在控制系統實時Runge-Kutta算法中,為了滿足實時仿真快速性需求,希望盡可能地採用大的計算步長.如果採用大步長,那麼數值計算就會引起數值不穩定或者計算誤差太大的問題.在現有低階實時龍格-庫塔公式基礎上,首先利用RK公式的穩定性方程求解出最大穩定域,然後根據截斷誤差與相關係數的關系,將其化為一個約束求極小最優問題,並最終推導出實時最優三級二階RK公式和四級三階RK公式.仿真結果表明,該算法具有一定的優越性.
Inreal-timeRunge-Kuttaalgorithmforcontrolsystem,forsatisfyingthequicknessneedofreal-timesimulation,itisexpecttochooselargerintegrationstep-size.However,thelargerstep-sizewouldresultintheunsteadinessofnumericalvalueandlargererrorinnumeration.So,basedontheexistinglow-orderreal-timeRKformula,usingthestabilityequationofRKformula,themaximumstabilityregionisfound.Then,atthebasisoftherelationoftruncationerrorandrelatedcoefficients,aproblemofrestrictedoptimizationforminisgotten,andthereal-timeoptimumthird-gradesecond-orderRKformulaandfourth-gradethird-orderRKformulaarededucedfinally.Thesimulationresultsshowthatthisalgorithmissuperiorinacertainextent.
在控制系統實時Runge-Kutta算法中,為了滿足實時仿真快速性需求,希望盡可能地採用大的計算步長.如果採用大步長,那麼數值計算就會引起數值不穩定或者計算誤差太大的問題.在現有低階實時龍格-庫塔公式基礎上,首先利用RK公式的穩定性方程求解出最大穩定域,然後根據截斷誤差與相關係數的關系,將其化為一個約束求極小最優問題,並最終推導出實時最優三級二階RK公式和四級三階RK公式.仿真結果表明,該算法具有一定的優越性.
Inreal-timeRunge-Kuttaalgorithmforcontrolsystem,forsatisfyingthequicknessneedofreal-timesimulation,itisexpecttochooselargerintegrationstep-size.However,thelargerstep-sizewouldresultintheunsteadinessofnumericalvalueandlargererrorinnumeration.So,basedontheexistinglow-orderreal-timeRKformula,usingthestabilityequationofRKformula,themaximumstabilityregionisfound.Then,atthebasisoftherelationoftruncationerrorandrelatedcoefficients,aproblemofrestrictedoptimizationforminisgotten,andthereal-timeoptimumthird-gradesecond-orderRKformulaandfourth-gradethird-orderRKformulaarededucedfinally.Thesimulationresultsshowthatthisalgorithmissuperiorinacertainextent.