Mathworks SIMSCAPE 3 user guide

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Simscape™ 3

User’s Guide

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Simscape™ User’s Guide

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Revision History

March 2007 Online only New for Version 1.0 (Release 2007a) September 2007 O nline only Revised for Version 2.0 (Release 2007b) March 2008 Online only Revised for Version 2.1 (Release 2008a) October 2008 Online only Revised for Version 3.0 (Release 2008b) March 2009 Online only Revised for Version 3.1 (Release 2009a) September 2009 O nline only Revised for Version 3.2 (Release 2009b) March 2010 Online only Revised for Version 3.3 (Release 2010a)

Modeling Physical Systems

Basic Principles of Modeling Physical Networks ..... 1-2

Overview of the Physical Network Approach to Modeling

Physical Systems Variable Types Building the Mathematical Model Direction of Variables Connector Ports and Connection Lines Connecting Simscape Diagrams to Simulink Sources and

Scopes

........................................ 1-10

............................... 1-2

.................................... 1-4

.................... 1-5

............................. 1-6

................ 1-8

Contents

Introducing the Simscape Block Libraries

Library Structure Overview Using the Simulink Library Browser to Access the Block

Libraries Using the Command Prompt to Access the Block

Libraries

Essential Steps to Building a Physical Model

Building Your Model Using the Conserving Ports Using the Physical Signal Ports

Creating a Simple Model

Building a Simscape Diagram Modifying Initial Settings Running the Simulation Adjusting the Parameters

Modeling Best Practices

Grounding Rules Avoiding Numerical Simulation Issues

Modeling Pneumatic Systems

...................................... 1-11

...................................... 1-12

............................... 1-14

.................................. 1-35

......................... 1-11

......................... 1-15

...................... 1-16

........................... 1-17

....................... 1-17

........................... 1-25

............................ 1-26

........................... 1-29

............................ 1-35

....................... 1-42

........... 1-11

......... 1-14

................ 1-38

Intended Applications .............................. 1-42

Assumptions and Limitations Fundamental Equations Network Variables Connection Constraints References

....................................... 1-45

................................ 1-44

....................... 1-42

............................ 1-43

............................ 1-45

Simulating Physical Models

How Sim scap e Simulation Works ................... 2-2

Simscape Simulation Phases Model Validation Network Construction Equation Construction Computing Initial Conditions Performing Transient Initialization Transient Solve

.................................. 2-4

.............................. 2-4

................................... 2-6

........................ 2-2

............................. 2-5

........................ 2-5

................... 2-6

vi Contents

Working with Solvers

Selecting a Solver Input Filtering

Troubleshooting Simulation Errors

Troubleshooting Tips and Techniques System Configuration Errors Numerical Simulation Issues Initial Conditions Solve Failure Transient Simulation Issues

Finding an Operating Point

What Is an Operating Point? How to Find Operating Points Finding Operating Points with Simscap e, Simulink, and

Related P roducts

Linearizing at an Operating Point

What Is Linearization? How to Linearize a Model

.................................... 2-10

.............................. 2-8

................................. 2-8

................. 2-13

........................ 2-14

........................ 2-17

...................... 2-19

........................ 2-20

........................ 2-22

....................... 2-23

................................ 2-24

.................. 2-28

............................. 2-28

........................... 2-30

Linearizing a Model with Si mscape, Simulink, and Related

Products

References

....................................... 2-30

....................................... 2-34

Generating Code

About Code Generation from Simscape Models Related Simulink Code Generation Documentation Reasons for Generating Code Using Code-Related Products and Features How Simscape Code Generation Differs from Simulink

Limitations

Sample Time and Solver Restrictions Algebraic Loops Restricted Simulink Tools Unsupported Simulink Tools Simulink Tools Not Compatible with Simscape Blocks Code Generation

.................................. 2-35

......... 2-35

...... 2-35

........................ 2-36

............ 2-36

....................................... 2-39

................. 2-39

................................... 2-39

.......................... 2-40

........................ 2-42

.................................. 2-42

Logging Simulation Data

About Simulation Data Logging ..................... 3-2

Suggested Workflows Limitations

...................................... 3-2

.............................. 3-2

... 2-37

... 2-42

How to Log Simulation Data

How to Enable Data Logging Data Logging Options

Data Logging Example

.............................. 3-4

............................. 3-6

........................ 3-3

vii

Working with Physical Units

Overview ......................................... 4-2

Unit Definitions

Specifying Units in Block Dialogs

Thermal Unit Conversions

About Affine Units When to Apply Affine Conversion How to Apply Affine C onversion

Angular Units

References

................................... 4-4

................... 4-9

.......................... 4-11

................................ 4-11

.................... 4-11

..................... 4-12

..................................... 4-14

....................................... 4-14

Using the Simscape Editing Mode

About the Simscape Editing Mode ................... 5-2

Suggested Workflows What You Can Do in Restricted Mode What You Can Do in Full Mode Switching Between Modes Working with Block Libraries

.............................. 5-2

................. 5-3

...................... 5-4

.......................... 5-4

....................... 5-7

viii Contents

Working with Restricted and Full Modes

Setting the Model Loading Preference Saving a Model in Restricted Mode Working with a Model in Restricted Mode Switching from Restricted to Full Mode

Editing Mode Information

What Is the Current Mode? Which Licenses Are Checked Out?

.......................... 5-23

......................... 5-23

................. 5-9

................... 5-10

.................... 5-23

............ 5-9

............. 5-13

............... 5-21

Examples

Getting Started .................................... A-2

Best Practices

Editing Mode

..................................... A-2

...................................... A-2

Index

x Contents

Modeling Physical Systems

• “Basic Principles of Modeling Physical Networks” on page 1-2

• “Introducing the Simscape Block Libraries” on page 1-11

• “Essential Steps to Building a Physical Model” on page 1-14

• “Creating a Simple Model” on page 1-17

• “Modeling Best Practices” o n page 1-35

• “Modeling Pneumatic Systems” on page 1-42

1 Modeling Physical Systems

Basic Principles of Modeling Physical Networks

In this section...

“Overview of the Physical Network Approach to Modeling Physical Systems” on page 1-2

“Variable Types” on page 1 -4

“Building the Mathematical Model” on page 1-5

“Direction of Variables ” on page 1-6

“Connector Ports and Connection Lines” on page 1-8

“Connecting Simscape Diagr ams to Simulink Sources a n d Scopes” on page 1-10

Overview of the Physical Network Approach to Modeling Physical Systems

Simscape™ software is a set of block libraries and special simu lat ion features for modeling physical systems in the Simulink the Physical Network approach, which differs from the standard Simulink modeling approach and is particularly suited to simulating systems that consist of real physical components.

environment. It employs

1-2

Simulink blocks represent basic mathematical operations. When you connect Simulink blocks together, the resulting diagram is equivalent to the mathematical model, or representation, of the system under design. Simscape technology lets you create a network representation of the system under design, bas ed on the Physical Network approach. According to this approach, each system is represented as consisting of functional elements that interact with each other by exchanging energy through their ports.

These connection ports are bidirectional. They mimic physical connections between elements. Connecting Simscape blocks together is analogous to connecting real components, such as pumps, valves, and so on. In other words, Simscape diagrams mimic the physical system layout. If physical components can be connected, their models can be connected, too. You do not have to specify flow directions and information flow when connecting Simscape blocks, just as you do not have to specify this information when you connect

Basic Principles of Modeling Physical Networks

real physical components. The Physical Network approach, with its Through and Across variables and bidirectional physical connections, automatically resolves all the traditional issues with variables, directionality, and so on.

The number of connection ports for each element is determined by the number of energy flows it exchanges with other elements in the system, and depends on the level of idealization. For example, a fixed-displacement hydraulic pump in its simplest form can be represented as a two-port element, with one energy flow associated with the inlet (suction) and the other with the outlet. In this representation, the angular velocity of the driving shaft is assumed constant, making it possible to neglect the energy exchange between the pump and the shaft. To account for a variable driving torque, you need a third port associated with the driving shaft.

An energy flow is characterized by its variables. Each energy flow is associated with two variables, one Through and one Across (see “Variable Types” on page 1-4 for more information). Usually, these are the variables whose product is the energy flow in w atts. They are called the basic, or conjugate, variables. For example, the basic variables for mechanical translational systems are force and velocity, for mechanical rotational systems—torque and angular velocity, for hydraulic systems—flow rate and pressure, for electrical systems—current and voltage.

The following example illustrates a Physical Network representation of a double-acting hydraulic cylinder.

The element is represented with three energy flows: two flows of hydraulic energy through the inlet and outlet of the cylinder and a flow of mechanical

1-3

1 Modeling Physical Systems

energy associated with the rod motion. It therefore has the following three connector ports:

• A — Hydraulic conserving port associated with pres sure

variable) and flow rate

(a Through vari abl e)

• B — Hydraulic conserving port associated with pres sure

variable) and flow rate

(a Through vari abl e)

(an Across

• R — Mechanical translational conserving port associated with rod velocity

(an A cross variable) and force F3(a Through variable)

See “Connector Ports and Connection Lines” on page 1-8 for more information on connector port types.

Variable Types

Physical Network approach supports two types of variables:

• Through — Variables that are measured with a gauge connected in series

to an element.

• Across — Variables that are measured with a gauge connected in parallel

to an element.

ThefollowingtableliststheThroughand Across variables associated with each type of physical domain in Simscape software:

Physical Domain Across Variable Through Variable

1-4

Electrical Voltage

Hydraulic

Magnetic

Pressure

Magnetomotive force (mmf)

Mechanical rotational

Mechanical

Angular velocity

Translational velocity

translational

Current

Flow rate

Flux

Torque

Force

Basic Principles of Modeling Physical Networks

Physical Domain Across Variable Through Variable

Pneumatic Pressure and

temperature

Thermal

Temperature

Mass flow rate and heat flow

Heat flow

Note Generally, the product of each pair of Across and Through variables associated w ith a domain is power (energy flow in watts). The exceptions are pneumatic domain, where the product of pressure and mass flow rate is not power, and magnetic domain, where the product of mmf and flux is not power, but energy. These result in a pseudo-bond graph.

