In this study, kinetic energy budget equations of rotational and divergent flow in pressure coordinates are derived on terrain-following coordinates. The new formulation explicitly shows the terrain effects and can be...In this study, kinetic energy budget equations of rotational and divergent flow in pressure coordinates are derived on terrain-following coordinates. The new formulation explicitly shows the terrain effects and can be applied directly to model-simulated dynamic and thermodynamic fields on the model's original vertical grid. Such application eliminates interpolation error and avoids errors in virtual weather systems in mountainous areas. These advantages and their significance are demonstrated by a numerical study in terrain-following coordinates of a developing vortex after it moves over the Tibetan Plateau in China.展开更多
Based on classical terrain following (TF) algorithm (adaptive angle method), a new method for TF controller is proposed by using angle of attack. A method of obtaining terrain outline data from Digital Elevation Map (...Based on classical terrain following (TF) algorithm (adaptive angle method), a new method for TF controller is proposed by using angle of attack. A method of obtaining terrain outline data from Digital Elevation Map (DEM) for TF control is discussed in order to save store space. The block control model, which is suitable for backstepping design, is given for nonlinear model of aircraft. Making full use of the characteristics of the system and combining block control principle, backstepping technique, a robust controller design method is proposed. Uncertainties in every sub-block are allowed, and can be canceled by using the idea of nonlinear damping. It is proved that the state tracking errors converge to the neighborhood of the origin exponentially. Finally, nonlinear six-degree-of-freedom simulation results for the aircraft model are presented to demonstrate the effectiveness of the proposed control law.展开更多
Based on the optimal control theory, a 3-dimensionnal direct generation algorithm is proposed for anti-ground low altitude penetration tasks under complex terrain. By optimizing the terrain following(TF) objective fun...Based on the optimal control theory, a 3-dimensionnal direct generation algorithm is proposed for anti-ground low altitude penetration tasks under complex terrain. By optimizing the terrain following(TF) objective function,terrain coordinate system, missile dynamic model and control vector, the TF issue is turning into the improved optimal control problem whose mathmatical model is simple and need not solve the second order terrain derivative. Simulation results prove that this method is reasonable and feasible. The TF precision is in the scope from 0.3 m to 3.0 m,and the planning time is less than 30 min. This method have the strongpionts such as rapidness, precision and has great application value.展开更多
This study is designed to solve supply chain inefficiencies caused by some members’financial problems,such as capital shortages and financing restrictions in a stochastic environment.To this end,we have established a...This study is designed to solve supply chain inefficiencies caused by some members’financial problems,such as capital shortages and financing restrictions in a stochastic environment.To this end,we have established a supply chain finance framework by designing two novel coordinating contracts based on trade credit financing for different problem settings.These contracts are modeled in the form of multi-leader Stackelberg games that address horizontal and vertical competition in a supply chain consisting of multiple suppliers and a financially constrained manufacturer.However,previous studies in the trade credit literature have addressed only simple vertical competition,that is,seller-buyer competition.To solve the proposed models,two algorithms were developed by combining population-based metaheuristics,the Nash-domination concept,and the Nikaido-Isoda function.The results demonstrate that the proposed supply chain finance framework can eliminate supply chain inefficiencies and make a large profit for suppliers,as well as the financially constrained manufacturer.Furthermore,the results of the contracts’analysis showed that if the manufacturer is required to settle its payments to suppliers before the end of the period,the trade credit contract cannot coordinate the supply chain because of a lack of incentive for suppliers.However,if the manufacturer is allowed to extend its payments to the end of the period,the proposed trade credit financing contract can coordinate the supply chain.Finally,the sensitivity analysis results indicate that the worse the financial status of the manufacturer,the more bargaining power suppliers have in determining the contract parameters for more profit.展开更多
