cylinder and the bottom end of the cylinders remain stationary. The upper top boundary is the free surface of the working liquid between the inner and outer cylinders and it contacts with the air. While this flow appears in fluid machinery and chemical reactors and includes industrial interests, it also contains problems of fluid mechanics, which is about the behavior of the free surface in the rotating field. In this paper, we concretely show the developments of the one cell mode flow and the three cell mode flow at a small aspect ratio. We also represent the bifurcation diagram of the flow at the moderate aspect ratio about 5.5. In the numerical simulation, the flow is rest in the initial state, and the inner cylinder is linearly or suddenly accelerated to attain a flow with a prescribed Reynolds number. When the acceleration of the inner cylinder is high, an imperfect bifurcation occurs and the flows of the secondary modes emerge. At high Reynolds numbers, the flow first has many vortices and then some of the vortices collapse and the final stable flow arises. The loci of the normal five cell mode, the anomalous six cell mode and the secondary seven cell mode are determined.展开更多
To determine the correlation between the stem taperingness and central shaft by free spindle pruning mode on different apple cultivars, the central shaft growth data of three cultivars of free spindle short shoot "F...To determine the correlation between the stem taperingness and central shaft by free spindle pruning mode on different apple cultivars, the central shaft growth data of three cultivars of free spindle short shoot "Fuji", free spindle long shoot "Fuji", free spindle "Huaguan" were investigated in Xingtang County of Hebei Province by SPSS analysis. The results showed that the stem taperingness on free spindle short shoot "Fuji" was in negative correlation with central shaft, but the correlation was not significant. While the stem taperingness on free spindle long shoot "Fuji" was in positive correlation with central shaft, but the correlation was not significant either. The stern taperingness on free spindle "Huaguan" was in negative correlation with central shaft, and the correlation between the stem taperingness and the central shaft total length was significant at the level of 0.01. The results.provided scientific theoretical basis for guiding the dwarfing rootstocks close planting apple tree pruning technology.展开更多
The possible inclusion modes of berberine(Berb) with β-cyclodextrin(BCD) in aqueous solution were predicted by molecular docking,molecular dynamics(MD) simulation and binding free energy calculations.Firstly,th...The possible inclusion modes of berberine(Berb) with β-cyclodextrin(BCD) in aqueous solution were predicted by molecular docking,molecular dynamics(MD) simulation and binding free energy calculations.Firstly,the molecular docking result reveals that the docking conformations of Berb appeared in two clusters ranked in two opposite orientations.Then,10 ns MD simulation was performed separately on the lowest energy conformation of each orientation(Mode I and Mode II) obtained by molecular docking.Moreover,based on the trajectories from MD simulation,the binding free energies of the two different modes were calculated by the Molecular Mechanics/Poisson Boltzmann surface area(MM/PBSA) method.Through analyzing the binding free energies of Berb with BCD,we found that Mode II was the preferential inclusion mode,which was in good agreement with the experimental result.In addition,the computed results show that the main impetus for the complex was the van der Waals interaction,but the solvation energy and the entropy change produced an adverse effect on the complex.展开更多
A new type of element which is suitable for solving the modes of thegalloping long multi-span bundle conductor structures is presented. The element is composed of allsub-conductor segments between two spacers. Based o...A new type of element which is suitable for solving the modes of thegalloping long multi-span bundle conductor structures is presented. The element is composed of allsub-conductor segments between two spacers. Based on the linearized governing differential equationsof the conductors, the mass matrix and stiffness matrix of the element in consideration of theconstrained relations imposed on the conductors by spacers are derived. The dynamic characteristicsof the galloping control devices can be directly added to the element. The modes for an actual powerline structure are computed by using the element formula and FEM procedures, where seven cases ofdifferent galloping control device allocations are considered. Compared with the measured data, themethod is shown to be reliable and effective. Analysis and discussions of the computational resultsare given. Some hints that are helpful to further investigation of galloping are also obtained .展开更多
The mode serials of the Earth’s free oscillation provide some important information on the Earth’s deep structure and superconducting gravimeters (SG) can investigate the phenomena of the Earth’s free oscillation...The mode serials of the Earth’s free oscillation provide some important information on the Earth’s deep structure and superconducting gravimeters (SG) can investigate the phenomena of the Earth’s free oscillations with high accuracy. The great Sumatra-Andaman earthquake fully excited the Earth’s free oscillations and these signals were perfectly recorded by five superconducting gravimeters in the globe. After the pre-treatment and spectral analysis on the SG observation data, we obtained the experimented mode serials of the Earth’s free oscillations consisting of 147 modes with GGP station data. These observed modes were themselves some new important data for the study of the Earth’s deep structure. On the basis of the discussions on some checked inner-core-sensitive modes, we distinguished three layers from the inner core, and the boundary of the upper layer was compatible with the formerly known transition zone in the inner core based on seismic body waves and supported that there were the hemispherical variation and very lower shear velocity zone in the lower inner core.展开更多