Building the Mathematical Model

Through and Across variables associated with all the energy flows form the basis of the mathematical model of the block.

For example, the model of a double-acting hydraulic cylinder shown in the previous illustration can be described with a simple set of equation s :

FpApA

=−ii

31122

= i

qAv

113

= i

qAv

223

1-5

1 Modeling Physical Systems

where

1,q2

1,p2

1,A2

Flow rates through ports A and B , respectively (Through variables)

Gauge pressures at ports A and B, respectively (Across variables)

Piston effective areas

Rod force (Through variable)

Rod velocity (A cross variable)

The model could be considerably more complex, for example, it could account for friction, fluid compressibility, inertia of the moving parts, and so on. For all these different mathematical models, however, the element configuration (that is, the number and type of ports and the associated Through and Across variables) would remain the same, meaning that the Physical Network approach lets you substitute models of different levels of complexity w ithout introducing any changes to the schematic. For example, you can start dev eloping your s ystem by using the Resistive Tube block from the Foundation library, which accounts only for friction losses. At a later stage in development, you may want to account for fluid compressibility. You can then replace it with a Hydraulic Pipeline block, available with SimHydraulics

block libraries, or, depending on your application, even with a S eg mented Pipeline block if you also need to account for fluid inertia. This modeling principle is called incremental modeling.

1-6

Direction of Variables

Each variable is characterized by its magnitude and sign. The sign is the result of measure ment orientation. The same variable can be positive or negative, depending on the polarity of a measurement gauge. That is why it is very important to apply exactly the same rule to all the variables in the Physical Network.

Elements w ith only two ports are characterized with one pair of variables, a Through variable and an Across variable. Since these variables are closely related, their orientation is defined with one direction. For example, if an element is oriented from port A to port B, it implies that the Through variable (TV) is positive if it “flows” from A to B, and the Across variable is determined

Basic Principles of Modeling Physical Networks

as AV = AVA–AVB,whereAVAand AVBare the element node potentials or, in other w ords, the values of this Across variable at ports A and B, respectively.

This approach to the direction of variables has the following benefits:

• Provides a simple and consiste nt way to determine whether an element is

active or passive. Energy is one of the most important characteristics to be determined during simulation. If the variables direction, or sign, is determined as described above, their product (that is, the energy) is positive if the element consumes energy, and is negative if it provides energy to a system. This rule is followed throughout the Simscape software.

• Simplifies the model description. Symbol

ABis enough to specify

variable polarity for both the Across and the Through variables.

• Lets you apply the oriented graph theory to network analysis and design.

As an example of variables direction rules, let us consider the Ideal Force Source block. In this block, as in many other mechanical blocks, port C is associated with the source reference point (case), and port R is asso ciated with the rod.

1-7

1 Modeling Physical Systems

The block pos is positive to port R to a determined and C, respe at port C. T force and v

All the el dependin it. Activ etc.) mu that the (damper

Connec

Simsca

• Physi

or mec vari

• Phys

an in

if it acts in the direction from C to R, and causes bodies connected

he power generated by the source is computed as the product of

elocity, and is negative if the source provides energy to the system.

ements in a network are divided into active and passive elements,

g on whether they deliver energy to the sy stem or dissipate (or store) e elements (force and velocity sources, flow rate and pressure sources, st be oriented strictly in accordance with the line of action or function y are expected to perform in the system, while passive elements

s, resis tors, springs, pipeline s, etc.) can be oriented either way.

tor Ports and Connection Lines

pe blocks may have the following types of ports:

cal Conserving ports — Bidirectional ports (for example, hydraulic

hanical) that represent physical connections and relate physical

ables based on the Physical Network approach.

ical Signal ports — Unid irectional ports transferring signals that use

ternal Simscape engine for computations.

itive direction is from port C to port R. This means that the force

ccelerate in the positive direction. The relative velocity is

v = v

– vR,wherevR, vCare the absolute velocities at ports R

ctively, and it is negative if velocity at port R is greater than that

1-8

h of these ports and connections between them are described in greater

Eac

ail below.

det

Basic Principles of Modeling Physical Networks

Physical Conserving Ports

Simscape blocks have special Conserving ports . You connect Conserving ports with Physical connection lines, distinct from normal Simulink lines. Physical connection lines have no inherent directionality and represent the exchange of energy flows, according to the Physical Network approach.

• You can connect Conserving ports only to other Conserving ports of the

same type.

• The Physical connection lines that connect Conserving ports together

are bidirectional lines that carry physical variables (Across and Through variables, as described above) rather than signals. You cannot connect Physical lines to Simulink ports or to Physical Signal ports.

• Two directly connected Conserving ports must have the same values for all

their A cross variables (such as pressure or angular velocity).

• You can branch Physical connection lines. When you do so, components

directly connected with one another continue to share the same Across variables. Any Through variable (such as flow rate or torque) transferred along the Physical connection line is divided among the multiple components connected by the branches. How the Through variable is divided is determined by the system dynamics.

For each Through variable, the sum of all its values flowing into a branch point equals the sum of all its values flowing out.

Each type of Physical Conserving ports used in Simscape blocks uniquely represents a physical modeling domain. For a list of port types, along with the T hrough and Across variables associated with each type, see the table in “Variable Types” on p ag e 1-4.

Physical Signal Ports

Physical Signal ports carry signals between Simscape blocks. Y ou connect them with regular connection lines, similar to Simulink signal connections. Physical Signal ports are used in Simscape block diagrams instead of Simulink input and output ports to increase computation speed and avoid issues with algebra ic loops. Unlike Simulink signals, which are essentially unitless, physical signals can have units associated with them. Y ou specify the units along with the parameter values in the block dialogs, and Simscape

1-9

1 Modeling Physical Systems

software performs the necessary unit conversion operations when solving a physical network.

Simscape Foundation library contains, among other sublibraries, a Physical Signals block library. These blocks perform math operations and other functions on physical signals, and allow you to graphically implement equations inside the Physical Network.

Connecting Simscape Diagrams to Simulink Sources and Scopes

Simscape block diagrams use physical signals instead of regular Simulink signals. Therefore, you need converter blocks to connect Simscape diagrams to Simulink sources and scopes.

Use the Simulink-PS Converter block to connect Simulink sources or other Simulink blocks to the inputs of a Physical Network diagram. You can also use it to specify the input signal units. For more information, see the Simulink-PS Converter block reference page.

1-10

Use the PS-Simulink Converter block to connect outputs of a Physical Network diagram to Simulink scopes or other Simulink blocks. You can also use it to specify the desired output signal units. For more information, see the PS-Simulink Converter block reference page.

For an example of using converter blocks to connect Simscape diagrams to Simulink sources and scopes, see “Creating a Simple Model” on page 1-17.

Introducing the Simscape Block Libraries

In this section...

“Library Structure Overview” on page 1-11

“Using the Simulink Library Browser to Access the Block Libraries” on page 1-11

“Using the Command Prompt to Access the Block Libraries” on page 1-12

Library Structure Overview

Simscape block library contains two libraries that belong to the Simscape product:

• Foundatio n library — Contains basic hydraulic, pneumatic, mechanical,

electrical, magnetic, thermal, and physicalsignalblocks,organizedinto sublibraries according to technical discipline and function performed

• Utilities library — Contains essential environment blocks for creating

Physical Networks models

Introducing the Simscape™ Block Libraries

In addition, if you have installed any of the add-on products of the Physical Modeling family, you will see the corresponding libraries under the main Simscape library.

You can combine all these blocks in your Simscape diagrams to model physical systems. You can also use the basic Simulink blocks in your d iagrams, such as sources or scopes. See “Connecting Simscape Diagrams to Simulink Sources and S copes” on page 1-10 for more information on how to do this.

Using the Simulink Library Browser to Access the Block Libraries

You can access the blocks through the Simulink Library Browser. To display the Library Browser, click the Library Browser button in the toolbar of the MATLAB

desktop or Simulink model window:

1-11

1 Modeling Physical Systems

Alternatively, you can type simulink in the MATLAB Command Window. Then expand the Simscape entry in the contents tree.

1-12

For more information on using the Library Brow ser, see “Library Browser” in the Simulink Graphical User Interface documentation.

Using the Command Prompt to Access the Block Libraries

To access individual block libraries by using the command prompt:

• To open the Simscape library, type

Window.

• To open the main Simulink library (to access generic Simulink blocks), type

simulink in the MATLAB Command Window.

The Simscape library consists of two top-level libraries, Foundation and Utilities. In addition, if you have installed any of the add-on products of the Physical Modeling family, you will see the corresponding libraries under Simscape library, as shown in the following illustration. Some of these libraries contain second-level and thi rd-level sublibraries. You can expand

simscape in the MATLAB Command

Introducing the Simscape™ Block Libraries

each library by d ouble-clicking its icon. For more details on library hierarchy and descriptions of block categories, see “Block Reference”.

1-13

1 Modeling Physical Systems

Essential Steps to Building a Physical Model

Building Your Model

The ru les that you must follow when building a physical model with Simscape software are described in “Basic Principles of Modeling Physical Networks” on page 1-2. This section bri efly reviews these rules.

• Build your physical model by using a combination of blocks from the

Simscape Foundation and Utilities libraries. Simscape software lets you create a network representation of the system under design, based on the Physical Network approach. According to this approach, each system is represented as cons isting of functional elements that interact with e ach other by exchanging energy through their ports.

