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Company
LOGO
High Performance Physical Modeling and Simulation
The MapleSim Advantage
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Company
LOGO Physical Modeling in Industry
Physical modeling helps to reduce model development time and prototype costs
“X” by wire Green power Autonomous vehicles Mechatronics Global competition
Reduce cost, reduce product development time
Increase efficiency, increase performance, increase safety
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Company
LOGO Pain Points
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Increasingly complex systems Creation and organization of physical models is difficult Debugging and diagnostics is difficult
Simultaneous controller + model development Many systems not naturally suited to this
Real-time deployment Required for most applications Speed of generated code a concern
Current analysis tools are limiting Verification and validation a challenge Limited access to underlying models and equations
Company
LOGO Engineering Challenge: Stability Control
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Automotive OEM
High-fidelity model of vehicle dynamics (plant model)
Plant model needs to compute fast enough for real-time controller testing (HIL)
Company
LOGO Stability Control, cont’d…
© Maplesoft, a division of Waterloo Maple Inc., 2010.
With Stability ControllerWithout Stability Controller
Company
LOGO Results
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Infeasible with other tools Signal flow: infeasible
due to complexity Real-time performance
unacceptable
Full automotive chassis with detailed suspension models
Double wishbone at front Semi-trailing arm at rear
Fiala tire model 15 degrees of freedom Whole model runs in real-time
Total model development time: 2 days
Company
LOGO Key application areas
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Automotive• Vehicle dynamics• Powertrain• Climate control• NVH
Aero/defence• Guidance,
navigation• UAV robotics• Simulators• Command and
control
Power• Wind turbines• New generation
power sources
Space• Space vehicle
control• Guidance and
navigation• Space robotics
Medical• Intelligent
prosthetics• Artificial
organs
Company
LOGO Introduction to MapleSim
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Rapid Physical Model
Development
ExceptionalMulti-bodyDynamics
ExtensiveAnalysis Tools
Fast, High-fidelityPlant ModelsFor RT/HIL
Company
LOGO
Identify redundant calculationsPre-compute expensive functionsStandard real-time toolchains
Optimized code generation
The MapleSim Symbolic Advantage
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Easy to read and documentFlexible and reusableParameter management
1, 0, cancellations etc.Algebraic, trig identities etc.DAE index reduction
Model simplification
SensitivityParameter optimizationCompletely extensible
Advanced analysis
EQUATIONS
Company
LOGO Simple Introductory Application
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Single arm robot control system
Company
LOGO Conventional Control Systems Design Process
Hardware in the loop (HIL)
simulation tests controller without the expense of a
physical plant
Plant modeling is deeply mathematical, time-consuming, and error-prone. Model complexity can also
be a real barrier.
Controller HW +
Controller code
Real-time platform
Plant model
Embeddedcode system
Controller design
Transfer plant model to RT system
If the plant model cannot compute quicker than
the real-time cycle, you cannot do an HIL test. If the system is complex, the model slows down.
Company
LOGO MapleSim Control Systems Design Process
Controller HW +Controller code
Real-time platform
Embeddedcode system
Optimized plant code generation
Plant model
Controller design
MapleSim automates the plant modeling process.
From monthsto days ().
MapleSim produces the
fastest plant code for HIL testing.
Infeasible becomes feasible
($$$$).
Company
LOGO Sample Applications
© Maplesoft, a division of Waterloo Maple Inc., 2010.
• Mean Value Engine• Mean Value Engine: Real-Time
Execution• Lead Acid Battery
Company
LOGO Mean Value Engine
© Maplesoft, a division of Waterloo Maple Inc., 2010.
• Collaboration with automotive company
• Used for engine control development
• Provides overall power, speed, torque output– Throttle– Intake manifold– Engine power– Applied load
• Custom components incorporate standard engine equations
Company
LOGO Mean Value Engine: Real-Time Execution
© Maplesoft, a division of Waterloo Maple Inc., 2010.
• LabVIEW/Extended Model Interface (EMI)• LabVIEW/Simulation Interface Tookit (SIT)• NI VeriStand
• Real-time execution on NI PXI system• Also tested with Simulink®
Simulink is a registered trademark of The Mathworks, Inc.
Company
LOGO Lead Acid Battery
© Maplesoft, a division of Waterloo Maple Inc., 2010.