With consideration of a high-rise coupled building system,a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system.The general motion equation for the two beams interconnecte...With consideration of a high-rise coupled building system,a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system.The general motion equation for the two beams interconnected by multiple viscous/visco-elastic dampers is rewritten into a non-dimensional form to identify the minimal set of parameters governing the dynamic characteristics.The corresponding exact solution suitable for arbitrary boundary conditions is presented.Furthermore,the methodology for computing the coefficients of the modal shape function is proposed.As an example,the explicit expression of the modal shape function is derived,provided only one damper is adopted to connect the adjacent buildings.Finally,to validate the proposed methodologies,three case studies are performed,in which the existence of the overdamping and the optimal damping coefficient are revealed.In the case of using one damper in connecting two similar buildings,the estimating equations for the first modal damping ratio are formulated.展开更多
A periodic packing mode of trickle-bed reactor (TBR) for the gas limited reaction was proposed. Hy-drogenation of 2-ethylanthraquinone over Pd/Al2O3 in a laboratory-scale TBR was taken as a test reaction for determini...A periodic packing mode of trickle-bed reactor (TBR) for the gas limited reaction was proposed. Hy-drogenation of 2-ethylanthraquinone over Pd/Al2O3 in a laboratory-scale TBR was taken as a test reaction for determining whether the periodic packing mode is advantageous. The effects of operating conditions and packing type on TBR performance were experimentally examined to demonstrate the cause-effect relationships. A mathe-matic model of TBR considering axial dispersion and fractional wetting was developed to quantitatively illuminate the reason of performance enhancement.展开更多
The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system's flexural deformatio...The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system's flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement's mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.展开更多
Steel 20Mn23AlV is a type of high aluminum steel with a very low ladle free-opening rate. The aluminum composition of 20Mn23AlV ranges from 1.6% to 2.45% ,which is significantly higher than other types of steel. Accor...Steel 20Mn23AlV is a type of high aluminum steel with a very low ladle free-opening rate. The aluminum composition of 20Mn23AlV ranges from 1.6% to 2.45% ,which is significantly higher than other types of steel. According to the real condition of 40 t ladle in steel-making plant of Baosteel Special Steel Company, previous works show that the key factors affecting the ladle free-opening rate of high aluminum steel in continuous casting are:sand material, accessories baking, ladle nozzle cleaning, the process and amount of adding sand, and the rate of argon stirring during refining. Therefore, improving the ladle filler sand quality, baking all of the raw materials, controlling the addition of ladle filler sand, cleaning the ladle nozzle, and optimizing argon stirring during the refining process can resolve the problem of a low ladle free-opening rate of high aluminum steel caused by the long ladle time of liquid steel.展开更多
We have been developing debris-free laser plasma sources for EUV lithography since 1996. Two types of debris-free sources, such as cryogenic target and gas-puff target laser plasma sources, were designed and built up ...We have been developing debris-free laser plasma sources for EUV lithography since 1996. Two types of debris-free sources, such as cryogenic target and gas-puff target laser plasma sources, were designed and built up in CIOMP. EUV radiation spectra of the sources with a variety of targets have been obtained by different ways.展开更多
A new adaptive quasi-sliding mode control algorithm is developed for a class of nonlinear discrete-time systems, which is especially useful for nonlinear systems with vaguely known dynamics. This design is model-free,...A new adaptive quasi-sliding mode control algorithm is developed for a class of nonlinear discrete-time systems, which is especially useful for nonlinear systems with vaguely known dynamics. This design is model-free, and is based directly on pseudo-partial-derivatives derived on-line from the input and output information of the system using an improved recursive projection type of identification algorithm. The theoretical analysis and simulation results show that the adaptive quasi-sliding mode control system is stable and convergent.展开更多
This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode...This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode shape functions and inherent frequencies are deduced. The results can be gained by means of computer. The analysis shows that the effect of liquid and water on vibration of cylindrical tank is respectively equivalent to a generalized distributive mass attached to the tank.展开更多