Virtual simulation technology is of great importance for the teleoperation of lunar rovers during the exploration phase, as well as the design of locomotion systems, performance evaluation, and control strategy verifi...Virtual simulation technology is of great importance for the teleoperation of lunar rovers during the exploration phase, as well as the design of locomotion systems, performance evaluation, and control strategy verification during the R&D phase. The currently used simulation methods for lunar rovers have several disadvantages such as poor fidelity for wheel-soil interaction mechanics, difficulty in simulating rough terrains, and high complexity making it difficult to realize mobility control in simulation systems. This paper presents an approach for the construction of a virtual simulation system that integrates the features of 3D modeling, wheel-soil interaction mechanics, dynamics analysis, mobility control, and visualization for lunar rovers. Wheel-soil interaction experiments are carried out to test the forces and moments acted on a lunar rover’s wheel by the soil with a vertical load of 80 N and slip ratios of 0, 0.03, 0.05, 0.1, 0.2, 0.3, 0.4, and 0.6. The experimental results are referenced in order to set the parameters’ values for the PAC2002 tire model of the ADAMS/Tire module. In addition, the rough lunar terrain is simulated with 3DS Max software after analyzing its characteristics, and a data-transfer program is developed with Matlab to simulate the 3D reappearance of a lunar environment in ADAMS. The 3D model of a lunar rover is developed by using Pro/E software and is then imported into ADAMS. Finally, a virtual simulation system for lunar rovers is developed. A path-following control strategy based on slip compensation for a six-wheeled lunar rover prototype is researched. The controller is implemented by using Matlab/Simulink to carry out joint simulations with ADAMS. The designed virtual lunar rover could follow the planned path on a rough terrain. This paper can also provide a reference scheme for virtual simulation and performance analysis of rovers moving on rough lunar terrains.展开更多
In this paper output predictive algorithm is applied to the design of predictive controller for an optimal path terrain following system. In this way, the error of path tracking is decreased to a minimum degree simply...In this paper output predictive algorithm is applied to the design of predictive controller for an optimal path terrain following system. In this way, the error of path tracking is decreased to a minimum degree simply and efficiently and the computation time for the optimal path is shortened greatly. Therefore, the real-time processing of the optimal path terrain following system is made to be very helpful.展开更多
An optimal preview method is applied to the design of terrain following controller for cruise missile. In this method, tracking errors and control increments are both considered in the quadratic cost function. Integra...An optimal preview method is applied to the design of terrain following controller for cruise missile. In this method, tracking errors and control increments are both considered in the quadratic cost function. Integrating the general optimal servo system with a preview feedforward compensation that feeds forward future command and future disturbance produces an optimal preview servo system. In the terrain following system, the flight altitude of the cruise missile is a command signal, and its future information can be known apriori. Hence, we have designed a terrain following controller with a basic state feedback and a feedforward compensation for future altitude information. Simulation results show that the performance of the terrain following system with such an optimal preview controller has been improved dramatically.展开更多
In the terrain following coordinate,Gal-Chen and Somerville[1]and other proposed a vertical coordinate z∝(z−z_(bottom))/(ztop−z_(bottom))and constant spatial intervals ofδx andδy along the other directions.Because ...In the terrain following coordinate,Gal-Chen and Somerville[1]and other proposed a vertical coordinate z∝(z−z_(bottom))/(ztop−z_(bottom))and constant spatial intervals ofδx andδy along the other directions.Because the variation ofδx andδy was ignored,their coordinate does not really follow the terrain.It fails to reproduce the divergence and curl over a complex terrain.Aligning the coordinate with real terrain,the divergence and curl we obtained from the curvilinear coordinate are consistent with the Cartesian coordinate.With a modification,the simulated total mass,energy,and momentum from the Navier-Stokes equations are conserved and in agreement with those calculated from Cartesian coordinate.展开更多
The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smoo...The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this difficulty.Therefore,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical models.However,improper vertical layering in HTF coordinates may also increase the incidence of error.Except for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep terrain.The errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic thickVLs.Furthermore,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the coordinates.More importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time integration.Only the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this propagation.This optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.展开更多