• Each Simscape diagram (or each topologically distinct physical network in

a diagram) must contain a Solver Configuration block from the Simscape Utilities library.

• If you have hydraulic elements in your model, the working fluid used in

the hydraulic circuit defines their globa l parameters, such as fluid density, fluid kinematic viscosity, fluid bulk modulus, and so on. To specify the working fluid, attach a Custom Hydraulic Fluid block (or a Hydraulic Fluid block, available with SimHydraulics block libraries) to each topologically distinct hydraulic circuit. If no Hydraulic Fluid block or Custom Hydraulic Fluid block is attached to a circuit, the hydraulic blocks use the default fluid, which is Skydrol LD-4 at 60°C and with a 0.005 ratio of entrapped air.

1-14

• If you have pneumatic elements in your model, default gas properties are

for dry air and ambient conditions of 101325 Pa and 20 degrees Celsius. Attach a Gas Properties block to each topologically distinct pneumatic circuit to change gas properties and ambient conditions.

• To connect regular Simulink blocks (such as sources or scopes) to your

physical network diagram, use the connector blocks, as described in “Using the Physical Signal Ports” on page 1-16.

• Use the incremental modeling approach. Start with a simple model, run

and troubleshoo t it, then add the desired special effects. For example, you can start developing your system by using the Resistive Tube block from the Foundation library, which accounts only for friction losses. At a later stage in development, you may want to account for fluid compressibility.

Essential Steps to Building a Physical Model

You can then replace it with a Hydraulic Pipeline block, available with SimHydraulics block libraries, or, depending on your application, even with a Segmented Pipeline block if you also need to account for fluid inertia. For all these different mathematical models, the element configuration (that is, the number and type of ports and the associated Through and Across variables) would remain the same, meaning that the Physical Network approach lets you substitute models of different levels of complexity without introducing any changes to the schematic.

Simscape blocks, in general, feature both Conserving ports Signal inports and outports

and Physical

Using the Conserving Ports

ThefollowingrulesapplytoConservingports:

• There are different types of Physical Conserving ports used in Simscape

block diagrams, such as hydraulic, pneumatic, electrical, magnetic, thermal, mechanical translational, and mechanical rotational. Each type has specific Through and Across variables associated with it. For more information, see “Variable Types” on page 1-4.

• You can connect Conserving ports only to other Conserving ports of the

same type.

• The Physical connection lines that connect Conserving ports together

• Two directly connected Conserving ports must have the same values for all

their Across variables (such as voltage or angular velocity).

• You can branch Physical connection lines. When you do so, components

directly connected with one another continue to share the same Across variables. Any Through variable (such as current or torque) transferred along the Physical connection line is divided among the multiple components connected by the branches. How the Through variable is divided is determined by the system dynamics.

For each Through variable, the sum of all its values flowing into a branch point equals the sum of all its values flowing out.

1-15

1 Modeling Physical Systems

Using the Physic

The following ru

• You can connect

regular connec connection li

• You can connec

converter blo outports to P to connect Ph

• Unlike Simu

can have uni the units al converter desired ou

For examp see the fo

llowing section, “Creating a Simple Model” on page 1-17.

les apply to Physical Signal ports:

Physical Signal ports to other Physical Signal ports with

tion lines, similar to Simulink signal connections. These

nes ca rry physical signals between Simscape block s.

t Physical Signal ports to Simulink ports through special cks. Use the Simulink-PS Converter block to connect Simulink hysical Signal inports. Use the PS-Simulink Converter block

ysical Signal outports to Simulink inports.

link signals, which a re essentially unitless, Physical Signals ts associated with them. Simscape block dialogs let you specify

ong with the parameter values, where appropriate. Use the

blocks to associate units with an input signal and to specify the

tput signal units.

les of applying these rules when creating an actual physical model,

al Signal Ports

1-16

Creating a Simple Model

In this section...

“Building a Simscape Diagram” on page 1-17

“Modifying Initial Settings” on page 1-25

“Running the Simulation” on page 1-26

“Adjusting the Parameters” on page 1-29

Building a Simscape Diagram

In this example, you are going to model a simple mechanical system and observe its behavior under various conditions. This tutorial illustrates the essential steps to building a physical model, described in the previous section, and makes you familiar with using the basic Simscape blocks.

The following schematic represents a simple model of a car suspension. It consists of a spring and damper connected to a body (represented as a mass), which is agitated b y a force. You can vary the model parameters, such as the stiffness of the spring, the mass of the body, or the force profile, and view the resulting changes to the velocity and position of the body.

Creating a Simple Model

1-17

1 Modeling Physical Systems

To create an equivalent Simscape diagram, follow these steps:

1-18

1 Open the Simscape and Simulink block libraries, as described in

“Introducing the Simscape Block Libraries” on page 1-11.

2 Create a

Browse File me memory

Note A promp comm Sims

3 Ope

Ele

4 Drag the M ass, Translational Spring, Translational Damper, and two

new model. To do this, click the New button on the Library

r’s too lbar (Windows only) or choose New from the library window’s

nu and select Model. The software creates an empty model in

and displays it in a new model editor window.

lternately, you can type

ssc_new at the M ATLA B Command

t, to create a new model prepopulated with certain required and

only-used blocks. For more information, see “Creating a New

cape Model”.

n the Simscape > Foundation Library > Mechanical > Translational

ments library.

Mechanical Translational Reference blocks into the model window.

Creating a Simple Model

5 Orient the blocks as show n in the following illustration. To rotate a block,

select it and press Ctrl+R.

6 Connect the Translational Spring, Translational Damper, and Mass blocks

to one of the Mechanical Translational Reference blocks as shown in the next illustration.

1-19

1 Modeling Physical Systems

1-20

7 To add the representation of the f orce acting on the mass, open the

Simscape > Foundation Library > Mechanical > Mechanical Sources library and add the Ideal Force Source block to your diagram.

To reflect the correct direction of the force shown in the original schematic, flip the blo ck by selecting Format > Flip Block > Up-Down from the top menu bar of the model window. Connect the block’s port C (for “case”) to the second Mechanical Translational Reference block, and its port R (for “rod”) to the Mass block, as shown below.

Creating a Simple Model

8 Add the sensor to measure sp eed a nd position of the mass. Place the Ideal

Translational Motion S en so r block from the Mechanical Sensors library into your diagram and co nn ect it as shown below.

1-21

1 Modeling Physical Systems

1-22

9 Now you need to add the sources and scopes. They are found in the regular

Simulink libraries. Open the Simulink > Sources library and copy the Signal Builder block into the model. Then open the Simulink > Sinks library and copy two Scope blocks. Rename one of the Scope blocks to

Velocity and the other to Position.

Creating a Simple Model

10 Every time you connect a Simulink source or scope to a Simscape diagram,

you have to use an appropriate converter block, to convert Simulink signals into p h ysical signals and vice versa. Open the Simscape > Utilities library and copy a Simulink-PS Converter block and two PS-Simulink Converter blocks into the model. Connect the blo cks as shown below.

1-23

1 Modeling Physical Systems

1-24

11 Each topologically distinct physical network in a diagram requires

exactly one Solver Configuration block, found in the Simscape > Utilities library. Copy this block into your model and connect it to the circuit by creating a branching point and connecting it to the only port of the Solver Configuration block. Your diagram now should look like this.

Creating a Simple Model

12 Your block diagram is now complete. Save it as simple_mech1.mdl.

Modifying Initial Settings

After you have put together a block diagram of your model, as described in the previous section, you need to select a solver and provide the correct values for configuration param eters.

To prepare for simulating the model, follow these steps:

1 Select a Simulink solver. On the top menu bar of the model window,

select Simulation > Configuration Parameters. The Configuration Parameters dialog box o pens, showing the Solver node.

Under Solver options,setSolver to size to

0.2.

ode15s (Stiff/NDF) and Max step

1-25

1 Modeling Physical Systems

Also note that Simulation time is specified to be between 0 and 10 seconds. You can adjust this setting later, if needed.

1-26

Click OK to close the Configuration Parameters dialog box.

2 Save the model.

Running the Simulation

After you’ve put together a block diagram and specified the initial settings for your model, you can run the simulation.

1 The input signal for the force is provided by the Signal Builder block. The

signal profile is shown in the illustrat ion below. It starts with a value of 0, then at 4 seconds there is a step change to 1, and then it changes back to 0 at 6 seconds. This is the default profile.

Creating a Simple Model

The Velo output scopes

2 To run the simulation, click in the model window toolbar. The Simscape

city scope outputs the mass velocity, and the Position scope

s the mass displacement as a function of time. Double-click both

to open them.

solver evaluates the model, calculates the initial conditions, and runs the simulation. For a detailed description of this process, see “How Sim scape Simulation Works” on page 2-2. Completion of this step may take a few seconds. The message in the bottom-left corner of the model window provides the status update.

3 Once the simulation starts running, the Velocity and Position scope

windows display the simulation results, as shown in the next illustration.

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1 Modeling Physical Systems

1-28

In the beginning, the mass is at rest. Then at 4 seconds, as the input signal changes abruptly, the mass velocity spikes in the positive direction and gradually returns to zero. The mass position at the same time changes more gradually, on account of inertia and damping, and stays at the new value as long as the force is acting upon it. At 6 seconds, when the input signal changes back to zero, the velocity gets a mirror spike, and the mass gradually returns to its initial position.

Creating a Simple Model

You can now adjust various inputs and block parameters and see their effect on the mass velocity and displacement.

Adjusting the Parameters

After running the initial simulation, you can experiment with adjusting various inputs and block parameters.

Try the following adjustments:

1 Change the force profile.

2 Change the model parameters.

3 Change the mass position output units.

Changing the Force Profile

This example shows how a change in the input signal affects the force profile, and therefore the mass displacement.

