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A Composable Simulation Environment for Mechatronic Systems. Antonio Diaz-Calderon Christiaan J. J. Paredis Pradeep K. Khosla Carnegie Mellon University Work sponsored by DARPA RaDEO program and CMU 1999 European Simulation Symposium October 26-28, 1999, Erlangen, Germany. Hydraulic
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A Composable Simulation Environment for Mechatronic Systems Antonio Diaz-CalderonChristiaan J. J. Paredis Pradeep K. Khosla Carnegie Mellon University Work sponsored by DARPA RaDEO program and CMU 1999 European Simulation Symposium October 26-28, 1999, Erlangen, Germany.
Hydraulic cylinder Controller Control signal Reference Actuation mechanism Flaps Flaps Motivation CAD Simulation Simulation-based Design 80% design verification By designers
Composable Simulation: Overview • A New Modeling Paradigm • Integration with CAD • Differential Algebraic Equation Solving
A New Modeling Paradigm • Modeling with system components • Reconfigurable models • Automatic model selection
Designer Modeling with System Components • Composition of components + Interactions
Configuration of model classes Set of interaction rules Defines a family of models Model realization Electsystem Conv system Mechsystem Reconfigurable Models Electric Motor
Reconfigurable Models DC Motor • Two principles: • Model composition • Model instantiation • Hierarchical • Models containmeta-knowledge • Operating conditions • Compatibility constraints • Approximations • Semantics • … ModelComposition Electmodel Conv system Mechmodel Series + leakage nofriction Series ModelInstantiation Series + core losses
Experiment Model Experiment Experiment Model Phys. Syst. Phys. Syst. Sim. Cost Model Selection • Ideal: • Model Validity Model Efficiency Find the least expensive model that is still valid for the given experiment
Integration With CAD • User-friendly interface • familiar to designers • very rich information • Extract lumped parameters • kinematics • inertial properties • thermal interaction • electro-magnetic interaction
Integration with CAD Kinematic Analysis Extraction of lumped parameters Mechanics Model
Model Compilation System-Level Simulation Composable Simulation Approach System Description Component Interfaces System Composition Model Fragments Model Selection Selection Criteria Software Components
Model Compilation • System graph approach • Intermediate representation capturing energy flow in system • Ascend • Solving DAEs • Object oriented modeling
Terminal variables Terminal graph a x,y + b + Two-terminal B A y x System Graph Approach x(t) = f(y(t)) • Based on work by Trent, Branin, and Roe
Topological Constraints • Basic postulates [Roe]: 1) Ay = 0 Kirchhoff current law 2) Bx = 0 Kirchhoff voltage law
System Graph for 3D Mechanics Kinematic Analysis Extraction of lumped parameters
System Graph for 3D Mechanics • Knowledge-dependent reduction • Avoid index problems Extended system graph • Identify composite bodies • Extract + combine inertial parameters • Remove redundant joints Reduced system graph
System Graph for Non-mechanical Domain A Terminal graphs C5 p1 R2 R3 B R4 C5 g7 R6 R4 System graph R2 R3 D C E R2 d R3 c e R4 R6 + g7(t) p1(t) p1 b g7 G H F C5 R6 a, f, g, h
TerminalEquations NodeEquations LoopEquations Dynamic Equations • Causality assignment • Terminal Equations: • d/dt (primary) = f (secondary) • Node + Loop Equations • secondary = g (primary) • Result • d/dt (primary) = f (g (primary))
Causality Assignment • Normal tree: • Defines primary (p) and secondary variables (s) • Properties • Minimum cost spanning tree algorithm • Weighted system graph • classification based on form of terminal equation • Kruskal algorithm
Low Power Component Modeling • Hybrid model representation: • Block diagrams (signals) • System graph • Variable elements • Signal-controlled across or through driver • X(t) = f(t) • Y(t) = h(t) • Fixed causality
Low Power Component Modeling • Unknowns: state derivatives and algebraic variables • Software component: x states y u
Low Power Component Modeling • Classification of a software component based on fo(l) • algebraic • non-algebraic • Augmented system of equations and
Simulation Compute BLT schedule Evaluate BLT schedule Integration step Evaluate derivatives
Pitch Motor Pitch Control Signal Reference PID Mechanical System Control Signal Reference PID Yaw Yaw Motor Example: Missile Seeker Enhanced CAD model • 2 DOFs • 3 energy domains: • Mechanical • Electrical • Signal • 17-part assembly • PID controllers and position sensors • Electric motors and signal amplifiers
Summary • Composable simulation • A new modeling paradigm • For simulation of mechatronic systems • Approach: • System graph: single representation across domains • Integration with CAD