With increasing resolution in numerical weather prediction （NWP） models, the model topography can be described with finer resolution and includes steeper slopes. Consequently, negative effects of the traditional ter...With increasing resolution in numerical weather prediction （NWP） models, the model topography can be described with finer resolution and includes steeper slopes. Consequently, negative effects of the traditional terrain-following vertical coordinate on high-resolution numerical simulations become more distinct due to larger errors in the pressure gradient force （PGF） calculation and associated distortions of the gravity wave along the coordinate surface. A series of numerical experiments have been conducted in this study, including idealized test cases of gravity wave simulation over a complex mountain, error analysis of the PGF estimation over a real topography, and a suite of real-data test cases. The GRAPES-Meso model is utilized with four different coordinates, i.e., the traditional terrain-following vertical coordinate proposed by Gal-Chen and Somerville （hereinafter referred to as the Gal.C.S coordinate）, the one-scale smoothed level （SLEVE1）, the two-scale smoothed level （SLEVE2）, and the COSINE （COS） coordinates. The results of the gravity wave simulation indicate that the GRAPES-Meso model generally can reproduce the mountain-induced gravity waves, which are consistent with the analytic solution. However, the shapes, vertical structures, and intensities Of the waves are better simulated with the SLEVE2 coordinate than with the other three coordinates. The model with the COS coordinate also performs well, except at lower levels where it is not as effective as the SLEVE2 coordinate in suppressing the PGF errors. In contrast, the gravity waves simulated in both the Gal.C.S and SLEVE1 coordinates are relatively distorted. The estimated PGF errors in a rest atmosphere over the real complex topography are much smaller （even disappear at the middle and upper levels） in the GRAPES-Meso model using the SLEVE2 and COS coordinates than those using the Gal.C.S and SLEVE1 coordinates. The results of the real-data test cases conducted over a one-month period suggest that the three modified vertical coordinates （SLEVE1, SLEVE2, and COS coordinates） give better results than the traditional Gal.C.S coordinate in terms of forecasting bias and root mean square error, and forecasting anomaly correlation coefficients. In conclusion, the SLEVE2 coordinate is proved to be the best option for the GRAPES-Meso model.展开更多
基金supported by the Key Program of the Chinese Academy of Sciences(No.KZZD-EW-05-01)the Supporting Program for Science and Technological Research of China(No.2008BAC37B01)+1 种基金the National Basic Research Program of China(Nos.2012CB417201 and 2009CB421505)the National Natural Sciences Foundation of China(Nos.41205033 and 41175056)
文摘In this study, kinetic energy budget equations of rotational and divergent flow in pressure coordinates are derived on terrain-following coordinates. The new formulation explicitly shows the terrain effects and can be applied directly to model-simulated dynamic and thermodynamic fields on the model's original vertical grid. Such application eliminates interpolation error and avoids errors in virtual weather systems in mountainous areas. These advantages and their significance are demonstrated by a numerical study in terrain-following coordinates of a developing vortex after it moves over the Tibetan Plateau in China.
基金jointly supported by the National Basic Research Program of China[973 Program,grant number 2015CB954102]National Natural Science Foundation of China[grant numbers41305095 and 41175064]
文摘Based on classical terrain following (TF) algorithm (adaptive angle method), a new method for TF controller is proposed by using angle of attack. A method of obtaining terrain outline data from Digital Elevation Map (DEM) for TF control is discussed in order to save store space. The block control model, which is suitable for backstepping design, is given for nonlinear model of aircraft. Making full use of the characteristics of the system and combining block control principle, backstepping technique, a robust controller design method is proposed. Uncertainties in every sub-block are allowed, and can be canceled by using the idea of nonlinear damping. It is proved that the state tracking errors converge to the neighborhood of the origin exponentially. Finally, nonlinear six-degree-of-freedom simulation results for the aircraft model are presented to demonstrate the effectiveness of the proposed control law.
