Because the normal operation of the engine is located near the equilibrium manifold, the method of equilibrium mani fold nonlinear dynamic modeling is adopted for turbofan engine more than the local train modeling. Th...Because the normal operation of the engine is located near the equilibrium manifold, the method of equilibrium mani fold nonlinear dynamic modeling is adopted for turbofan engine more than the local train modeling. The method studies the sys tem characteristics near the equilibrium manifold. The modeling method can be realized through dynamic and static twostep, and for the specific parameter modeling steps and algorithm are given. The output of the test data is compared with the model output through numerical simulation, to check the model with an additional set of test data. The simulation results show that the model has reached the requirements of engineering accuracy.展开更多
The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analy...The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme.展开更多
Stable operation of aircraft engine compressions is constrained by rotating surge. In this paper, an approximate nonlinear surge margin model of aircraft engine compression system by using equilibrium manifold is pres...Stable operation of aircraft engine compressions is constrained by rotating surge. In this paper, an approximate nonlinear surge margin model of aircraft engine compression system by using equilibrium manifold is presented. Firstly, this paper gives an overview of the current state of modeling aerodynamic flow instabilities in engine compressors. Secondly, the expansion form of equilibrium manifold is introduced, and the choosing scheduling variable method is discussed. Then, this paper also gives the identification procedure of modeling the approximate nonlinear model. Finally, the modeling and simulations with high pressure （liP） compressor surge margin of the aircraft engine show that this real-time model has the same accuracy with the thermody- namic model, but has simpler structure and shorter computation time.展开更多
The objective of this paper is to analyze the stability of equilibrium manifolds for a ratio-dependent two-predators one-prey model. Some model results are presented first with the bifurcation without parameters metho...The objective of this paper is to analyze the stability of equilibrium manifolds for a ratio-dependent two-predators one-prey model. Some model results are presented first with the bifurcation without parameters method, and then the method was used to study bifurcation along the equilibrium manifold for the model The model does not lose stability even when some equilibria are locally unstable because the equilibrium manifold is stable when treated as a whole. The ecological implications of the results are discussed.展开更多
Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the general...Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.展开更多
The authors study bifurcations from a heteroclinic manifold connecting two non-hyperbolic equilibrium P-0 and P-1 for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium P-i split...The authors study bifurcations from a heteroclinic manifold connecting two non-hyperbolic equilibrium P-0 and P-1 for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium P-i splits into two equilibria <(P)over tilde (i)> and P-i(alpha), i = 0, 1, and find the Melnikov vector conditions assuring the existence of a heteroclinic orbit from P-1(alpha) to P-0(alpha) along directions that are tangent to the strong unstable (resp.strong stable) manifold of P-1(alpha) (resp.P-0(alpha)). The exponential trichotomy and the unified and geometrical method are used to prove their results.展开更多
静止无功补偿器(static var compensator,SVC)自身动态特性对电压稳定有着重大的影响。提出了一种电压稳定动态分析方法,解决了分割法存在的交接误差问题,并具有满意的计算精度和速度。利用该方法,在不同的失稳模式下,分析了SVC间常数...静止无功补偿器(static var compensator,SVC)自身动态特性对电压稳定有着重大的影响。提出了一种电压稳定动态分析方法,解决了分割法存在的交接误差问题,并具有满意的计算精度和速度。利用该方法,在不同的失稳模式下,分析了SVC间常数对电压稳定的影响。通过分析发现,当系统单调失稳时,时间常数越大,失稳速度越快;当系统振荡失稳时,时间常数越大,振荡幅度越大。利用双参数延拓法,求取了分叉边界曲线,结果表明,SVC放大倍数越大,分叉边界值也越大。展开更多
文摘Because the normal operation of the engine is located near the equilibrium manifold, the method of equilibrium mani fold nonlinear dynamic modeling is adopted for turbofan engine more than the local train modeling. The method studies the sys tem characteristics near the equilibrium manifold. The modeling method can be realized through dynamic and static twostep, and for the specific parameter modeling steps and algorithm are given. The output of the test data is compared with the model output through numerical simulation, to check the model with an additional set of test data. The simulation results show that the model has reached the requirements of engineering accuracy.
基金Hie-Tch Research and Development Program of China (2002AA723011)
文摘The equilibrium manifold linearization model of nonlinear shock motion is of higher accuracy and lower complexity over other models such as the small perturbation model and the piecewise-linear model. This paper analyzes the physical significance of the equilibrium manifold linearization model, and the self-feedback mechanism of shock motion is revealed. This helps to describe the stability and dynamics of shock motion. Based on the model, the paper puts forwards a gain scheduling control method for nonlinear shock motion. Simulation has shown the validity of the control scheme.
基金National Natural Science Foundation of China (61104146)Innovation Plan of Aero Engine Complex System Safety by the Ministry of Education Chang Jiang Scholars of China (IRT0905)
文摘Stable operation of aircraft engine compressions is constrained by rotating surge. In this paper, an approximate nonlinear surge margin model of aircraft engine compression system by using equilibrium manifold is presented. Firstly, this paper gives an overview of the current state of modeling aerodynamic flow instabilities in engine compressors. Secondly, the expansion form of equilibrium manifold is introduced, and the choosing scheduling variable method is discussed. Then, this paper also gives the identification procedure of modeling the approximate nonlinear model. Finally, the modeling and simulations with high pressure （liP） compressor surge margin of the aircraft engine show that this real-time model has the same accuracy with the thermody- namic model, but has simpler structure and shorter computation time.
基金Supported by the National Natural Science Foundation of China (No. 10272059)
文摘The objective of this paper is to analyze the stability of equilibrium manifolds for a ratio-dependent two-predators one-prey model. Some model results are presented first with the bifurcation without parameters method, and then the method was used to study bifurcation along the equilibrium manifold for the model The model does not lose stability even when some equilibria are locally unstable because the equilibrium manifold is stable when treated as a whole. The ecological implications of the results are discussed.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10772025,10932002 and 10972127)the Natural Science Foundation of Henan Province,China(Grant No.102300410144)the Beijing Municipal Key Disciplines Fund for General Mechanics and Foundation of Mechanics,China
文摘Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.
文摘The authors study bifurcations from a heteroclinic manifold connecting two non-hyperbolic equilibrium P-0 and P-1 for a n-dimensional dynamical system. They show that under some assumptions, each equilibrium P-i splits into two equilibria <(P)over tilde (i)> and P-i(alpha), i = 0, 1, and find the Melnikov vector conditions assuring the existence of a heteroclinic orbit from P-1(alpha) to P-0(alpha) along directions that are tangent to the strong unstable (resp.strong stable) manifold of P-1(alpha) (resp.P-0(alpha)). The exponential trichotomy and the unified and geometrical method are used to prove their results.
文摘静止无功补偿器(static var compensator,SVC)自身动态特性对电压稳定有着重大的影响。提出了一种电压稳定动态分析方法,解决了分割法存在的交接误差问题,并具有满意的计算精度和速度。利用该方法,在不同的失稳模式下,分析了SVC间常数对电压稳定的影响。通过分析发现,当系统单调失稳时,时间常数越大,失稳速度越快;当系统振荡失稳时,时间常数越大,振荡幅度越大。利用双参数延拓法,求取了分叉边界曲线,结果表明,SVC放大倍数越大,分叉边界值也越大。