The HAZ microstructure and performance of Quenching and Tempering mode temper bead welding and general welded joints which were made on SA508-3 steel of 60 mm thickness were compared in this article. The result shows ...The HAZ microstructure and performance of Quenching and Tempering mode temper bead welding and general welded joints which were made on SA508-3 steel of 60 mm thickness were compared in this article. The result shows that tempering sorbite which has excellent overall performance was obtained in both modes. The microstructure of Quenching and Tempering mode welded joints got more fine grain. Even though the hardness of tempering bead welded joints is higher than the general one,it still meets the standards which is lower than 350 HV. The impact absorbing energy of each district of tempering bead welded joints HAZ reached 170 J,which is equal to general one.展开更多
A self-tuning reaching law based sliding mode control(SMC)theory is proposed to stabilize the nonlinear continuous stirred tank reactor(CSTR).T-S fuzzy logic is used to build a global fuzzy state-space linear model.Co...A self-tuning reaching law based sliding mode control(SMC)theory is proposed to stabilize the nonlinear continuous stirred tank reactor(CSTR).T-S fuzzy logic is used to build a global fuzzy state-space linear model.Combing the traits of SMC and CSTR,three fuzzy rules can meet the requirements of controlled system.The self-tuning switch control law which can drive the state variables to the sliding surface as soon as possible is designed to ensure the robustness of uncertain fuzzy system.Lyapunov equation is applied to proving the stability of the sliding surface.The simulations show that the proposed approach can achieve desired performance with less chattering problem.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.51979029)。
文摘Vessels with semi-closed tanks(i.e.,well docks)are widely applied in the military operation and maritime engineer-ing.The water is bound by the semi-closed floating tank and forced by both the incident waves and ship’s motions.The free surface oscillations inside the flooded well dock is thus distinctive and very complicated.So far,the natural modes of semi-closed floating tanks have not yet been studied.This paper investigates the characteristics of natural modes of a floating semi-closed tank by combining a mode-resolving model based on mild-slope equations and a hydrodynamic model based on computational fluid dynamics.Results show that the first three natural periods(i.e.,74,23.6,and 14 s)of the tank fall into the band of swell and infragravity waves and they could be triggered under certain circumstance.Multi-period free surface oscillations are observed inside the tank,including the longest natural period(i.e.,74 s),though the incident waves are monochromatic.A possible generation mechanism for the long-period mode is explained on the basis of liquid sloshing and harbor oscillations.Moreover,a long-period component with a period close to the natural mode of well dock is observed in the ship motions,which is generated by the interaction between the waves and ship.
文摘We have numerically and experimentally investigated the flow modes of Taylor-Couette system consisting of coaxial two cylinders with vertical axes. The inner cylinder rotates and the outer cylinder and the bottom end of the cylinders remain stationary. The upper top boundary is the free surface of the working liquid between the inner and outer cylinders and it contacts with the air. While this flow appears in fluid machinery and chemical reactors and includes industrial interests, it also contains problems of fluid mechanics, which is about the behavior of the free surface in the rotating field. In this paper, we concretely show the developments of the one cell mode flow and the three cell mode flow at a small aspect ratio. We also represent the bifurcation diagram of the flow at the moderate aspect ratio about 5.5. In the numerical simulation, the flow is rest in the initial state, and the inner cylinder is linearly or suddenly accelerated to attain a flow with a prescribed Reynolds number. When the acceleration of the inner cylinder is high, an imperfect bifurcation occurs and the flows of the secondary modes emerge. At high Reynolds numbers, the flow first has many vortices and then some of the vortices collapse and the final stable flow arises. The loci of the normal five cell mode, the anomalous six cell mode and the secondary seven cell mode are determined.
基金Supported by the China Agriculture Research System(CARS-28)the Project of the Science and Technology Department of Hebei Province(11220104D-1)~~
文摘To determine the correlation between the stem taperingness and central shaft by free spindle pruning mode on different apple cultivars, the central shaft growth data of three cultivars of free spindle short shoot "Fuji", free spindle long shoot "Fuji", free spindle "Huaguan" were investigated in Xingtang County of Hebei Province by SPSS analysis. The results showed that the stem taperingness on free spindle short shoot "Fuji" was in negative correlation with central shaft, but the correlation was not significant. While the stem taperingness on free spindle long shoot "Fuji" was in positive correlation with central shaft, but the correlation was not significant either. The stern taperingness on free spindle "Huaguan" was in negative correlation with central shaft, and the correlation between the stem taperingness and the central shaft total length was significant at the level of 0.01. The results.provided scientific theoretical basis for guiding the dwarfing rootstocks close planting apple tree pruning technology.