• Collaboration with automotive company
• Terminal voltage, internal resistance is highly nonlinear
• State of charge, temperature, rate of charging and discharging
• Coupled electrical and thermal model
Company
LOGO Key Takeaways
© Maplesoft, a division of Waterloo Maple Inc., 2010.
• Rapidly develop complex physical models
• Advanced multibody dynamics tools
• Direct access to equations supports deeper analysis and greater insight into your system
• Symbolic preprocessing provides highly optimized plant model code for RT/HIL applications
Company
LOGO Discussion and Questions
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Questions?
Company
LOGO Symbolic Model Preprocessing
© Maplesoft, a division of Waterloo Maple Inc., 2010.
• Standard Numeric Formulation• MapleSim Symbolic Formulation
Company
LOGO Symbolic Computation for Plant Modeling
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Coordinate Selection
Equation Generation
Symbolic Simplification
Code Optimization
Simulation Procedure Generation
Model Definition
Simulation
MapleSim Symbolic Formulation Standard Numeric Formulation
Model Definition
Simulation Procedure Generation with Limited
Optimization
Simulation
Simulation Procedure Generation with Limited
Optimization
Numerical black box
Company
LOGO Symbolic Computation for Plant Modeling
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Coordinate Selection
Equation Generation
Symbolic Simplification
Code Optimization
Simulation Procedure Generation
Model Definition
Simulation
MapleSim Symbolic Formulation Standard Numeric Formulation
Model Definition
Simulation Procedure Generation with Limited
Optimization
Simulation
Coordinate Selection
Equation Generation
Symbolic Simplification
Code Optimization
MapleSim applies 4 levels of model
optimization
Simulation Procedure Generation with Limited
Optimization
Numerical black box
Company
LOGO Standard Numeric Formulation
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Model Definition
Simulation
• Full matrix equation is populated and calculated at each iteration
6 multiplications, 4 additions per step
• Any optimization is limited and is applied prior to iteration.
Simulation Procedure Generation with Limited
Optimization
Numerical black box
Company
LOGO MapleSim Symbolic Formulation
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Coordinate Selection
Equation Generation
Symbolic Simplification
Code Optimization
Simulation Procedure Generation
Model Definition
Simulation
T
T
yxyxyxmmmrrTree
sshhrrTree
],,,,,,,,[},,,{
],,[},,,{
33322211132174
111081110874
q
q
Example using Linear Graph Theory (MapleSim)
Company
LOGO MapleSim Symbolic Formulation
© Maplesoft, a division of Waterloo Maple Inc., 2010.
Coordinate Selection
Equation Generation
Symbolic Simplification
Code Optimization
Simulation Procedure Generation
Model Definition
Simulation
Absolute coordinates (e.g. ADAMS):• 78 coords (12 per leg, 6 for the
platform), • 78 dynamic equations, +72 constraint equations = 150 equations
Relative coordinates (MapleSim):• 24 coords( 3 per leg, 6 for the platform)• 24 dynamic equations+ 18 constraints = 42 equations
Example: Stewart Platform
Company
LOGO MapleSim Symbolic Formulation
© Maplesoft, a division of Waterloo Maple Inc., 2010.
• Symbolic generation automatically performs first level simplification (e.g. 1’s, 0’s, subtraction, cancellation)
•
• Symbolic equations are also accessible for more analysis
Coordinate Selection
Equation Generation
Symbolic Simplification
Code Optimization
Simulation Procedure Generation
Model Definition
Simulation
6 mult4 add/sub
2 mult1 add/sub
Company
LOGO MapleSim Symbolic Formulation
© Maplesoft, a division of Waterloo Maple Inc., 2010.
• Simple equations directly solved• Reduces number of integration
variables• Trigonometric simplifications
• All these examples are “loss-less” simplifications
Coordinate Selection
Symbolic Simplification
Code Optimization
Simulation Procedure Generation
Model Definition
Simulation
Equation Generation
Company
LOGO MapleSim Symbolic Formulation
© Maplesoft, a division of Waterloo Maple Inc., 2010.
• Repeated equations are isolated so they are only computed once
• Issues between symbolic simplification and code optimization
Coordinate Selection
Symbolic Simplification
Code Optimization
Simulation Procedure Generation
Model Definition
Simulation
Equation Generation