Simulator Coupling for the Simulation of Heterogeneous Systems

Transcription

1 Workshop of CFDR in Berlin am 17. Juni 1999 Simulator Coupling for the Simulation of Heterogeneous Systems Peter Schwarz Simulation of heterogeneous systems Principles of the coupling of simulators Examples 1

2 Example of a Heterogeneous System acceleration sensor acceleration a = a max * sin ( ωt + φ ) electrode capacitor C 1 electrode electrostatic force electronic circuit beam displacement seismic mass electrode capacitor C 2 electrode beam elektrostatic force 2

3 Connection of Different Domains in Heterogeneous Systems mechanical subsystem Capacity C 1 elektrical subsystem Capacity C 2 Seismic Mass thermal subsystem domains interact via the exchange of signals 3

4 Modelling of Heterogeneous Systems f 1 (x 1, x 2, x 3,..., x m ) = 0 e. g. circuit diagram bond graph description TF s I R part of x 1 f 2 (x 1, x 2, x 3,..., x m ) = 0 e. g. ODE, PDE F T.. part of x 2 = M.. v + D v. + S ϕ ϕ. v ϕ... part of x 3 - K - f(.) f 3 (x 1, x 2, x 3,..., x m ) = 0 e. g. control blocks 4

5 Simulation Tools for Subsystems (at EAS) VHDL Simulation Logic Simulation Analog Simulation Analog + Digital FEM Neural Network Symbolic Analysis System Design VSS, Leapfrog, ModelSim, Fusion Verilog-XL, Lsim, ViewSim, VCS SPICE3, HSPICE, MDS, ITI-Sim, Matlab/Simulink, Spectre SABER, ELDO, Lsim, PSpice (DesignLab7.1), KOSIM, ViewSim/AD CAPA, ANSYS SNNS, InterAct, Neural Works Explorer, DESIRE/NEUNET, Matlab-Toolbox Neural Networks Analog Insydes (Mathematica) VisualHDL (Summit), Renoir (Mentor), Statemate MAGNUM (i-logix) 5

6 Coupled Simulation of Heterogeneous Systems Mathematical description f 1 (x 1, x 2, x 3,..., x m ) = 0 f 2 (x 1, x 2, x 3,..., x m ) = 0 f 3 (x 1, x 2, x 3,..., x m ) = 0 Method 1 Simulation with one circuit and system simulator... f m (x 1, x 2, x 3,..., x m ) = 0 Method 2 Coupling of simulators for different domains relaxation method Newton method 6

