A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear syste...A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.展开更多
Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and repr...Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.展开更多
In recent years,the Active Flutter Suppression(AFS)employing Linear ParameterVarying(LPV)framework has become a hot spot in the research field.Nevertheless,the flutter suppression technique is facing two severe challe...In recent years,the Active Flutter Suppression(AFS)employing Linear ParameterVarying(LPV)framework has become a hot spot in the research field.Nevertheless,the flutter suppression technique is facing two severe challenges.On the one hand,due to the fatal risk of flight test near critical airspeed,it is hard to obtain the accurate mathematical model of the aeroelastic system from the testing data.On the other hand,saturation of the actuator may degrade the closed-loop performance,which was often neglected in the past work.To tackle these two problems,a new active controller design procedure is proposed to suppress flutter in this paper.Firstly,with the aid of LPV model order reduction method and State-space Model Interpolation of Local Estimates(SMILE)technique,a set of high-fidelity Linear Time-Invariant(LTI)models which are usually derived from flight tests at different subcritical airspeeds are reduced and interpolated to construct an LPV model of an aeroelastic system.And then,the unstable aeroelastic dynamics beyond critical airspeed are‘predicted’by extrapolating the resulting LPV model.Secondly,based on the control-oriented LPV model,an AFS controller in LPV framework which is composed of a nominal LPV controller and an LPV anti-windup compensator is designed to suppress the aeroelastic vibration and overcome the performance degradation caused by actuator saturation.Although the nominal LPV controller may have superior performance in linear simulation in which the saturation effect is ignored,the results of the numerical simulations show that the nominal LPV controller fails to suppress the Body Freedom Flutter(BFF)when encountering the actuator saturation.However,the LPV anti-windup compensator not only enhances the nominal controller’s performance but also helps the nominal controller to stabilize the unstable aeroelastic system whenencountering serious actuator saturation.展开更多
Stabilization of a plant with variable operating conditions was considered. The plant is assumed to lie in a set of interpolated models composed of all interpolations generated between certain sets of proper stable co...Stabilization of a plant with variable operating conditions was considered. The plant is assumed to lie in a set of interpolated models composed of all interpolations generated between certain sets of proper stable coprime factorizations of transfer functions of two representative models that are defined at two representative operating points. An interpolated controller that is linear interpolation of coprime factorizations of two stabilizing controllers for the two representative models is designed to stabilize this set of interpolated models. Design of such an interpolated controller was converted to a feasibility problem constrained by several LMIs and a BMI, and a two step iteration algorithm was employed to solve it.展开更多
GRAPES(Global/Regional Assimilation and PrEdiction System)模式动力框架中垂直方向变量的跳层设置采用Charney-Phillips分布,在整层上进行位温、水物质的计算,物理过程中在半层上对其进行处理。这样在GRAPES模式中,进入物理过程之...GRAPES(Global/Regional Assimilation and PrEdiction System)模式动力框架中垂直方向变量的跳层设置采用Charney-Phillips分布,在整层上进行位温、水物质的计算,物理过程中在半层上对其进行处理。这样在GRAPES模式中,进入物理过程之前和物理过程计算完毕之后,都要采用线性插值进行整层和半层之间物理量的转换。由于线性插值精度欠佳,为提高上述反馈过程的精度,并保证水物质的正定性。该研究引入样条插值,并在水物质的插值过程中进行保单调处理,有效减小了位温场、水物质场的预报偏差,并提升了模式的综合预报性能。展开更多
基金supported by the National Natural Science Foundation of China （Grant No.10271074）
文摘A theorem for osculatory rational interpolation was shown to establish a new criterion of interpolation. On the basis of this conclusion a practical algorithm was presented to get a reduction model of the linear systems. Some numerical examples were given to explain the result in this paper.