文摘Based on the optimal control theory, a 3-dimensionnal direct generation algorithm is proposed for anti-ground low altitude penetration tasks under complex terrain. By optimizing the terrain following(TF) objective function,terrain coordinate system, missile dynamic model and control vector, the TF issue is turning into the improved optimal control problem whose mathmatical model is simple and need not solve the second order terrain derivative. Simulation results prove that this method is reasonable and feasible. The TF precision is in the scope from 0.3 m to 3.0 m,and the planning time is less than 30 min. This method have the strongpionts such as rapidness, precision and has great application value.
文摘This study is designed to solve supply chain inefficiencies caused by some members’financial problems,such as capital shortages and financing restrictions in a stochastic environment.To this end,we have established a supply chain finance framework by designing two novel coordinating contracts based on trade credit financing for different problem settings.These contracts are modeled in the form of multi-leader Stackelberg games that address horizontal and vertical competition in a supply chain consisting of multiple suppliers and a financially constrained manufacturer.However,previous studies in the trade credit literature have addressed only simple vertical competition,that is,seller-buyer competition.To solve the proposed models,two algorithms were developed by combining population-based metaheuristics,the Nash-domination concept,and the Nikaido-Isoda function.The results demonstrate that the proposed supply chain finance framework can eliminate supply chain inefficiencies and make a large profit for suppliers,as well as the financially constrained manufacturer.Furthermore,the results of the contracts’analysis showed that if the manufacturer is required to settle its payments to suppliers before the end of the period,the trade credit contract cannot coordinate the supply chain because of a lack of incentive for suppliers.However,if the manufacturer is allowed to extend its payments to the end of the period,the proposed trade credit financing contract can coordinate the supply chain.Finally,the sensitivity analysis results indicate that the worse the financial status of the manufacturer,the more bargaining power suppliers have in determining the contract parameters for more profit.
基金supported by National Natural Science Foundation of China (Grant No. 50975059, Grant No. 61005080)Postdoctoral Foundation of China (Grant No. 20100480994)+1 种基金Postdoctoral Foundation of Heilongjiang Province, Foundation of Chinese State Key Laboratory of Robotics and Systems (Grant No. SKLRS200801A02)College Discipline Innovation Wisdom Plan of China (111 Project, Grant No. B07018)
文摘Virtual simulation technology is of great importance for the teleoperation of lunar rovers during the exploration phase, as well as the design of locomotion systems, performance evaluation, and control strategy verification during the R&D phase. The currently used simulation methods for lunar rovers have several disadvantages such as poor fidelity for wheel-soil interaction mechanics, difficulty in simulating rough terrains, and high complexity making it difficult to realize mobility control in simulation systems. This paper presents an approach for the construction of a virtual simulation system that integrates the features of 3D modeling, wheel-soil interaction mechanics, dynamics analysis, mobility control, and visualization for lunar rovers. Wheel-soil interaction experiments are carried out to test the forces and moments acted on a lunar rover’s wheel by the soil with a vertical load of 80 N and slip ratios of 0, 0.03, 0.05, 0.1, 0.2, 0.3, 0.4, and 0.6. The experimental results are referenced in order to set the parameters’ values for the PAC2002 tire model of the ADAMS/Tire module. In addition, the rough lunar terrain is simulated with 3DS Max software after analyzing its characteristics, and a data-transfer program is developed with Matlab to simulate the 3D reappearance of a lunar environment in ADAMS. The 3D model of a lunar rover is developed by using Pro/E software and is then imported into ADAMS. Finally, a virtual simulation system for lunar rovers is developed. A path-following control strategy based on slip compensation for a six-wheeled lunar rover prototype is researched. The controller is implemented by using Matlab/Simulink to carry out joint simulations with ADAMS. The designed virtual lunar rover could follow the planned path on a rough terrain. This paper can also provide a reference scheme for virtual simulation and performance analysis of rovers moving on rough lunar terrains.
文摘In this paper output predictive algorithm is applied to the design of predictive controller for an optimal path terrain following system. In this way, the error of path tracking is decreased to a minimum degree simply and efficiently and the computation time for the optimal path is shortened greatly. Therefore, the real-time processing of the optimal path terrain following system is made to be very helpful.
