This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either...This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.展开更多
针对传统电压源逆变器无模型预测电流控制(model-free predictive current control,MFPCC)方法存在电流纹波大、电流梯度更新停滞以及预测性能易受采样扰动影响的问题。该文提出一种计及采样扰动的三矢量MFPCC方法。在一个控制周期应用...针对传统电压源逆变器无模型预测电流控制(model-free predictive current control,MFPCC)方法存在电流纹波大、电流梯度更新停滞以及预测性能易受采样扰动影响的问题。该文提出一种计及采样扰动的三矢量MFPCC方法。在一个控制周期应用3个基本矢量,并根据价值函数计算矢量作用时间,降低了输出电流纹波;其次,通过建立不同矢量作用下的电流梯度方程组,实现电流梯度数据的实时更新,消除了停滞现象;再次,分析采样扰动对MFPCC的影响,采用扩张状态观测器估计采样扰动以补偿预测电流控制,抑制其对输出电流的影响。最后,通过仿真和实验,对所提方法的有效性进行了验证。展开更多
基金supported by the NSF under Grant DMS-2208391sponsored by the NSF under Grant DMS-1753581.
文摘This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.
基金Project supported by the National Natural Science Foundation of China(11571225)the Scientific Research Foundation(SRF) for the Returned Overseas Chinese Scholarsthe Shanghai Leading Academic Discipline Project(J50101)
文摘针对传统电压源逆变器无模型预测电流控制(model-free predictive current control,MFPCC)方法存在电流纹波大、电流梯度更新停滞以及预测性能易受采样扰动影响的问题。该文提出一种计及采样扰动的三矢量MFPCC方法。在一个控制周期应用3个基本矢量,并根据价值函数计算矢量作用时间,降低了输出电流纹波;其次,通过建立不同矢量作用下的电流梯度方程组,实现电流梯度数据的实时更新,消除了停滞现象;再次,分析采样扰动对MFPCC的影响,采用扩张状态观测器估计采样扰动以补偿预测电流控制,抑制其对输出电流的影响。最后,通过仿真和实验,对所提方法的有效性进行了验证。