1 Double-click the Signal Builder block to open it.

2 Click the first vertical segment of the signal profile and drag it from 4 to 2

seconds, as shown below. Close the block dialog.

1-29

1 Modeling Physical Systems

1-30

3 Run the s

ration.

illust

imulation. The simulation results are shown in the following

Creating a Simple Model

Changing the Model Parameters

In our model, the force acts on a mass against a translational spring and damper, connected in parallel. This example shows how changes in the spring stiffness a nd damper viscosity affect the mass displacement.

1 Double-click the Translational Spring block. Set its Spring rate to 2000

N/m

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1 Modeling Physical Systems

2 Run the simulation. The increase in spring stiffness results in smaller

amplitude of mass displacement, as shown in the following illustration.

3 Next, double-click the Translational Damper block. Set its Damping

coefficient to

500 N/(m/s).

1-32

4 Run the simulation. Because of the increase in viscosity, the mass is slower

both in reaching its maximum displacement and in returning to the initial position, as shown in the following illustration.

Creating a Simple Model

Changing the Mass Position Output Units

In our model, we have used the PS-Simulink Converter block in its default parameter configuration, which does not specify units. Therefore, the

Position scope outputs the mass displacement in the default length units,

that is, in meters. This example shows how to change the output units for the mass displacement to millimeters.

1 Double-click the PS-Simulink Converter block. Type mm in the Output

signal unit combo box and click OK.

2 Run the

ope axes. The mass displacement is now output in millimeters, as

the sc shown

simulation. In the

in the following illustration.

Position scope window, click to autoscale

1-33

1 Modeling Physical Systems

1-34

Modeling Best Practices

In this section...

“Grounding Rules” on page 1-35

“Avoiding Numerical Simulation Issues” on page 1-38

Grounding Rules

This section contains guidelines for using domain-specific ref erence blocks (such as Electrical Reference, Mechanical Translational Reference, and so on) in Simscape diagrams, along with examples of correct and incorrect configurations.

Add reference blocks to your models according to the following rules:

• “Each Domain Requires at Least One Reference Block” on page 1-35

• “Each Circuit Requires at Least One Reference Block” on page 1-36

Modeling Best Practices

• “Multiple Connections to the Domain Reference Are Allowed Within a

Circuit” on page 1-37

Each Domain Requires at Least One Reference Block

Within a physical network, each domain must contain at least one reference block of the appropriate type. For example, the electromechanical model shown in the following diagram has both Electrical Reference and Rotational Reference blocks attached to the appropriate circuits.

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1 Modeling Physical Systems

Each Circuit Requires at Least One Reference Block

Each topologically distinct circuit within a domain must contain at least one reference block. Some blocks, such as an Ideal Transformer, interface two parts of the network but do not convey information about signal levels relative to the reference block. In the following diagram , there are two separate electrical circuits, and the Electrical Reference blocks are required on both sides of the Ideal Transformer block.

1-36

Modeling Best Practices

The next diagram would produce an error because it is lacking an electrical reference in the circuit of the secondary winding.

The following diagram, however, will not produce an error because the resistor defines the output voltage relative to the ground reference.

Multiple Connections to the Domain Reference Are Allowed Within a Circuit

More that one reference block m ay be used within a circuit to define multiple connections to the domain reference:

1-37

1 Modeling Physical Systems

• Electrical conserving ports of all the blocks that are directly connected to

• All translational ports that are rigidly clamped to the frame (ground) must

• All rotational ports that are rigidly clamped to the frame (ground) must be

• Hydraulic conserving ports of all the blocks that are referenced to

For example, the following diagram correctly indicates two separate connections to an electrical ground.

ground must be connected to an Electrical Reference block.

be connected to a Mechanical Translational Reference block.

connected to a Mechanical Rotational Reference block.

atmosphere (for example, suction ports of hydraulic pum ps, or return ports of valves, cylinders, pipelines, if they are considered directly connected to atmosphere) must be connected to a Hydraulic Reference block.

1-38

Avoiding Numerical Simulation Issues

Certain configurations of physical modeling blocks can cause numerical difficulties or slow down your simulation. When this happens, Simscape solver issues a warning in the MATLAB workspace and, if it fails to initialize, a Simscape error.

Modeling Best Practices

In e lectrical circuits, common examples that can cause this behavior include voltage sources connected in parallel with capacitors, inductors connected in series with current sources, voltage sources connected in parallel, and current sources connected in series. Often, the cause of the numerical difficulty is immediately apparent. For example, tw o voltage sources in parallel must have identical voltage values; otherwise, the ports connecting them would not be physical conserving ports. In practical circuits, topologies such as parallel voltage sources are possible, and small difference in their instantaneous voltages is possible due to parasitic series resistance.

Note Mathematically, these topologies result in Index-2 differential algebraic equations (DAEs). Th e ir solu tion requires two differentiations of the

constraint equations and, as such, it is numerically better to avoid these component topologies where possible.

Therearetwoapproachestoresolvingthesedifficulties.Thefirstistochange the circuit to an equivalent simpler one. In the example of two parallel voltage sources, one source can be simply deleted. The same applies to two series current sources, the deleted one being replaced by a short circuit. For some circuit topologies, however, it is not possibletofindanequivalentsimplerone that resolves the problem, and the second approach is needed.

The second approach is to inclu de small parasitic resistances in the component. In the Simscape Foundation library, the Capacitor and Inductor blocks include such parasitic terms, so that you can connect capacitances in parallel with voltage sources and inductors in series with current sources. If your circuit does not have any such topologies, then you can change the default parasitic terms to zero. Note that other blocks do not contain these parasitic terms, for example, the Mutual Inductor block. Therefore, if you wanted to connect a mutual inductor primary in series with a current source, you would need to introduce your own parasitic conductance acros s the primary winding.

Example of Using a Parasitic Resistance to Avoid Numerical Simulation Issues

The following diagram models a differentiator that might be used as part of a Proportional-Integral-Derivative (PID ) controller. You can open this model by typing

ssc_differentiator in the MATLAB Command Window.

1-39

1 Modeling Physical Systems

Simulate the model, a nd you will see thattheoutputisminusthederivative of the input sinusoid.

1-40

Now open the capacitor C block dialog, and set the series resistance to zero. The model now runs very slowly, and issues a warning:

Warning: problems possible for transient initialization, as well as stepsize control

for transient solve, due to equations of one or more components:

'ssc_differentiator/2V pk-k, 1KHz'

Modeling Best Practices

'ssc_differentiator/Op-Amp'

'ssc_differentiator/C'

The cause of the warning is that the circuit effectively connects the voltage source in parallel with the capacitor. This is because an ideal op-amp satisfies

V+ = V- ,whereV+ and V- are the noninverting and inverting inputs,

respectively. This is an example where it is not possible to replace the circuit with an equivalent simpler one, and a parasitic small resistance has to be introduced.

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1 Modeling Physical Systems

Modeling Pneumatic Systems

In this section...

“Intended Applications” on page 1-42

“Assumptions and Limitations” on page 1-42

“Fundamental Equations” on page 1-43

“Network Variables” on page 1-44

“Connection Constraints” on page 1-45

“References” on page 1-45

Intended Applications

The Foundation library contains basic pneumatic elements, such as orifices, chambers, and pneumatic-mechanical converters, as well as pneumatic sensors and sources. Use these blocks to model p neumatic systems, for applications such as:

1-42

• Factory automation — basic pneumatic linear/rotational actuators, valves

(variable orifices), and air supply

• Robotics — robotic arms and haptic interfaces

• Gaseous transportation systems and pipelines

You can also use these blocks to model dry air and low-pressure flows, for example, for HVAC applications.

Assumptions and Limitations

Pneumatic block models are based on the following assumptions:

• Working fluid is an ideal gas satisfying the ideal gas law.

• Specific heats at constant pressure and constant volume, c

constant.

and cv,are

Modeling Pneumatic Systems

• Processes are adiabatic, that is, there is no heat transfer between

components and the environment (except for components with a separate thermal port).

• Gravitational effects can be neglected, that is, underlying equations contain

no head pressures due to gravity.

Fundamental Equations

The energy balance for a control volume [1] is

⎛

⎜ ⎜

⎝

⎞

⎞ ⎟

⎟ ⎠

⎛

⎟

⎜

−++

∑

⎟ ⎠

⎜ ⎝

⎜

⎜ ⎝

⎞

⎟

⎠

=−+ ++

QW mhvgz m h

cv cv i i

∑

⎛ ⎜

⎜

⎝

where

i,ho

i,vo

i,zo

i,mo

The

tes that the rate of energy increase or decrease within the control volume

sta

als the difference between the rates of energy transfer in and out across the

equ

ndary. The mechanisms of energy transfer are heat and work, as for closed

bou

stems, and the energy that accompanies the mass entering and exiting.

Control volume total energy

Heat energy per second added to the gas through the boundary

Mechanical w ork per second performed by the gas

Inlet and outlet enthalpies

Gas inlet and outlet velocities

Acceleration due to gravity

Elevations at inlet and outlet ports

Mass flow rates in and out of the control volume

equation is an accounting balance for the energy of the control volume. It

eumatic block models make several simplifying assumptions, as described

eviously.

1-43

1 Modeling Physical Systems

The ideal gas law relates pressure, density, and temperature:

where

pRT=ρ

Also, the specific enthalpies for an ideal gas at temperature T and constant pressure and constant volume are given by:

hcT

The pneumatic components also use the mass continuity equation:

where ρ is the density of the gas within the component. For components with no internal mass of gas, the equation simplifies to:

Gm m

Absolute pressure

Gas density

Specific gas constant

Absolute gas temperature

=−

()

dt V

1-44

where G isthemassflowratethroughthecomponent.

