Seminar Modeling and Simulation of Dynamical Systems

Presented by the IEEE Control Systems Society Santa Clara Valley

Sunnyvale, 5 February 2011

1 Program

Welcome 08:45 – 09:10am Coffee and bagels, Seminar kickoff at 9:00am

Session 1 09:10 – 10:00am Mathematical models of dynamical systems Dr. P.K. Menon, Optimal Synthesis

Session 2 10:10 – 11:00am System Identification - Theory and Practice Dr. Mark B. Tischler, Ames Research Center

Session 3 11:10 – 12:00am Visualization and Virtual Environments Dr. Hadi Aggggoune, Cogswell Polytech. College

Lunch 12:00 – 12:40pm Sandwiches, sodas, discussions and product demos

SiSession 4 12:40 – 01:30pm AlitiApplications of HdHardware-in-the-Loop Simu la tors Christoph Wimmer, National Instruments

Session 5 01:40 – 2:30pm Simulation with Software Tools Elliot English, Dr. Martin Aalund, Dr. Karl Mathia

2 Session 5

Simulation Software Tools Martin Aalund

3 Historical Simulation Tools

Historically dynamical systems were often simulated with: ƒ Scaled Models ƒ Such as the Antikythera mechanism used by the Greeks to calculate astronomical positions in 100 BC ƒ Mechanical Analogue Computers ƒ French ppyhysicist Gas pard-Gustave Coriolis designed a mechanical device to integrate differential equations of the first order in 1839 ƒ Differential Analyzers such as the Thomson Disk and Sphere analyzer used to simulate tides ƒ Simplified Systems Lumped models ƒ SiSpring as Capac itor ƒ Damper as Resistor ƒ Inertia as Inductors ƒ Analog Computers (Gained Popularity in 1940s) ƒ Use Active circuits integrate, differentiate and scale signals. ƒ Can model complex electro mechanical systems. ƒ Real time operation and reprogrammable

From Wikipedia 4 Current State of the Art

ƒ Analog Solutions were ƒ Hard to setup, ƒ problem size limited, ƒ must carefully scale problems, ƒ Have limited dynamic range ƒ Advent of Modern Computers and Advanced Software have replaced analog computers in most cases ƒ Allow for unlimited size of model ƒ Reusable models ƒ Large choice of tools available ƒ Domain Specific ƒ Commercial ƒ Free

5 Simulation SW (Open/Free)

ƒ Octave http://www.gnu.org/software/octave/ ƒ Matlab like language ƒ Numerical Computations ƒ Linear and Non-linear solvers ƒ http://www.scilab.org/products/scilab/features ƒ 2d and 3d Visualization ƒ Numerical Computation ƒ Data Analysis ƒ Xcos: hybrid dynamic systems modeler and simulator ƒ http://maxima.sourceforge.net/ ƒ manipulation of symbolic and numerical expressions ƒ Math Toolbox http://eumat.sourceforge.net/ ƒ Built on Maxima ƒ Provides notebook style interface ƒ Advanced Graphics, Numerical functions ƒ Sage http://www.sagemath.org/ ƒ Open source alternative to Magma, , Mathematica and Matlab. ƒ Web Based Interface

6 Simulation SW (commercial)

ƒ Matchcad http://www.ptc.com/products/mathcad/ ƒ Visual Interface WYSIWYG ƒ Symbolic and numerical simulations ƒ MapleSim http://www.maplesoft.com/products/maplesim/# ƒ Based on Maple Symbolic Computation technology ƒ Multi-Domain Systems ƒ Matlab/Simulink http://www.mathworks .com/products/simulink/ ƒ Powerful modeling and simulation capability ƒ Can generate code based on models ƒ Anykode/Marilou http://www.anykode.com/marilou.php ƒ MdliModeling an d s imu ltilation too ls for mo bile ro btibotics ƒ Microsoft Robotics Studio http://www.microsoft.com/robotics/ ƒ Simulations and development environment ƒ Contains Physics models for Gravity ƒ PHYSX http://www.nvidia.com/object/physx_new.html ƒ Free commercial Physics engine from NVIDIA

7 Demo

8 Demo Continued

Can define functions and plot them we can use built in functions to find the laplace transform u(t) := Φ(t)

1 1 Us( ) := ut( ) laplace → s

ut() 0.5 We can define a in s domain and do an inverse transform

0 ω := 3 − 10 − 5 0 5 10 t ω H()s := 2 2 s + ω

H()t := Hs( ) invlaplace→ sin() 3⋅ t

9 Other Open SW for simulation

ƒ FreeMat http://freemat.sourceforge.net/ ƒ JMathLib Java Clone http://www.jmathlib.de/ ƒ Octave, SciLab and Matlab functionality ƒ Mathnium http://www.mathnium.com/ ƒ Numerical Computing, Data Analysis, and Graphics ƒ TeLa http://www.geo.fmi.fi/prog/tela.html ƒ Algae httppg://algae.sourcefor ge.net/ ƒ Language For Large Systems ƒ Lush http://lush.sourceforge.net/ ƒ Lisp Based for Large scale numerical and graphical applications ƒ Yoocrick http://yo ric k.sou rce fo rge .n et/ ƒ Rlab http://rlab.sourceforge.net/ ƒ Python Extensions http://www.python.org/ ƒ NumPy http://sourceforge.net/projects/numpy/ ƒ SciPy http://www.scipy .org/ ƒ The Project http://www.r-project.org/ ƒ Statistical Computing

10 Other Open SW for simulation

ƒ Delta3D http://www.delta3d.org/ ƒ 3D visualization and simulations ƒ Dynamic Engine based on ODE ƒ ODEhttp://ode.org/ ƒ Open Dynamics Engine ƒ Simulation of Ridged body dynamics ƒ Physics Abstraction Layer http://www.adrianboeing . com/pal/index. html ƒ Fluids ƒ Dynamics ƒ Actuators, Sensor

11 Sponsors

h//http://www.adi .com http://www.applimotion.com

http://www.ni.com

http://www.willowgarage.com

http://www.cogswell.edu http://www.asme.org

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