文摘An optimal preview method is applied to the design of terrain following controller for cruise missile. In this method, tracking errors and control increments are both considered in the quadratic cost function. Integrating the general optimal servo system with a preview feedforward compensation that feeds forward future command and future disturbance produces an optimal preview servo system. In the terrain following system, the flight altitude of the cruise missile is a command signal, and its future information can be known apriori. Hence, we have designed a terrain following controller with a basic state feedback and a feedforward compensation for future altitude information. Simulation results show that the performance of the terrain following system with such an optimal preview controller has been improved dramatically.
文摘In the terrain following coordinate,Gal-Chen and Somerville[1]and other proposed a vertical coordinate z∝(z−z_(bottom))/(ztop−z_(bottom))and constant spatial intervals ofδx andδy along the other directions.Because the variation ofδx andδy was ignored,their coordinate does not really follow the terrain.It fails to reproduce the divergence and curl over a complex terrain.Aligning the coordinate with real terrain,the divergence and curl we obtained from the curvilinear coordinate are consistent with the Cartesian coordinate.With a modification,the simulated total mass,energy,and momentum from the Navier-Stokes equations are conserved and in agreement with those calculated from Cartesian coordinate.
基金Supported by the National Natural Science Foundation of China(42230606)14th Five-Year Plan Basic Research Program of Institute of Atmospheric Physics,Chinese Academy of Sciences(E268081801)National Key Research and Development Program of China(2017YFA0603901)。
文摘The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this difficulty.Therefore,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical models.However,improper vertical layering in HTF coordinates may also increase the incidence of error.Except for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep terrain.The errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic thickVLs.Furthermore,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the coordinates.More importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time integration.Only the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this propagation.This optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.
基金Supported by the National(Key)Basic Research and Development(973)Program of China(2013CB430106)National Natural Science Foundation of China(41375108)National Science and Technology Support Program of China(2012BAC22B01)
文摘With increasing resolution in numerical weather prediction （NWP） models, the model topography can be described with finer resolution and includes steeper slopes. Consequently, negative effects of the traditional terrain-following vertical coordinate on high-resolution numerical simulations become more distinct due to larger errors in the pressure gradient force （PGF） calculation and associated distortions of the gravity wave along the coordinate surface. A series of numerical experiments have been conducted in this study, including idealized test cases of gravity wave simulation over a complex mountain, error analysis of the PGF estimation over a real topography, and a suite of real-data test cases. The GRAPES-Meso model is utilized with four different coordinates, i.e., the traditional terrain-following vertical coordinate proposed by Gal-Chen and Somerville （hereinafter referred to as the Gal.C.S coordinate）, the one-scale smoothed level （SLEVE1）, the two-scale smoothed level （SLEVE2）, and the COSINE （COS） coordinates. The results of the gravity wave simulation indicate that the GRAPES-Meso model generally can reproduce the mountain-induced gravity waves, which are consistent with the analytic solution. However, the shapes, vertical structures, and intensities Of the waves are better simulated with the SLEVE2 coordinate than with the other three coordinates. The model with the COS coordinate also performs well, except at lower levels where it is not as effective as the SLEVE2 coordinate in suppressing the PGF errors. In contrast, the gravity waves simulated in both the Gal.C.S and SLEVE1 coordinates are relatively distorted. The estimated PGF errors in a rest atmosphere over the real complex topography are much smaller （even disappear at the middle and upper levels） in the GRAPES-Meso model using the SLEVE2 and COS coordinates than those using the Gal.C.S and SLEVE1 coordinates. The results of the real-data test cases conducted over a one-month period suggest that the three modified vertical coordinates （SLEVE1, SLEVE2, and COS coordinates） give better results than the traditional Gal.C.S coordinate in terms of forecasting bias and root mean square error, and forecasting anomaly correlation coefficients. In conclusion, the SLEVE2 coordinate is proved to be the best option for the GRAPES-Meso model.