For specific equations used in each block, see the block reference pages.

Network Variables

The Across variables are pressure and temperature, and the Through variables are mass flow rate and heat flow. Note that these choices result in

Modeling Pneumatic Systems

a pseudo-bond graph, because the product of pressure and mass flow rate is not power.

Connection Constraints

Every node in a pneumatic network must have a defined temperature as well as pressure. This rule places some constraints on how you connect the pneumatic elements. In effect, every node should have a volume of fluid associated with it. When the ideal gas law is applied, this volume of fluid determines the relationship between temperature and pressure. Some elements already have a volume of fluid associated with them, and therefore having just one of these components connected to a node satisfies this condition. Such blocks include Constant Volume Pneumatic Chamber, Pneumatic Piston Chamber, Rotary Pneumatic Piston Chamber, and Pneumatic Atmospheric Reference.

Anexceptiontotheaboverule(thateverynodemusthaveavolumeoffluid associated with it) occurs when two nodes are connected by a component for which the heat equation says that the temperatures are equal. In this case, just one of the nodes needs to be connected to a component with associated volume of fluid. Such components include the pressure and flow rate sources.

For models that represent an actual pneumatic network, these constraints should have no impact. For example, connecting two orifices in series makes no physical sense because the underlying assumption of the orifice equation is that gas is discharged into a volume of fluid. Therefore, modeling actual physical systems should automatically satisfy these constraints.

References

[1] Moran M.J. and Shapiro H.N. Fundamentals of Engineering Thermodynamics. Second edition. New York: John Wiley & Sons, 1992.

1-45

1 Modeling Physical Systems

1-46

Simulating Physical Models

• “How Simscape Simulation Works” on page 2-2

• “Working with Solvers” on page 2-8

• “Troubleshooting Simulation Errors” on page 2-13

• “Finding an Operating Point” on page 2-22

• “Linearizing at an Operating Point” on page 2-28

• “Generating Code” on page 2-35

• “Limitations” on page 2-39

2 Simulating Physical Models

How Simscape Simulation Works

In this section...

“Simscape Simulation Phases” on page 2-2

“Model Validation” on page 2-4

“Network Construction” on page 2-4

“Equation Construction” on page 2-5

“Computing Initial Conditions” on page 2-5

“Performing Transient Initialization” on page 2-6

“Transient Solve” on page 2-6

Simscape Simulation Phases

Simscape software gives you multiple ways to simulate and analyze physical systems in the Simulink environment. Running a physical model simulation is similar to running a simulation of any other Simulink model. It entails setting various simulation options, starting the simulation, and viewing the simulation results. See the Using Simulink documentation for a gene ral discussion of these topics. This chapter focuses on aspects of simulation specific to Simscape and Sim Hydraulics models. Refer to the SimMechanics™ and SimDriveline™ documentation for specifics of simu l ating and analyzing SimMechanics and SimDriveline models.

2-2

You might find this brief overview helpful for constructing models and understanding errors.

Simscape simulation seq uence is shown in the following flow chart.

How Simscape™ Simulation Works

It consists of the following major phases:

1 “Model Validation” on page 2-4

2 “Network Construction” on page 2-4

3 “Equation Construction” on page 2-5

4 “Computing Initial Conditions” on page 2-5

2-3

2 Simulating Physical Models

Model Validation

Simscape solver first validates the m odel configuration and checks your data entries from the block dialogs. In particular:

• Each topologically distinct physical network in a diagram requires exactly

• If your model contains hydraulic elements, each topologically distinct

5 “Performing Transient Initialization” on page 2-6

6 “Transient Solve” on page 2-6

one Solver Configuration block.

hydraulic circuit in a diagram requires a Custom Hydraulic Fluid block (or Hydraulic Fl u id block, available with S imHydraulics block libraries) to be connected to it. These blocks define the fluid properties that act as global parameters for all the blocks connected to the hydraulic circuit. If no hydraulic fluid block is attached to a loop, the hydraulic blocks in this loop use the default fluid. However, more than one hydraulic fluid block in a loop generates an error.

2-4

Similarly, if your model contains pneumatic elements, default gas properties fo r a pne umatic netw ork are for dry air and ambient conditions of 101325 Pa and 20 degrees Celsius. Attaching a Gas Properties block to a pneumatic circuit lets you change gas properties and ambient conditions for all the blocks connected to the circuit. However, more than one Gas Properties block in a pneumatic circuit generates an error.

• Signal units specified in a Simulink-PS Converter block must match

the input type expected by the Simscape block connected to it. For example, when you provide the input signal for an Ideal Angular Velocity Source block, specify angular velocity units, such as Simulink-PS Converter block, or leave it unitle ss. Similarly, units specified in a PS-Simulink Converter block must match the type of physical signal provided by the Simscape block outport.

rad/s or rpm,inthe

Network Construction

After validating the model, Simscape solver constructs the physical network based on the following principles:

• Two directly connected Conserving ports have the sam e values for all their

Across variables (such as voltage or angular velocity).

How Simscape™ Simulation Works

• Any Through variable (such as current or torque) transferred along

the Physical connection line is divided among the multiple components connected by the branches. For each Through variable, the sum of all its values flowing into a branch point equals the sum of all its values flowing out.

Equation Construction

Based on the network configuration, the parameter value s provided in the block dialogs, and the global parameters defined by the fluid properties, if applicable, Simscape solver constructs the system of equations for the model.

These equations contain variables of the following types:

• Dynamic —Timederivativeofthisvariableappearsinequations.Dynamic

variables are the independent s tates for simulation.

• Algebraic — Time d erivative of this variable does not appear in equations.

Algebraic variables a re always dependent (on dynamic variables, other algebraic variables, or inputs).

Computing Initial Conditions

Simscape solver computes the initial conditions only once, in the beginning of simulation (t=0).

Initial conditions are computed by se tting all dynamic variables to 0, except those corresponding to blocks that have an initial condition field in their block dialogs, and solving for all the system variables. The blocks with initial conditions have their dynamic variables set according to the user-provided value in the block dialog. In itial conditions can only be set on dynamic variables, because these are the independent states for simulation. For example, the Translational Spring block has the Initial deformation parameter, so the corresponding spring position state is set to the initial offset specified in the block dialog. Refer to the block reference documentatio n to find which blocks have initial con ditions specified through their dialogs.

It is required that the initial conditions for dependent dynamic states be set consistently. For example, the initial voltages on two parallel capacitors must be equal. When the solver detects dependent dynamic variables, it performs

2-5

2 Simulating Physical Models

a check and issues an error if the initial conditions on dynamic states are not set consistently.

This concludes the initial conditions computation when the Start simulation from steady state check box in the Solver block dialog box is not selected (this is the default).

When this box is selected, the solver attempts to find the steady state that would result if the inputs to the system were held constant for a sufficiently largetime,startingfromtheinitialstateobtainedfromtheinitialconditions computation, described previously. Although the solver tries to find the particular steady state resulting from the given initial conditions, it is not guaranteed to do so. All that is guaranteed is that if the steady-state solve succeeds, the state found is a steady state (within tolerance). Steady state means that the system variables are no longer changing with time. Simulation then starts from this steady state.

Note If the simulation fails at or near the start time when you use the Start simulation from steady state option, consider clearing the check box and

simulating with the plain initial conditions computation only.

2-6

Performing Transient Initialization

After computing the initial conditions, or after a subsequent event (such as a discontinuity resulting, for example, from a valve opening, or a hard stop hitting the stop), Simscape solver performs transient initialization. This is done by fixing all dynamic variables and solving for algebraic variables and derivatives of dynamic va riables. The goal of transient initialization is to provide a consistent set of initial conditions for the next transient solve phase.

Transient Solve

Finally, Simscape solver performs transient solve of the system of equations. In transient solve, continuous differential equations are integrated in time to compute all the variables as a function of time.

Simscape solver continues to perform the simulation according to the results of the transient solve until it encounters an event, such as a zero crossing or

How Simscape™ Simulation Works

discontinuity. The event may be within the physical network or elsewhere in the Simulink mo de l. If an event is encountered, Simscape solver returns to the phase of transient initialization, and then back to transient solve. This cycle continues until the end of simulation.

2-7

2 Simulating Physical Models

Working with Solvers

In this section...

“Selecting a Solver” on page 2-8

“Input Filtering” on page 2-10

Selecting a Solver

It is possible to choose any variable-step or fixed-step solver for models containing Simscape blocks. However, implicit solvers, such as ode14x, ode23t, and ode15s, are a better choice for a typical model. In particular, for stiff systems, implicit solvers typically take many fewer timesteps than explicit solvers, such as ode45, ode113, and ode1.

When you first create a m odel, the default Simulink solver is ode45. To select a different solver, follow a procedure similar to th at in “Modifying Initial Settings” on page 1-25.

2-8

If you do not modify the default solver and your system is stiff, your performancemaynotbeoptimal. Toalert you to a potential issue, the system issues a warning when you use an explicit solver in a model containing Simscape blocks. You can turn off this default warning or changed it to an error for a particular m odel, by following these steps:

1 From the top menu bar in the model window, select Simulation >

Configuration Parameters. The Configuration Parameters dialog box

opens.

2 In the left pane of the Configuration Parameters dialog box, select

Simscape.

Working with Solvers

3 Select the desired option from the Explicit solver used in model

containing Physical Networks blocks drop-down list:

•

warning — Makes the system issue a warning upon simulation if the

model uses an explicit solver. This is the default option, design ed to alert you to a potential issue if you use the default solver.

•

error — Makes the system issue an error upon simulation if the model

uses an explicit solver. If your model is stiff, and the use of explicit solvers undesirable, you may choose to select this option to avoid troubleshooting errors in the future.

