©20

06 T

he M

athW

orks

, Inc

.

Terry Denery, Ph.D.

Physics-Based Modeling Tools

Modeling Mechanical, Electric, and Hydraulic Systems in Simulink®

2

Physics-Based Modeling Methods Improve Control System Design

Multidomain systems (mechanical, electrical, hydraulic, chemical, . . .)Successful controller development requires thorough and accurate understanding of plant

ControllerElectricalMechanicalDevice

Actuators

Sensors

Plant+u y

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ElectricalMechanicalDevice

Actuators

Sensors

Plant

Important Physical Domains

Mechanical-3D Multi-Body Dynamics-Driveline Mechanics SimDriveline

SimMechanics

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ElectricalMechanicalDevice

Actuators

Sensors

Plant

Important Physical Domains

Electrical-Circuits-Motors and Actuators-Power Systems

SimPowerSystems

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ElectricalMechanicalDevice

Actuators

Sensors

Plant

Important Physical Domains

Hydraulics-Circuits-Motors and Actuators-Power Systems

SimHydraulics

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Controller+u y

ElectricalMechanical

Device

Actuators

Sensors

PlantControl System

7

Control System

8

Electrical Power NetworkHydraulic Power Network

Mechanical Driveline Power Network

Power Delivery

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Electrical Power NetworkHydraulic Power Network

Mechanical Driveline Power Network

Electrical

Mechanical

Device

10

Plant

Electrical

Mechanical

Device

Actuators

SensorsController+u y

Control Systems within Control Systems

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Biggest Benefit – Delivered Through Simulink®

Rich Modeling Environment– Physical– Behavioral– Data-Driven

Control System Development Tool– One environment for controller and plant– Code generation that enables HIL testing– Easy access to control tools

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Why did we build SimHydraulics?

Hydraulics is widely used in motion actuation systemsCustomer Feedback – “Extend benefits of Model-Based Design to hydraulic

system design”– “Develop better plant models for better controller

development”– “Co simulation with other products is difficult and

impractical”

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Pros and Cons for Hydraulics

Pros:High power densityStraight-line actuators are simple, efficient and reliableVariable speed is easily obtainedSimple, efficient, and centralized control Overload protection

Cons:High costComplex and costly maintenanceExtremely vulnerable to dirt and contaminationPossible leaksNoise and vibrationsFire hazards

Design Trend is Electro-Hydraulics:Transmit power electrically, but deliver through local hydraulic networks

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Hydraulic System Schematic Diagram

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Block Diagrams

( ) ( ).,,

,

,,

),(

211

1211

TAAPTP

OOAOP

AA

TAOAPO

pp

ppppppqqqqq

dtdpKqA

ppKqppKq

tpp

−+−=−−==

⋅=

−=−=

=

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Physical System Diagrams

Hydraulic Schematic SimHydraulics Model

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Demonstrations

18

Building Blocks

Hydraulic Hydraulic

Mechanical

Signal

Mechanical

19

Actuation

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Multidomain with SimMechanics

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First-Principles Modeling

Use an understanding of the system’s physics to derive a mathematical representation

∫ −−−−−−−−−−+−

=)(sin1

)cos()cos())sin(()sin())sin(()sin(2

2222

γαγγααγαγαγγααα

nennenwL &&

& dγ

Two Approaches to Modeling Dynamic Systems

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First-Principles Modeling Data-Driven Modeling

Use system test data to derive a mathematical representation

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+++

+++

=

13

231

)(

2

2

23

sss

sss

sH

Use an understanding of the system’s physics to derive a mathematical representation

∫ −−−−−−−−−−+−

=)(sin1

)cos()cos())sin(()sin())sin(()sin(2

2222

γαγγααγαγαγγααα

nennenwL &&

& dγ

Two Approaches to Modeling Dynamic Systems

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First-Principles Modeling Data-Driven Modeling

Advantages:Provides insight into the system’s underlying behaviorEnables performance prediction for unbuilt systems

Disadvantages:Effects like friction and turbulence are difficult to characterizeMay be time consuming to develop

Advantages:Can be a fast method for developing an accurate modelInstills confidence because it uses data from an actual system

Disadvantages:Requires a physical system to acquire test dataLacks description of physics of the systemMay need multiple data sets to cover range of system operation

Each Approach Has Its Merits

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Simulink®

ParameterEstimation

Complete Modeling Environment

Simulink

SimHydraulicsSimMechanicsSimDriveline

SimPowerSystems

First-Principles

Neural NetworkToolbox

SystemIdentification

Toolbox

Fuzzy LogicToolbox

Data-Driven

Tools that Span Both Modeling Approaches

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Inform Model with Test Data

Data fitting and optimization techniquesSets parameters defined by physics-based modeling tools

Simulink Parameter Estimation

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Code Generation with Real-Time Workshop®

Generate ANSI C codeHardware-in-the-loop (HIL) simulationsS-functions In-house code

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MATH EngineeringSimulation

MATLAB &Simulink

DomainKnowledge

ProgrammingEffort

Flexibility of mathematical modeling enables you to simulate almost anything.

General Engineering Simulation

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MATH HydraulicSimulation

SimHydraulics Dom.Know.

Prog.Effort

SimHydraulics brings you further by reducing your requirementsfor hydraulic domain knowledge and programming effort.

MATLAB &Simulink

DomainKnowledge

ProgrammingEffort

Hydraulic Engineering Simulation

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MATH MultidomainSimulation

The MathWorks provides the best combination of tools for multidomain simulations.

Multidomain Simulation

Controls Tools DK PE

Real Time Workshop DK. PE

Parameter Estimation DK. PE

SimMechanics DK. PE

MATLAB &Simulink DK PE

SimPowerSystems DK. PE

SimDriveline DK. PE

SimHydraulics DK. PE