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1 FMI WG FMI 27 3 19 FMI i Revision 2015/03/19 Ve r 1 . 0 FMI ii 1 .. 1 .. 1 .. 2 .. 3 .. 3 .. 4 2 .. 5 .. 5 .. 5 .. 7 .. 7 .. 7 .. 8 OS .. 8 3 .. 9 ODE: Ordinary Differential Equation DAE: Differential Algebraic Equation .. 9 .. 10 .. 10 .. 11 .. 12 .. 12 .. 12 .. 14.

2 15 .. 16 .. 17 .. 18 4 .. 21 VHDL-AMS .. 21 .. 21 QUANTITY .. 22 ENTITY - ARCHITECTURE .. 22 PACKAGE .. 24 (Behavor Modeling) .. 25 FMI iii (Structural Modeling) .. 26 .. 28 .. 29 Modelica .. 30 .. 30 Modelica .. 31 Modelica .. 33 5 FMI FMU .. 37 .. 37 MODELISAR .. 37 MODELISAR .. 37 FMI .. 37 FMI .. 38 FMI .. 38 .. 39 FMU .. 40 FMU .. 41 .. 41 xml .. 41 6 FMU .. 44 .. 44 .. 44 .. 45 .. 45 .. 47 FMU .. 48 .. 52 FMU .. 52 FMU.

3 54 JSAE .. 56 .. 57 .. 57 .. 58 FMU CS ME .. 60 ME .. 60 CS .. 60 FMI iv ME CS .. 60 FMU .. 64 .. 64 .. 67 FMU .. 71 (Algebraic loop) .. 71 (Stiff System) .. 72 FMU .. 72 .. 72 .. 75 .. 76 .. 79 FMU .. 79 .. 79 .. 81 FMU .. 83 .. 83 7 .. 86 8 .. 88 9 .. 89 FMI WG 1 1 [1] Acausal modeling [2]

4 2012 3 WG Functional Mock-up Interface FMI FMI Co-Simulation FMI FMI 1 Co-Simulation 5 AZAPA 50 FMI WG 2 1-1 1-1 1-2 FMI WG 3 1-2

5 FMI FMI WG 4 FMI FMI WG 5 2 2-1 2-1 4 2-2 FMI WG 6 2-2 FMI Model

6 Exchange FMI 5 FMI Co-Simulation FMI 5 2 CPU FMI WG 7 2-1 2-1 No.

7 1 2 VHDL-AMS Modelica 3 C C++ Fortran 4 OS dll Windows so (Linux) VHDL-AMS Modelica FMI WG 8 4 C C++ Fortran OS

8 Windows dll OS FMI FMI Model Exchange Co-Simulation Windows OS dll FMI 5 FMI WG 9 3 ODE: Ordinary Differential Equation DAE: Differential Algebraic Equation (ODE) (DAE) (3-1) x u t (3-2) u (3-2) dx/dt = f(x,u,t) (3-1) 0= g(x,u,t) (3-2) (3-1) x dx/dt ODE (3-3) dx/dt 0 = F(dx/dt, x, u, t) (3-3) (3-3) (3-1) ODE (3-3) DAE (Causal modeling) (Acausal modeling)

9 ODE Simulink Bond Graph , DAE DAE FMI WG 10 3-1 3-1 e i e = R i R 3-1 ODE

10 Newton-Laphson DAE INDEX ODE ODE (Explicit method) (Implicit method) : E0 = f(t), iC = C duC/dt e1 = R1 i1, eL = L diL/dt e2 = R2 i2 : i0 = i1 + iL, i1 = i2 + iC : E0 = e1 + eC, eL = e1 + e2 eC = e2 E0 e1 e2 eC eL FMI WG 11 HILS(Hardware In the Loop Simulation) 3-1 3-2 3-1 Explicit (Implicit) (Single Step) Euler Runge-Kutta Runge-Kutta (Multi Step) Adams-Bashforth Adams-Moulton (BDF)