A Composable Simulation Environment to Support the Design of Mechatronic Systems

1. A Composable Simulation Environment to Support the Design of Mechatronic Systems Antonio Diaz-Calderon June 9, 2000

2. Goal Provide simulation support to the design of mechatronic systems

3. Simulation-based Design • Faster and less expensive design verification • Immediate feedback for designers • Allows for the efficient exploration of the system design space • Companies report up to 50% time reduction in the design process [Whitney 95]

4. Simulation-based Design • Problem • Hard to create models • Hard to maintain and use them throughout the design process

5. Simulation-based Design • Easy to generate simulation models • Facilitate model re-use • Composition of models • Integrated with design environment • Multi-disciplinary • Mechanical, electrical, signal • Collaborative • Design teams in different locations

6. Composable simulation What is Missing? Modeling and simulation languages; e.g., Modelica, Dymola, VHDL-AMS Requirements for simulation-based design environments

7. Designer Composable Simulation • Composition of system components • Components + interactions Component library Component editor 3D CAD modeling Component graph

8. Component graph Reconfigurable models Port-based models Neutral format XML-based representation Target language VHDL-AMS representation Composable Simulation Modeling paradigm

9. Approach • Four model abstraction layers: Composable simulation Reconfigurable models Port-based modeling Linear graphs

10. System Graph-based Modeling 2 Terminals f f v21,f Element v1 v2 1 v21 Terminal graph

11. Terminal Equations f (through variable) x=Lf v=f R L f=x/L R h x (integrated across variable) (integrated through variable) v=h/C C f=v/R h=C v v (across variable)

12. Terminal Equations • Across-type source: • v21 = f(t) • Through-type source: • f = g(t)

13. Topological Constraints • Kirchhoffian network constraints: 1) Af = 0 Kirchhoff current law 2) Bv = 0 Kirchhoff voltage law

14. System Equations • More variables than DOFs • 2e terminal variables • e terminal equations • e constraint equations • Find a minimal set of state space equations • Use algebraic properties of linear graphs

15. System Equations • Causality assignment • Terminal equations: • d/dt (primary) = f (secondary) • Constraint equations • secondary = g (primary) • Result • d/dt (primary) = f (g (primary))

16. a c b R2 R4 R2 b L3 c d F7 C5 L3 R4 R6 v1 V1 f7 a d R6 C5 gnd gnd Gnd Algebraic Properties of a Linear Graph Component graph System graph

17. R2 R4 L3 v1 C5 R6 f7 1 3 2 Algebraic Properties of a Linear Graph Incidence matrix A R2 L3 b c d a b R4 c v1 f7 a d AT R6 AC C5 Loop matrix B v1 C5 R2 L3 f7 R6 R4 Loop1 gnd Loop2 • Tree: v1, R2, R4, C5 • Cotree: R3, R6, f7 Loop3 BT UC

18. Algebraic Properties of a Linear Graph • Cut-set equations: • Circuit equations:

19. R2 R2 Cotree Cotree L3 L3 Tree Tree b b c c d d R4 R4 v1 v1 f7 f7 a a R6 R6 C5 C5 gnd gnd Algebraic Properties of a Linear Graph

20. Normal Tree • Normal tree: • Defines primary (p) and secondary variables (s) • Causal orientation of terminal equations • Minimum cost spanning tree algorithm • Weighted system graph

21. Normal Tree D: across driver a: accumulator d: dissipation t: delay F: through driver • Weight assignment. • MCT will derive a normal tree: • Max. Number of accumulator elements assigned to the tree • Max. Number of delay elements assigned to the cotree

22. Terminal graphs a c b System components Instantiate terminal graphs R2 R4 R2 b L3 c d f7 v1 C5 R2 R6 L3 R4 F7 C5 L3 R4 System graph R6 v1 V1 f7 a d R6 C5 Reduce to a connected graph Connections gnd gnd Gnd Synthesis of the System Graph for Non-mechanical Domain

23. Kinematic Analysis [Sinha 2000] Synthesis of the System Graph for 3D Mechanics

24. Low Power Component Modeling • Fixed causality • Hybrid model representation • Block diagrams (signals) • System graph • Variable elements • Signal-controlled across or through driver • X(t) = f(t) • Y(t) = h(t)

26. Approach Composable simulation Reconfigurable models Port-based modeling Linear graphs

27. System Port-based Modeling: A New Modeling Paradigm • Ports correspond to physical interfaces • Lumped interactions Ports Environment Interface

28. Behavior described by a linear graph Ports correspond to nodes Connecting two ports defines a node in the graph Across and through variable for each port a c b R2 R4 F7 C5 L3 R6 V1 d gnd Gnd Port-based Models

29. Hierarchical Connections define interactions between components Non-causal connections Impose algebraic constraints on the port variables  Kirchhoffian network constraints Port-based Models

30. Approach Composable simulation Reconfigurable models Port-based modeling Linear graphs

31. Extension to port-based models Composed of two parts: Interface Implementation Provides: Changes in structure Parameter configuration Reconfigurable Models

32. Reconfigurable Models • Based on two principles • Composition • Describes component behavior in terms of interfaces and interactions of subcomponents • Instantiation • The mechanism by which the interface of a model is bound to its implementation

33. Interface Implementation Model Space: AND-OR Tree DC motor OR OR Loss Free Implementation Electro - Mech. n Implementation Power Conversion AND AND Conversion Electrical Mechanical OR OR No Friction Armature Ideal Model Friction Losses AND AND Resistance Resistance Inductance

34. Approach Composable simulation Reconfigurable models Port-based modeling Linear graphs

36. Summary • Goal: simulation-based design environment of mechatronic systems • Composable simulation • Port-based multi-domain modeling of mechatronic systems • Reconfigurable models

37. Summary • Characterization of component structure: AND-OR tree • Multidisciplinary modeling and simulation representation