文摘Modelling and simulation of projectile flight is at the core of ballistic computer software and is essential to the study of performance of rifles and projectiles in various engagement conditions.An effective and representative numerical model of projectile flight requires a relatively good approximation of the aerodynamics.The aerodynamic coefficients of the projectile model should be described as a series of piecewise polynomial functions of the Mach number that ideally meet the following conditions:they are continuous,differentiable at least once,and have a relatively low degree.The paper provides the steps needed to generate such piecewise polynomial functions using readily available tools,and then compares Piecewise Cubic Hermite Interpolating Polynomial(PCHIP),cubic splines,and piecewise linear functions,and their variant,as potential curve fitting methods to approximate the aerodynamics of a generic small arms projectile.A key contribution of the paper is the application of PCHIP to the approximation of projectile aerodynamics,and its evaluation against a set of criteria.Finally,the paper provides a baseline assessment of the impact of the polynomial functions on flight trajectory predictions obtained with 6-degree-of-freedom simulations of a generic projectile.
基金the National Natural Science Foundation of China(No.61573289)Space Science and Technology Fund,and Natural Science Basic Research Plan in Shaanxi Province of China(No.2019JM042)Fundamental Research Funds for the Central Universities of China(No.3102019ZDHKY11)。
文摘In recent years,the Active Flutter Suppression(AFS)employing Linear ParameterVarying(LPV)framework has become a hot spot in the research field.Nevertheless,the flutter suppression technique is facing two severe challenges.On the one hand,due to the fatal risk of flight test near critical airspeed,it is hard to obtain the accurate mathematical model of the aeroelastic system from the testing data.On the other hand,saturation of the actuator may degrade the closed-loop performance,which was often neglected in the past work.To tackle these two problems,a new active controller design procedure is proposed to suppress flutter in this paper.Firstly,with the aid of LPV model order reduction method and State-space Model Interpolation of Local Estimates(SMILE)technique,a set of high-fidelity Linear Time-Invariant(LTI)models which are usually derived from flight tests at different subcritical airspeeds are reduced and interpolated to construct an LPV model of an aeroelastic system.And then,the unstable aeroelastic dynamics beyond critical airspeed are‘predicted’by extrapolating the resulting LPV model.Secondly,based on the control-oriented LPV model,an AFS controller in LPV framework which is composed of a nominal LPV controller and an LPV anti-windup compensator is designed to suppress the aeroelastic vibration and overcome the performance degradation caused by actuator saturation.Although the nominal LPV controller may have superior performance in linear simulation in which the saturation effect is ignored,the results of the numerical simulations show that the nominal LPV controller fails to suppress the Body Freedom Flutter(BFF)when encountering the actuator saturation.However,the LPV anti-windup compensator not only enhances the nominal controller’s performance but also helps the nominal controller to stabilize the unstable aeroelastic system whenencountering serious actuator saturation.
文摘Stabilization of a plant with variable operating conditions was considered. The plant is assumed to lie in a set of interpolated models composed of all interpolations generated between certain sets of proper stable coprime factorizations of transfer functions of two representative models that are defined at two representative operating points. An interpolated controller that is linear interpolation of coprime factorizations of two stabilizing controllers for the two representative models is designed to stabilize this set of interpolated models. Design of such an interpolated controller was converted to a feasibility problem constrained by several LMIs and a BMI, and a two step iteration algorithm was employed to solve it.
文摘GRAPES(Global/Regional Assimilation and PrEdiction System)模式动力框架中垂直方向变量的跳层设置采用Charney-Phillips分布,在整层上进行位温、水物质的计算,物理过程中在半层上对其进行处理。这样在GRAPES模式中,进入物理过程之前和物理过程计算完毕之后,都要采用线性插值进行整层和半层之间物理量的转换。由于线性插值精度欠佳,为提高上述反馈过程的精度,并保证水物质的正定性。该研究引入样条插值,并在水物质的插值过程中进行保单调处理,有效减小了位温场、水物质场的预报偏差,并提升了模式的综合预报性能。