•

none — Turns off issuing a warning or error upon simulation with

explicit solver. For models that are not stiff, explicit solvers can be effective, often taking fewer timesteps than implicit solvers. If you work with such models and use expli c it solvers, select this option to tu rn off the warning upon simulation.

2-9

2 Simulating Physical Models

Input Filtering

If you use an explicit solver, you may need to provide time derivatives of some of the input signals. By default, needed input derivatives are provided by filtering the input through a low-pass filter. The derivative of the filtered input can then be computed by the Physical Networks simulation engine.

You can control the way you provide time derivatives for each input signal by configuring the Simulink-PS Converter block connected to it:

4 Click OK.

1 Double-click the Simulink-PS Converter block to open its dialog box.

2 Click the Derivatives tab.

2-10

Working with Solvers

3 To avoid filtering the input signal, set Input derivatives parameter to

First derivative of input user-provided.

When you select this option, a second Simulink input port appears on the Simulink-PS Conve rter block, to let you connect the signal providing input derivatives. Input filtering is then turned off.

4 If you cannot provide the first derivative of the input signal as an additional

input signal to the Simulink-PS Converter block, leave the Input derivatives parameter set to

No user-input provided derivatives.In

this case, however, it is important to set the appropriate Input filtering time constant parametervalueforyourmodel.

The filter time constant controls the filtering of the input signal. Th e filtered input follows the true input but is sm oothed, with a lag on the order ofthetimeconstantchosen. Youshouldsetthetimeconstanttoavalue no larger than the smallest time interval of interest in the system. The trade-off in choosing a very small time constant is that the filtered input signal will be closer to the true input signal, at the cost of increasing the stiffness of the system and slowing down the simulation.

Because input filtering can appreciably change the input signal and drastically affect simulation results if the time constant is too large, a warning is issued when input filtering is u sed. Th e warning indicates w hich Simulink-PS Conve rter blocks have their input signals filtered. You can turn off this warning (or change it to an error) by changing the preferences on the Simscape pane of the Configuration Parameters dialog box:

1 From the top menu bar in the model window, select Simulation >

Configuration Parameters. The Configuration Parameters dialog box

opens.

2 In the left pane of the Configuration Parameters dialog box, select

Simscape.

2-11

2 Simulating Physical Models

2-12

3 Select the desired option from the Input filtering used in model

containing Physical Networks blocks drop-down list:

•

warning — Makes the system issue a warning upon simulation if the

model uses input filtering. The warning contains a list of Simulink-PS Converter blocks that use input filtering. This is the default option.

•

error — Makes the system issue an error upon simulation if the model

uses input filtering. If you select this option and use an explicit solver, youhavetoprovidefirstderivativeoftheinputsignalasanadditional input signal to each Simulink-PS Converter block. For details, see the Simulink-PS Converter block reference page.

•

none — Turns off issuing a warning or error upon simulation when the

model uses input filtering.

4 Click OK.

Troubleshooting Simulation Errors

In this section...

“Troubleshooting Tips and Techniques” on page 2-13

“System Configuration Errors” on page 2-14

“Numerical Simulation Issues” on page 2-17

“Initial Conditions Solve Failure” on page 2-19

“Transient Simulation Issues” on page 2-20

Troubleshooting Tips and Techniques

Simscape simulations can stop before completion with one or more error messages. This section discusses generic error types and error-fixing strategies. You might find the previous s ection, “How Simscape Simulation Works” on page 2-2, useful for identifying and tracing errors.

Troubleshooting Simulation E rrors

If a simulation failed:

• Review the model configuration. If your error message contains a list of

blocks, look at these blocks first. Also look for:

- Wrong connections — Verify that the model makes sense as a physical

system. For example, look for actuators connected against each other, so that they try to move in opposite directions, or incorrect connections to re fere nce nodes that prevent movement. In electrical circuits, verify polarity and connections to ground.

- Wrong units — Simscape unit manager offers great flexibility in using

physical units. However, you must exercise care in specifying the correct units, especially in the Simulink-PS Converter and PS-Simulink Converter blocks. Start analyzing the circuit by opening all the converter blocks and checking the correctness of specified units.

• Try to simplify the circuit. Unnecessary circuit complexity is the most

common cause of simulation errors.

• Break the system into subsystems and test e very unit until you are positive

that the unit behaves as expected.

2-13

2 Simulating Physical Models

• Build the system by gradually increasing its complexity.

The MathWorks recommends that you build, simulate, and test your model incrementally. Start with an idealized, simplified model of your system, simulate it, verify that it works the way you expected. Then incrementally make your model more realistic, factoring in effects such as friction loss, motor shaft compliance, hard stops , and the other things that describe real-world phenomena. Simulate and test your model at every incremental step. Use subsystems to capture the model hierarchy, and simulate and test your subsystems separately before testing the whole model configuratio n. This approach helps you keep your models well organized and makes it easier to troubleshoot them.

System Configuration Errors

• “Missing Solver ConfigurationBlock”onpage2-14

• “Extra Fluid Block or Gas Properties Block” on page 2-14

• “Missing Reference Block” on page 2-15

2-14

• “Basic Errors in Physical System Representation” on page 2-15

Missing Solver Configuration Block

Each topologically distinct Simscape block diagram requires exactly one Solver Configuration block to be connected to it. The Solver Con f ig ura t ion block specifies the global environment information and provides parameters for the solver that your model needs before you can begin simulation.

If you get an error message about a missing Solver Configuration block, open the Simscape Utilities library and add the Solver Configuration block anywhere on the circuit.

Extra Fluid Block or Gas Properties Block

If your model contains hydraulic elements, each topologically distinct hydraulic circuit in a diagram requires a Custom Hydraulic Fluid block (or Hydraulic Fluid block, available with SimHyd ra ul ics block libraries) to be connected to it. These blocks define the fluid properties that act as global param eters for all the blocks connected to the hydraulic circuit. If no

Troubleshooting Simulation E rrors

hydraulic fluid block is attached to a loop, the hydraulic blocks in this loop use the default fluid. However, more than one hydraulic fluid block in a loop generates an error.

Similarly, more than one Gas Properties block in a pneumatic circuit generates an error.

If you get an error message about too many domain-specific global parameter blocks attached to the network, look for an extra Hydraulic Fluid block, Custom Hydraulic Fluid block, or Gas Properties block and remove it.

Missing Reference Block

Simscape libraries contain domain-specific reference blocks, which represent reference points for the conserving ports of the appropriate type. For example, each topologically distinct electrical circuit must contain at least one Electrical Reference block, which represents connection to ground. Similarly, hydraulic conserving ports of all the blocks that are referenced to atmosphere (for example, suction ports of hydraulic pumps, or return ports o f valves, cylinders, pipelines, if they are considered directly connected to atmosphere) must be connected to a Hydraulic Reference block, which represents connection to atmospheric pressure. Mechanical translational ports that are rigidly clamped to the frame (ground) must be connected to a Mechanical Translational Reference block, and so on.

If you get an error message about a missing reference block, or node, check your system configuration and add the appropriate reference block based on the rules described above. For more information and examples of best modeling practices, see “Grounding Rules” on page 1-35.

Basic Errors in Physical System Representation

Physical systems are represented in the Simscape modeling environment as Physical Networks according to the Kirchhoff’s generalized c i rcu it laws. Certain model configuratio ns violate these laws and are therefore illegal. There are tw o broad violations:

• Sources of domain-specific Across variable connected in parallel (for

example, voltage sources, hydraulic pressure sources, or velocity sources)

2-15

2 Simulating Physical Models

• Sources of domain-specific Through variable connected in series (for

These configurations are impossible in the real world and illegal theoretically. If your model contains such a configuration, upon simulation the solver issues an error followed by a lis t of blocks, as shown in the following ex ample.

Example. The model shown in the following illustration contains two Ideal Translational Velocity Sources co n nected in parallel. This produces two independent velocity loops, and the solver cannot construct a consistent system of equations for the circuit.

example, electric current sources, hydraulic flow rate sources, force or torque sources)

2-16

When you t ry to simulate the model, the solver issues the following error messages:

Nonlinear solver: failed to converge, residual norm too large.

Transient initialization, solving for consistent states and modes, failed to converge.

Warning: equations of one or more components may be dependent or inconsistent. This can

cause problems in transient initialization. Here is the set of components involved:

'vsloop_diagnostics_example/Ideal Translational Velocity Source1'

Troubleshooting Simulation E rrors

'vsloop_diagnostics_example/Ideal Translational Velocity Source'

Initial conditions solve failed to converge.

You can simplify the system by using a single Ideal Translational Velocity Source block, with its control signal supplied by the Sine Wave block. Add the constant value from the second source to the bias of the sine wave.

Numerical Simulation Issues

• “Dependent Dynamic States” on page 2-17

• “Parameter Discontinuities” on page 2-19

Numerical simulation issues can be either a result of certain circuit configurations or of parameter discontinuities.

Dependent Dynamic States

Certain circuit configurations can result in dependent dynamic states, or the so-called higher-index differential algebraic equations (DAEs). Simscape solver can handle dependencies among dynamic states that are linear in the states and independent of time and inputs to the system. For example, capacitors connected in parallel or inductors connected in series will not cause any problems. Other circuit configurations with dependent dynamic states, in certain cases, may slow down the simulationorleadtoanerrorwhenthe solver fails to initialize.

In e lectrical circuits, common examples that can cause this behavior include voltage sources connected in parallel with capacitors, inductors connected in series with current sources, and so on. To address this issue, the Capacitor and Inductor blocks include parasitic terms (parallel conductance and series resistance). For other blocks that do not contain these parasitic terms, you might need to introduce your own parasitic conductance or resistance into the circuit. For more information on best modeling practices, as well as for troubleshooting suggestions, see “Avoiding Numerical Simulation Issues” on page 1-38.