基金Supported by the National Natural Science Foundation of China(No. 20975081)the Open Foundation of the Key Laboratory of Synthetic and Natural Functional Molecular Chemistry of Ministry of Education,China(No.KF09014)the Northwest University Graduate Cross-discipline Funds,China(No.09YJC18)
文摘The possible inclusion modes of berberine(Berb) with β-cyclodextrin(BCD) in aqueous solution were predicted by molecular docking,molecular dynamics(MD) simulation and binding free energy calculations.Firstly,the molecular docking result reveals that the docking conformations of Berb appeared in two clusters ranked in two opposite orientations.Then,10 ns MD simulation was performed separately on the lowest energy conformation of each orientation(Mode I and Mode II) obtained by molecular docking.Moreover,based on the trajectories from MD simulation,the binding free energies of the two different modes were calculated by the Molecular Mechanics/Poisson Boltzmann surface area(MM/PBSA) method.Through analyzing the binding free energies of Berb with BCD,we found that Mode II was the preferential inclusion mode,which was in good agreement with the experimental result.In addition,the computed results show that the main impetus for the complex was the van der Waals interaction,but the solvation energy and the entropy change produced an adverse effect on the complex.
文摘A new type of element which is suitable for solving the modes of thegalloping long multi-span bundle conductor structures is presented. The element is composed of allsub-conductor segments between two spacers. Based on the linearized governing differential equationsof the conductors, the mass matrix and stiffness matrix of the element in consideration of theconstrained relations imposed on the conductors by spacers are derived. The dynamic characteristicsof the galloping control devices can be directly added to the element. The modes for an actual powerline structure are computed by using the element formula and FEM procedures, where seven cases ofdifferent galloping control device allocations are considered. Compared with the measured data, themethod is shown to be reliable and effective. Analysis and discussions of the computational resultsare given. Some hints that are helpful to further investigation of galloping are also obtained .
基金supported jointly by the National Natural Science Foundation of China (Nos. 40974046,90814009 and 40730316)the Natural Science Foundation of Hubei Province (No. 2008CDB389)the Knowledge Innovation Project of Chinese Academy of Sciences (No. KZCX2-YW-133)
文摘The mode serials of the Earth’s free oscillation provide some important information on the Earth’s deep structure and superconducting gravimeters (SG) can investigate the phenomena of the Earth’s free oscillations with high accuracy. The great Sumatra-Andaman earthquake fully excited the Earth’s free oscillations and these signals were perfectly recorded by five superconducting gravimeters in the globe. After the pre-treatment and spectral analysis on the SG observation data, we obtained the experimented mode serials of the Earth’s free oscillations consisting of 147 modes with GGP station data. These observed modes were themselves some new important data for the study of the Earth’s deep structure. On the basis of the discussions on some checked inner-core-sensitive modes, we distinguished three layers from the inner core, and the boundary of the upper layer was compatible with the formerly known transition zone in the inner core based on seismic body waves and supported that there were the hemispherical variation and very lower shear velocity zone in the lower inner core.
文摘With consideration of a high-rise coupled building system,a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system.The general motion equation for the two beams interconnected by multiple viscous/visco-elastic dampers is rewritten into a non-dimensional form to identify the minimal set of parameters governing the dynamic characteristics.The corresponding exact solution suitable for arbitrary boundary conditions is presented.Furthermore,the methodology for computing the coefficients of the modal shape function is proposed.As an example,the explicit expression of the modal shape function is derived,provided only one damper is adopted to connect the adjacent buildings.Finally,to validate the proposed methodologies,three case studies are performed,in which the existence of the overdamping and the optimal damping coefficient are revealed.In the case of using one damper in connecting two similar buildings,the estimating equations for the first modal damping ratio are formulated.
基金the State Key Development Program for Basic Research of China (No. G2000048005) the SINOPEC (No.X503023).
文摘A periodic packing mode of trickle-bed reactor (TBR) for the gas limited reaction was proposed. Hy-drogenation of 2-ethylanthraquinone over Pd/Al2O3 in a laboratory-scale TBR was taken as a test reaction for determining whether the periodic packing mode is advantageous. The effects of operating conditions and packing type on TBR performance were experimentally examined to demonstrate the cause-effect relationships. A mathe-matic model of TBR considering axial dispersion and fractional wetting was developed to quantitatively illuminate the reason of performance enhancement.