7 Method 1 Simulation with one Circuit and System Simulator ENTITY beam IS PORT ( TERMINAL t1_1 : kinematic ; TERMINAL t2_1 : kinematic ; TERMINAL t3_1 : kinematic ; TERMINAL t4_1 : rotational; TERMINAL t5_1 : rotational; TERMINAL t6_1 : rotational; TERMINAL t7_2 : kinematic ; TERMINAL t8_2 : kinematic ; TERMINAL t9_2 : kinematic ; TERMINAL Capacity t10_2 C: 1 rotational; TERMINAL t11_2 : rotational; TERMINAL t12_2 Seismic : rotational Mass ) ; END beam ; Capacity C 2 QUANTITY v_t1_1 ACROSS qval_14 THROUGH t1_1; QUANTITY v_t2_1 ACROSS qval_16 THROUGH t2_1; QUANTITY v_t3_1 ACROSS qval_18 THROUGH t3_1; QUANTITY v_t4_1 ACROSS qval_19 THROUGH t4_1; QUANTITY v_t5_1 ACROSS qval_20 THROUGH t5_1; QUANTITY v_t6_1 ACROSS qval_21 THROUGH t6_1; QUANTITY v_t7_2 ACROSS qval_23 THROUGH t7_2; QUANTITY v_t8_2 ACROSS qval_25 THROUGH t8_2; QUANTITY v_t9_2 ACROSS qval_27 THROUGH t9_2; QUANTITY v_t10_2 ACROSS qval_28 THROUGH t10_2; Way QUANTITY pv_t9_2 : REAL ; QUANTITY pv_t13_3 : REAL ; QUANTITY pv_t14_3 : REAL ; QUANTITY pv_t15_3 : REAL ; QUANTITY pv_t19_4 : REAL ; QUANTITY pv_t20_4 : REAL ; QUANTITY pv_t21_4 : REAL ; BEGIN Description of the terminal behavior of subsystems Modelling of the heterogenous system by a connection of multiports qval_14 == (-((((((( e-19 * pv_t1_1 DOT)+(( ) * v_t1_1))+(( ) * v_t2_1))+((-(0.0066)) * v_t6_1))+((- ( )) * v_t13_3))+((-( )) * v_t14_3))+((-(0.0066)) * v_t18_3))) ; -- tolerance "default_force"; Prerequisite qval_16 == (-((((((( e-19 * pv_t2_1 DOT)+(( ) * v_t1_1))+(( ) * v_t2_1))+((0.0066) * v_t6_1))+((- ( )) * v_t13_3))+((-( )) * v_t14_3))+((0.0066) * v_t18_3))) ; -- tolerance "default_force"; qval_18 == (-((((((( e-19 * pv_t3_1 DOT)+((0.0070) * v_t3_1))+(( ) * v_t4_1))+((-( )) * v_t5_1))+((- (0.0070)) * v_t15_3))+(( ) * v_t16_3))+((-( )) * v_t17_3))) ; -- tolerance "default_force"; qval_19 == (-((((((( ) * v_t3_1)+(( ) * v_t4_1))+((-( )) * v_t5_1))+((-( )) * Behavioral description language v_t15_3))+(( ) * v_t16_3))+((-( )) * v_t17_3))) ; -- tolerance "default_angular_force" ; qval_20 (e. == g. (-(((((((-( )) VHDL-AMS, * v_t3_1)+((-( )) MAST, HDL-A, * v_t4_1))+(( )...) * v_t5_1))+(( ) * v_t15_3))+((- ( )) * v_t16_3))+(( ) * v_t17_3))) ; -- tolerance "default_angular_force" ; qval_21 == (-(((((((-(0.0066)) * v_t1_1)+((0.0066) * v_t2_1))+(( ) * v_t6_1))+((0.0066) * v_t13_3))+((-(0.0066)) * v_t14_3))+(( ) * v_t18_3))) ; -- tolerance "default_angular_force" ; qval_23 == (-((((((( e-19 * pv_t7_2 DOT)+(( ) * v_t7_2))+(( ) * v_t8_2))+((0.0066) * v_t12_2))+((- ( )) * v_t19_4))+((-( )) * v_t20_4))+((0.0066) * v_t24_4))) ; -- tolerance "default_force"; Usage of simulators, solving systems qval_25 == (-((((((( e-19 * pv_t8_2 DOT)+(( ) * v_t7_2))+(( ) * v_t8_2))+((-(0.0066)) * v_t12_2))+((- ( )) of differential * v_t19_4))+((-( )) algebraic * v_t20_4))+((-(0.0066)) equations * v_t24_4))) ; -- tolerance "default_force"; qval_27 == (-((((((( e-19 * pv_t9_2 DOT)+((0.0070) * v_t9_2))+((-( )) * v_t10_2))+(( ) * v_t11_2))+((- (0.0070)) * v_t21_4))+((-( )) * v_t22_4))+(( ) * v_t23_4))) ; -- tolerance "default_force"; qval_28 == (-(((((((-( )) * v_t9_2)+(( ) * v_t10_2))+((-( )) * v_t11_2))+(( ) * v_t21_4))+(( ) Saber, ELDO, * v_t22_4))+((-( )) VHDL-AMS * v_t23_4))) Design ; -- tolerance station, "default_angular_force"... ; qval_29 == (-((((((( ) * v_t9_2)+((-( )) * v_t10_2))+(( ) * v_t11_2))+((-( )) * v_t21_4))+((- 7

8 Simulation with one circuit and system simulator Modelling of Micromechanical Systems m n l 1 2 L Across and Through quantities of a beam element: displacement w, angle ϕ, forces F, angular forces T B 5 FEM-formulas as starting point for the description of the terminal behavior B 3 B 4 C 1 Partitioning into B i : Beam elements C j : Coupling elements B 1 B 2 w l1 w m1 w n1 ϕ l1 ϕ m1 ϕ n1 F l1 F m1 F n1 T l1 T m1 T n1 F T = M w.. D w S ϕ ϕ w ϕ multi-pole as beam element F l2 w l2 F m2 w m2 F n2 w n2 T l2 ϕ l2 T m2 ϕ m2 T n2 ϕ n2 8