Examples in other domains include direct connections between a velocity source and a mass, a force source and a spring, a pressure source and a

2-17

2 Simulating Physical Models

hydraulic accumulator, or a flow rate source and a fluid inertia. If you encounter this error, try to either simplify th e circuit or include addition al blocks, such as spring-damper combinations or constant orifices, to avoid the direct connection that results in dependent states.

Example. The model shown in the following illustration contains an Ideal Translational Velocity Source directly connected to a Mass.

2-18

When you t ry to simulate the model, the solver issues the following error messages:

Nonlinear solver: failed to converge, residual norm too large.

Transient initialization, solving for consistent states and modes, failed to converge.

Warning: problems possible for transient initialization, as well as stepsize control

for transient solve, due to equations of one or more components:

'mech_model1/Mechanical Translational Reference'

'mech_model1//Ideal Translational Velocity Source'

'mech_model1/Mass'

Initial conditions solve failed to converge.

Troubleshooting Simulation E rrors

You can try adding a very stiff spring between the velocity source and the mass. To avoid the possibility of high-frequency oscillations introduced by the spring, connect it in parallel with a damper with a high damping coefficient.

Parameter Discontinuities

Nonline to nume issues “Trans

Initi

The in condi poss

• Syst

ar parameters, dependent on time or other variables, may also lead

rical simulation issues as a result of parameter discontinuity. These

usually manifest themselves a t the transient initialization stage (see

ient Simulation Issues” on page 2-20).

al Conditions Solve Failure

itial conditions solve, which solves for all system variables (with initial

tions specified on some system variables), may fail. This has several

ible causes:

em configuration error. In this case, the Simulation Diagnostics

ow usually contains additional, more specific, error messages, such

wind

missing reference node, or a warning about the component equations,

as a

lowed by a list of components involved. See “System Configuration

fol

ors” on page 2-14 for more information.

Err

2-19

2 Simulating Physical Models

• Dependent dynamic state. In this case, the Simulation Diagnostics

• The constraint residual tolerance may be too tight to produce a consistent

If the Simulation Diagnostics window has other, more specific, error messages, address them first and try rerunning the simulation. See also “Troubleshooting Tips and Techniques” on page 2-13.

Transient Simulation Issues

• “Transient Initialization Not Converging” on page 2-20

• “Step-Size-Related Errors” on page 2-21

window also may contain additional, more specific, error m ess ages, such as a warning about the component equations, followed by a list of components involved. See “Dependent Dynamic States” on page 2-17 for more information.

solution to the algebraic constraints at the beginning of simulation. You can try to increase the Constraint Residual Tolerance parameter v a lue (that is, relax the tolerance) in the Solver Configuration block.

2-20

Transient initialization h appens at the beginning of simulation (after computing the initial conditions) or after a subsequent event, such as a discontinuity (for example, when a hardstophitsthestop). Itisperformed by fixing all dynamic variables and solving for algebraic variables and derivatives of dynamic va riables. The goal of transient initialization is to provide a consistent set of initial conditions for the next transient solve step.

Transient Initialization Not Converging

Error messages stating that transient initialization failed to converge, or that a set of consistent initial conditions could not be generated, indicate transient initialization issues. They can be a result of parameter discontinuity. Review your model to find the possible sources of discontinuity. See also “Troubleshooting Tips and Techniques” on page 2-13.

You can also try to decrease the Constraint Residual Tolerance parameter value (that is, tighten the tolerance) i n the Solver Configuration block.

Troubleshooting Simulation E rrors

Step-Size-Related Errors

A typical step-size-related erro r message may state that the system is unable to reduce the step size without violating the minimum step size for a certain number of consecutive times. This error message indicates numerical difficulties in solving the Differential Algebraic Equations (DAEs) for the model. This might be caused by dependent dynamic states (higher-index DAEs) or by the high stiffness of the system. You can try the following:

• Tighten the solver tolerance (decrease the Relative Tolerance parameter

value in the Configuration Parameters dialog box)

• Specify a value, other than

auto,fortheAbsolute Tolerance parameter

in the Configuration Parameters dialog box. Experiment with this parameter value.

• Tighten the residual tolerance (decrease the Constraint Residual

Tolerance parameter value in the Solver Configuration block)

• Increase the value of the Number of consecutive min step size

violations allowed parameter in the Configuration Parameters dialog box

(set it to a value greater than the number of consecutive step size violations given in the error message)

• Review the model configuration and try to simplify the circuit, or add small

parasitic terms to your circuit to avoid dependent dynamic states. For more information, see “Numerical Simulation Issues” on page 2-17.

2-21

2 Simulating Physical Models

Finding an Operating Point

In this section...

“What Is an Operating Point?” on page 2-22

“How to Find Operating Points” on page 2-23

“Finding Operating Points with Simscape, Simulink, and Related Products” on page 2-24

What Is an Operating Point?

An operating point of a sys tem is a dynamic configuration that satisfies design and use requirements called operating specifications. You can express such operating specifications as requirements on the system state x and inputs u. It is not always possible t o find a dynamic state that satisfies all operating conditions. Also, a system might have multiple operating points satisfying thesamerequirements.

2-22

Operating points are essential for designing and implementing system controllers. You can optimize a system at an operating point for performance, stability, safety, and reliability.

The most important and common type of operating point is a steady state, where some or all of the system dynamic variables are constant.

Using Operating Points for Linearization

An important motive for finding operating points is linearization,which determines the system response to small disturbances at an operating point. Linearization results influence the design of feedback controllers to govern dynamic behavior near the operating point. A full linearization analysis requires one or more system outputs, y , in addition to inputs.

See “Linearizing at an Operating Point” on page 2-28.

Example

A pilot flying an aircraft wants to find, for a given environment, a state of the aircraft engine and control surfaces that produces level, constant-velocity, and

Finding an Operating Point

constant-altitude flight relative to the ground. The requirements of "level," "constant velocity," "constant altitude," and "relative to the ground" constitute operating specifications. This operating point is a steady state of the aircraft velocity, altitude, and orientation in space.

How to Find Operating Points

You can provide predefined state and input vectors, x0and u0,tospecify an operating point. If you do not know an operating point in advance, you have two methods of identifying an operating point that satisfies operating specifications.

• “Time-Based Search” on page 2-23: Observing the actual or simulated

behavior of the system in time is more general, but less precise, and usually requires a trial-and-error p rocess to find a precise operating point.

• “State-Based Search” on page 2-23: If you know the system dynamics, you

can solve for steady states, at least in principle.

Time-Based Search

You can sometimes find operating points and steady states by trial and error while operating or simulating over some length of time and varying the system parameters, inputs, and initial conditions. In such a time-based approach, you isolate and study instants or intervals of time when a system satisfies the operating specifications. The system state and inputs under those conditions constitute the operating point, which you can also specify by an operating or simulation time.

State-Based Search

The alternative to trial-and-error searching for steady states is trimming. In this state-based approach, you bypass time-based simulation and find solutions for inputs, outputs, states, and state derivatives satisfying an operating specification. Trimming specifies inputs and part of a state and solves the system dynamics for the re st of the state. The resulting full state and input vectors, x

There is no general guarantee that such solutions, x specifications and inputs, u

and u0, constitute the operating point.

, exist for given operating

2-23

2 Simulating Physical Models

Checking Discrete System States

An operating point includes the state of discrete system variables that change in a discontinuous way. In general, you cannot find these states by small, continuous changes of system variables. Such states usually require systematic exploration of the discrete variables over the full range of their possible values.

Finding Operating Points with Simscape, Simulink, and Related Products

You have a number of ways to find an operating point in a Simscape model. You can impose operating specifications a nd isolate operating points using Simscape and Simulink features and, in some cases, with such related products as Simulink software. The full state vector of your model contains:

• Simulink components, which can be continuous or discrete.

• Simscape components, which are continuous.

Control Design™ and Control System Toolbox™

2-24

Tip Whichever m ethod that you choose to find an operating point, if you want to use it for linearization, you must save the operating point information in the form of a simulation time t or an operating point object.

,astatevectorx0,andaninputvectoru0,

Simulating in Time to Search for an Operating Point

One way to identify operating points is to simulate your model and inspect its state x and output y as a time series.

1 In your Simscape model, set up sensor outputs for whatever block outputs

you want to observe.

2 Connect Scope blocks, To Workspace blocks, or both, to your Simscape

block outputs to observe and record simulation behavior.

3 In the Data Import/Export pane of your model Configuration Parameters

settings, select the Time, States,andOutput check boxes to record this simulation information in your workspace.

Finding an Operating Point

Using the Simscape Steady-State Solver

Most commonly, the operating point that you want is a steady state. You have a precise method for identifying steady states with the Simscape steady-state solver, which allows you to isolate steady states more exactly than you can with ordinary simulation. It is particularly recommended for isolating steady states of a strongly nonlinear character. You can search for multiple steady states with the steady-state solver by varying the model inputs, parameters, and initial conditions.

TheSimscapesteady-statesolverinitializes the system and inputs first, then determines a steady state. In general, the system does not remain in this initial steady state x(t=0) = x inputs u change independently, and the system has to respond by changing its state x(t).

To implement the steady-state solver:

1 In each, some, or all of the physical networks in your Simscape model,

open the Solver Configuration block.

during simulation, because the system

2 In each block dialog box, select the Start simulation from steady state

check box.

3 In the model Configuration Parameters settings, on the Data

Import/Export pane, select the States check box to record the time series

of x values in your workspace.

If you also have input signals u in the model, you can capture those inputs by connecting To Workspace blocks to the input Simulink signal lines.

4 Close these dialog boxes and start simulation.

The first vector of values x(t=0) that you capture during simulation reflects the steady state x

that the Simscape solver identified.

