High Performance Physical Modeling and Simulation The MapleSim Advantage High Performance Physical Modeling and Simulation © Maplesoft, a division of Waterloo Maple Inc., 2010.

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.

Pain Points 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 © Maplesoft, a division of Waterloo Maple Inc., 2010.

Engineering Challenge: Stability Control Automotive OEM High-fidelity model of vehicle dynamics (plant model) Plant model needs to compute fast enough for real-time controller testing (HIL) © Maplesoft, a division of Waterloo Maple Inc., 2010.

Stability Control, cont’d… Without Stability Controller With Stability Controller © Maplesoft, a division of Waterloo Maple Inc., 2010.

Results 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 Infeasible with other tools Signal flow: infeasible due to complexity Real-time performance unacceptable © Maplesoft, a division of Waterloo Maple Inc., 2010.

Key application areas Automotive Aero/defence Space Power Medical Vehicle dynamics Powertrain Climate control NVH Aero/defence Guidance, navigation UAV robotics Simulators Command and control Space Space vehicle control Guidance and navigation Space robotics Power Wind turbines New generation power sources Medical Intelligent prosthetics Artificial organs © Maplesoft, a division of Waterloo Maple Inc., 2010.

Introduction to MapleSim Rapid Physical Model Development Exceptional Multi-body Dynamics Fast, High-fidelity Plant Models For RT/HIL Extensive Analysis Tools © Maplesoft, a division of Waterloo Maple Inc., 2010.

The MapleSim Symbolic Advantage 1, 0, cancellations etc. Algebraic, trig identities etc. DAE index reduction Model simplification EQUATIONS Easy to read and document Flexible and reusable Parameter management Identify redundant calculations Pre-compute expensive functions Standard real-time toolchains Optimized code generation Sensitivity Parameter optimization Completely extensible Advanced analysis © Maplesoft, a division of Waterloo Maple Inc., 2010.

Simple Introductory Application Single arm robot control system © Maplesoft, a division of Waterloo Maple Inc., 2010.

Conventional Control Systems Design Process Real-time platform Plant model Transfer plant model to RT system Hardware in the loop (HIL) simulation tests controller without the expense of a physical plant Controller design Embedded code system Plant modeling is deeply mathematical, time-consuming, and error-prone. Model complexity can also be a real barrier. 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. Controller HW + Controller code

MapleSim Control Systems Design Process Plant model Controller design Real-time platform Optimized plant code generation Embedded code system MapleSim produces the fastest plant code for HIL testing. Infeasible becomes feasible ($$$$). MapleSim automates the plant modeling process. From months to days (). Controller HW + Controller code

Sample Applications Mean Value Engine Mean Value Engine: Real-Time Execution Lead Acid Battery © Maplesoft, a division of Waterloo Maple Inc., 2010.

Mean Value Engine 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 © Maplesoft, a division of Waterloo Maple Inc., 2010.

Mean Value Engine: Real-Time Execution LabVIEW/Extended Model Interface (EMI) LabVIEW/Simulation Interface Tookit (SIT) NI VeriStand Real-time execution on NI PXI system Also tested with Simulink® © Maplesoft, a division of Waterloo Maple Inc., 2010. Simulink is a registered trademark of The Mathworks, Inc.

Lead Acid Battery 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 © Maplesoft, a division of Waterloo Maple Inc., 2010.

Key Takeaways 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 © Maplesoft, a division of Waterloo Maple Inc., 2010.

Discussion and Questions © Maplesoft, a division of Waterloo Maple Inc., 2010.

Symbolic Model Preprocessing Standard Numeric Formulation MapleSim Symbolic Formulation The following slides are for more detailed discussion with customers regarding our Symbolic Computation Engine and how it provides its unique benefits © Maplesoft, a division of Waterloo Maple Inc., 2010.

Symbolic Computation for Plant Modeling MapleSim Symbolic Formulation Standard Numeric Formulation Model Definition Model Definition Coordinate Selection Equation Generation Symbolic Simplification Simulation Procedure Generation with Limited Optimization Numerical black box Code Optimization Simulation Procedure Generation with Limited Optimization Simulation Procedure Generation Simulation Simulation © Maplesoft, a division of Waterloo Maple Inc., 2010.

Symbolic Computation for Plant Modeling MapleSim Symbolic Formulation Standard Numeric Formulation Model Definition Model Definition Coordinate Selection Equation Generation Symbolic Simplification Code Optimization MapleSim applies 4 levels of model optimization Coordinate Selection Equation Generation Symbolic Simplification Simulation Procedure Generation with Limited Optimization Numerical black box Code Optimization Simulation Procedure Generation with Limited Optimization Simulation Procedure Generation Simulation Simulation © Maplesoft, a division of Waterloo Maple Inc., 2010.

Standard Numeric Formulation Model Definition 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 Simulation © Maplesoft, a division of Waterloo Maple Inc., 2010.

MapleSim Symbolic Formulation Model Definition Example using Linear Graph Theory (MapleSim) Coordinate Selection Equation Generation Symbolic Simplification Code Optimization Simulation Procedure Generation Simulation © Maplesoft, a division of Waterloo Maple Inc., 2010.

MapleSim Symbolic Formulation Example: Stewart Platform Model Definition Coordinate Selection Equation Generation Symbolic Simplification 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 Code Optimization Simulation Procedure Generation Simulation © Maplesoft, a division of Waterloo Maple Inc., 2010.

MapleSim Symbolic Formulation Symbolic generation automatically performs first level simplification (e.g. 1’s, 0’s, subtraction, cancellation) Symbolic equations are also accessible for more analysis Model Definition Coordinate Selection Equation Generation 6 mult 4 add/sub Symbolic Simplification Code Optimization 2 mult 1 add/sub Simulation Procedure Generation Simulation © Maplesoft, a division of Waterloo Maple Inc., 2010.

MapleSim Symbolic Formulation Simple equations directly solved Reduces number of integration variables Trigonometric simplifications All these examples are “loss-less” simplifications Model Definition Coordinate Selection Equation Generation Symbolic Simplification Code Optimization Simulation Procedure Generation Simulation © Maplesoft, a division of Waterloo Maple Inc., 2010.

MapleSim Symbolic Formulation Repeated equations are isolated so they are only computed once Issues between symbolic simplification and code optimization Model Definition Coordinate Selection Equation Generation Symbolic Simplification Code Optimization Simulation Procedure Generation Simulation © Maplesoft, a division of Waterloo Maple Inc., 2010.