9 Method 2 Simulator Coupling with Relaxation Method Situation at time t Simulator 1 f 1 (x 1, x 2 ) = 0 x 1 (i+1) = V 1 (x 2 (i) ) ( x 1 (0),x 2 (0) ) x 1 x 1 (2) x 1 = V 1 (x 2 ) Simulator 2 f 2 (x 1, x 2 ) = 0 x 1 (3) x 2 (i+1) = V 2 (x 1 (i+1) ) x 1 (1) x 2 = V 2 (x 1 ) x 2 i=i+1 x 1 (i+1) - x 1 (i) < ε next time step no x 2 (i+1) - x 2 (i) < ε yes Solution of a system of nonlinear equations in each time step 9

10 Simulator Coupling Requirements Increasing time, time intervals Repetition of time intervals The simulation time must increase monotonously. Time repetition is allowed only within well-known (user-defined) time intervals. The simulator must be able to receive commands from the counterpart to both repeat and change a time interval. Communication Both the usage of received data and sending must be possible during simulation. The communication has to take place at the end of the time intervals mentioned above. 10

11 Implementation of Couplings backplane Data exchange A B... M coupled simulators A B coupled simulators via a simulation backplane direct coupling Requirements open simulation interface source code of the simulator 11

12 Couplings Realized at EAS SABER + Verilog-XL ELDO + LSIM ELDO + Verilog-XL ELDO + KOSIM + VSystem KOSIM + ANSYS KOSIM + CAPA KOSIM + SNNS COSSAP + Verilog COSSAP + Leapfrog COSSAP + Leapfrog + Verilog COSSAP + SABER + Leapfrog KOSIM + ITISIM 12

13 Data Exchange between Different Processes Principle Applicability Performance Our applications Shared memory on one and the same host different processes best possible - Sockets different hosts, different platforms high COSSAP - Saber - Leapfrog Pipes PVM (Parallel Virtual Machine) File transfer on one and the same host parent-and-child-processes different processes (named pipe) different hosts, different platforms different hosts, different platforms common file system high lower than socket s performance very low (due to high synchronisation effort) KOSIM - ADDA KOSIM - ANSYS KOSIM - KOSIM Saber - ANSYS KOSIM - ANSYS Saber - ANSYS ELDO - ANSYS KOSIM - KOSIM KOSIM - ADDA 13

14 Simulator Coupling: Electro-Thermal Analysis of ICs and MEMS U CC Temperature at T R 1 R 2 Temperature at T 1 2 T 1 T 2 Power Dissipation P v1 P v2 Temperature Circuit Simulator Saber Thermal Simulator ANSYS Temperature Step Response Temperature Distribution (Header, Die) Temperature Distribution (Top of Die) 14

15 Electro-Mechanical System Controlled acceleration sensor acceleration 0 displacement [m] C 1 F 1 without control displacement C 2 F 2-1e-8 with control Coupling: FEM simulator and circuit simulator (mechanics) (control electronics) Zeit [ms] P.-C. Eccardt (Siemens AG) et.al.:coupled Finite Element and Network Simulation for Microsystem Components. MST 96,

16 Block Diagram Acceleration ANSYS KOSIM Reference Input Electrost. Force Mass Acceleration Force Resulting Force PID Controller Electro static Sensor Evaluation Circuit Displacement Control Voltage Displacement Proportional Voltage 16

17 Data Exchange ANSYS F a PVM, File Transfer Time t Displacement u KOSIM Displacement F e Time t Electrostatic Force F e Circuit Electrostatic Force use of interfaces to programable languages - user commands (FORTRAN77) in ANSYS - C-Interface of KOSIM inclusion of system and PVM comands into subroutines 17

18 Simulation Example of Electromechanical Interaction Mechanical subsystem Force Electrical subsystem Shifting of force target (disturbance variable) Mass Rotatory inertia - Preamplifier Position difference + + PI-Controller - ITI -SIM Elastic supportt Piezoactor Power amplifier KOSIM 18

19 Advantages and Disadvantages of Simulator Coupling Existing models for subsystems can be used Modelling efforts decrease Powerful well established tools for subsystems can be applicated Simulator Coupling Solutions have to be worked out User should be familiar with the simulators and the solution for the coupling Computation time is as a rule very large Convergence problems may occur using Relaxation method 19

20 Summary Increasing role of system modeling and simulation Two different methods - Modeling by generalized Kirchhoffian networks and application of modern circuit simulators with HDL entry (VHDL-AMS, Modelica,...) - Simulator Coupling Simulator Coupling may reduce modelling efforts for non-electrical/electrical systems Problems using Simulator Coupling may be large computation times and convergence 20