基金Supported by National Natural Science Foundation of China(Grant No.51375424)
文摘The existence of rolling deformation area in the rolling mill system is the main characteristic which dis- tinguishes the other machinery. In order to analyze the dynamic property of roll system's flexural deformation, it is necessary to consider the transverse periodic movement of stock in the rolling deformation area which is caused by the flexural deformation movement of roll system simul- taneously. Therefore, the displacement field of roll system and flow of metal in the deformation area is described by kinematic analysis in the dynamic system. Through intro- ducing the lateral displacement function of metal in the deformation area, the dynamic variation of per unit width rolling force can be determined at the same time. Then the coupling law caused by the co-effect of rigid movement and flexural deformation of the system structural elements is determined. Furthermore, a multi-parameter coupling dynamic model of the roll system and stock is established by the principle of virtual work. More explicitly, the cou- pled motion modal analysis was made for the roll system. Meanwhile, the analytical solutions for the flexural defor- mation movement's mode shape functions of rolls are discussed. In addition, the dynamic characteristic of the lateral flow of metal in the rolling deformation area has been analyzed at the same time. The establishment ofdynamic lateral displacement function of metal in the deformation area makes the foundation for analyzing the coupling law between roll system and rolling deformation area, and provides a theoretical basis for the realization of the dynamic shape control of steel strip.
文摘Steel 20Mn23AlV is a type of high aluminum steel with a very low ladle free-opening rate. The aluminum composition of 20Mn23AlV ranges from 1.6% to 2.45% ,which is significantly higher than other types of steel. According to the real condition of 40 t ladle in steel-making plant of Baosteel Special Steel Company, previous works show that the key factors affecting the ladle free-opening rate of high aluminum steel in continuous casting are:sand material, accessories baking, ladle nozzle cleaning, the process and amount of adding sand, and the rate of argon stirring during refining. Therefore, improving the ladle filler sand quality, baking all of the raw materials, controlling the addition of ladle filler sand, cleaning the ladle nozzle, and optimizing argon stirring during the refining process can resolve the problem of a low ladle free-opening rate of high aluminum steel caused by the long ladle time of liquid steel.
文摘We have been developing debris-free laser plasma sources for EUV lithography since 1996. Two types of debris-free sources, such as cryogenic target and gas-puff target laser plasma sources, were designed and built up in CIOMP. EUV radiation spectra of the sources with a variety of targets have been obtained by different ways.
文摘A new adaptive quasi-sliding mode control algorithm is developed for a class of nonlinear discrete-time systems, which is especially useful for nonlinear systems with vaguely known dynamics. This design is model-free, and is based directly on pseudo-partial-derivatives derived on-line from the input and output information of the system using an improved recursive projection type of identification algorithm. The theoretical analysis and simulation results show that the adaptive quasi-sliding mode control system is stable and convergent.
文摘This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode shape functions and inherent frequencies are deduced. The results can be gained by means of computer. The analysis shows that the effect of liquid and water on vibration of cylindrical tank is respectively equivalent to a generalized distributive mass attached to the tank.
基金supported by the Key State Science and Technology Projects(Grant No.2011ZX04016-061 and No.2012ZX06004-001-001-005)
文摘The HAZ microstructure and performance of Quenching and Tempering mode temper bead welding and general welded joints which were made on SA508-3 steel of 60 mm thickness were compared in this article. The result shows that tempering sorbite which has excellent overall performance was obtained in both modes. The microstructure of Quenching and Tempering mode welded joints got more fine grain. Even though the hardness of tempering bead welded joints is higher than the general one,it still meets the standards which is lower than 350 HV. The impact absorbing energy of each district of tempering bead welded joints HAZ reached 170 J,which is equal to general one.
文摘A self-tuning reaching law based sliding mode control(SMC)theory is proposed to stabilize the nonlinear continuous stirred tank reactor(CSTR).T-S fuzzy logic is used to build a global fuzzy state-space linear model.Combing the traits of SMC and CSTR,three fuzzy rules can meet the requirements of controlled system.The self-tuning switch control law which can drive the state variables to the sliding surface as soon as possible is designed to ensure the robustness of uncertain fuzzy system.Lyapunov equation is applied to proving the stability of the sliding surface.The simulations show that the proposed approach can achieve desired performance with less chattering problem.