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2 Simulating Physical Models

Using Simulink Control Design Techniques

Note The techniques described in this section require the Simulink Control

Design product. You must use the features of this product on the Simulink lines in your model, not directly on Simscape physical network lines or blocks.

The following methods are state-based, allowing you to impose operating specifications, and work well for simple to moderately complex Simscape models. The MathWorks™ does not recommend these methods for highly complex Simscape models.

To find operating points, use the where necessary. Create an operating specification object with then compute an operating point object with attempts to find an operating point that satisfies the operating specifications and reports on its success or failure. If the search is successful, returns state values satisfying the operating specifications.

You have several choices for operating specifications for the components of the state vector.

Assumed Operating Condition

Default

Nondefault Request any value you want independently for each

Nondefault

Operating Specification

Request that all state component derivatives be zero. This is a steady-state for the whole model, not just a Simscape network within the model.

state component.

Request that a particular state component derivative be zero. This is a steady-state condition for that state component.

operspec an d findop functions, customizing

operspec,

findop.Thefindop function

find_op

2-26

Finding an Operating Point

Additional Simulink Control Design Methods. Instead of the command line interface, you can use the associated graphical user interface, through the model menu bar: Tools > Control Design > Linear Analysis.Formore details on the use of operating point specification objects, related functions, and the graphical interface, see the Simulink Control Design documentation.

Using Sources to Find Operating Points Not Recommended

You can impose an operating specification on part of a Simscape model by inserting source blocks from the Simscape Foundation Library. These impose specified values of system variables in parts of the model. You can simulate and save the state vector.

However,youcannotobtainanoperatingpointfortheoriginalsystem (without the source blocks) by saving the state values from the model and then remo ving the source blocks. In general, the number, order, and identity of state components change after adding and removing Simscape blocks in a model.

Simulink trim Function Not Supported with Simscape Models

The Simulink trim function is not supported for models containing Simscape components.

2-27

2 Simulating Physical Models

Linearizing at an Operating Point

In this section...

“What Is Linearization?” on page 2-28

“How to Lin earize a Model” on page 2-30

“Linearizing a Model with Simscape, Simulink, and Related Products” on page 2-30

“References” on page 2-34

What Is Linearization?

Determining the response of a system to small perturbations at an operating point is a critical step in system and controller design. Once you find an operating point, you can linearize the model about that operating point to explore the response and stability of the system. To find an operating point in a Simscape model, see “Finding an Operating Point” on page 2-22.

2-28

Choosing a Good Operating Point for Linearization

Although steady-state and other operating points (state x0and inputs u0) might exist for your model, that is no guarantee that such operating points are suitable for linearization. The critical question is: how good is the l inearized approximation compared to the exact system dynamics?

• When perturbed slightly, a problematic operating point might exhibit

strong asymmetries, with strongly nonlinear behavior when perturbed in certain ways and smoother behavior in other ways.

• Small perturbations might change discrete states in a large, discontinuous

way that violates the linear approximation.

Operating points with a strongly nonlinear or discontinuous character are not suitable for linearization. You should analyze them in full simulation and perturb the system by varying its inputs, parameters, and initial conditions.

Linearizing at an Operating Point

Tip A reliable way to check for such an unsuitable operating point is to linearize a t several nearby operating points. If the results differ greatly, the operating point is strongly nonlinear.

What Is Linear Response?

Near an operating point, you can express the system state x, inputs u,and outputs y relative to that operating point in terms of x – x

. For convenience, shift the vectors by subtracting the operating point:

x – x

→ x,etc.

If the system dynamics does not explicitly depend on time and the operating point is a steady state, the system response to state and input perturbations near the steady state is approximately governed by a linear time-invariant (LTI) state space model:

dx/dt = A·x + B·u

, u – u0,andy –

y = C·x + D·u.

The matrices A, B, C, D have components and structures that are independent of the simulation time. A system is stable to changes in state at an operating point if the eigenvalues of A are negative.

If the operating point is not a steady state or the system dynamics depends explicitly on time, the linearized dynamics near the operating point is more complicated. The matrices A, B, C, D are not constant and depend on the simulation time t

, as well as the operating point x0and u0[1].

Tip While you can linearize a closed system with no inputs or outputs and obtain a nonzero A matrix, obtaining a nontrivial linearized input-output model requires at least one input component in u and one output component in y.

2-29

2 Simulating Physical Models

Example

A pilot is flying, or simulating, an aircraft in level, constant-velocity, and constant-altitude flight relative to the ground, with a known environment. A crucial question for the aircraft pilot and designers is: will the aircraft return to the steady state if perturbed from it by a disturbance, such as a wind gust — in other words, is this steady state stable? If the operating point is unstable, the aircraft trajectory can diverge from the steady state, requiring human or automatic intervention to maintain steady flight.

How to Linearize a Model

Once you know an operating point, you have three practical methods for investigating the system response to small disturbances.

Full Simulation- or Operation-Based Perturbations

You can experiment with the system or a system simulation by making repeated, different, and slight changes to the system parameters, inputs, and initial conditions, while operating at a steady state. This method requires costly trial and error and generates uncontrolled and imprecise approximations.

2-30

Analytic Approximations to Known State Dynamics

If you know the system state dynamics and an operating point x0and u0in analytic form, you can apply standard approximation techniques to derive an analytic form for the A, B, C, D matrices.

Numerical Approximations to Known State Dynamics

If you have a controlled numerical approximation to your system state dynamics and operating point, you can apply standard computational techniques to generate numerical approximations to the A, B, C, D matrices.

Linearizing a Model with Simscape, Simulink, and Related Products

Use the following methods to create numerical linearized state-space models from a model containing Simscape components .

Linearizing at an Operating Point

Independent Versus Dependent States

An important difference from normal Simulink models is that the states in a physical network are not independent in general, because some states have dependencies on other states through constraints.

• The independent states are a subset of system variables and consist of

Simscape dynamic variables and Simulink states.

• The dependent states consist of Simscape algebraic variables and

dependent (constrained) dynamic variables.

For more information on Simscape dyna m ic and algebraic variables, see “How Simscape Simulation Works” on page 2-2.

The only components of the A, B, C , D matrices that can be nonzero are those corresponding to independent states.

• The

A matrix, of size n_states by n_states,isallzerosexceptfor

asubmatrixofsize

n_ind by n_ind,wheren_ind is the number of

independent states.

• The

B matrix, of size n_states by n_inputs,isallzerosexceptfora

submatrix of size

C matrix, of size n_outputs by n_states,isallzerosexceptfora

submatrix of size

D ma trix, of size n_outputs by n_inputs, can be nonzeros everywhere.

n_ind by n_inputs.

n_outputs by n_ind.

Obtaining the Independent Subset of States. A complete linearized solution uses only an independent subset of the system states. From the matrices A, B, C, D, you can obtain a minimal input-output linearized model with the

minreal and sminreal functions from Control System Toolbox

software.

Linearizing with the Simulink linmod and dlinmod Functions

The Simulink functions linmod and dlinmod provide a way of linearizing a Simscape model. There are several ways that you can use

dlinmod, and the linearization results differ depending on the method chosen.

To use these functions, you do not have to open the model, just have the model file on your MATLAB path.

linmod and

2-31

2 Simulating Physical Models

For more information about Simulink linearization, see “Linearizing Models” in the Simulink documentation.

Note If your model has continuous states, use linmod. (Continuous states are the Simscape default.) If your model has mixed continuous and discrete states, or purely discrete states, use

Linearizing a model with the local solver enabled (in the Solver Configuration block) is not supported.

Linearizing with Default State and Input. You can call linmod without specifying state or input. Enter

dlinmod.

linmod('modelname') at the command line.

With this form of

linmod, Simulink linearization solv es for consistent initial

conditions in the same way it does on the first step of any simulation. In particular, any initial conditions, such as initial offset from equilibrium for a spring, are set as if the simulation were starting from the initial time.

linmod allowsyoutochangethetimeofexternally specified signals (but not

the internal system dynamics) from the default. For this and more d etails, see the function reference page.

Linearizing with the Steady-State Solver at an Initial Steady State.

If you have previously used the Simscape steady-state solver to find an operating point, you can linearize at that operating point:

1 Open one or more Solver Configuration blocks in your model.

2 Select the Start simulation from steady state check box for the physical

networks that you wan t to linearize.

3 Close the Solver Configuration dialog boxes and save the modified model.

4 Enter linmod('modelname') at the command line.

linmod linearizes at the first step of simulation. In this case, the initial state

is also an operating point, a steady state.

2-32

Linearizing at an Operating Point

For more about setting up the steady-state solver, see the Solver Configuration block reference page. F or more details on its use, see “Using the Simscape Steady-State Solver” on page 2-25.

Linearizing with Specified State and Input — Ensuring Consistency of States. You can call

linmod('modelname',x0,u0) at the command line. The extra arguments

specify, respectively, the steady state x the simulation. When you specify a state to

linmod and specify state and input. Enter

and inputs u0for linearizing

linmod, ensure that it is

self-consistent, within solver tolerance.

With this form of

linmod, Simulink linearization does not solve for initial

conditions. Because not a ll states in the model have to be independent, it is possible, though erroneous, to provide

linmod with an inconsistent state to

linearize about.

If you specify a state that is not self-consistent (within solver tolerance), the Simscape solver issues a warning at the command line when you attempt linearization. The Simscape solver then a ttempts to make the specified

consistent by changing some of its components, possibly by large amounts.

Tip You most easily ensure a self-consistent state by taking the state from some simulated time. For example, by selecting the States check box on the Data Import/Export pane of the model Configuration Parameters dialog box, you can capture a time series of state values in a simulation run.

Linearizing with Simulink Linearization Blocks

You can generate linearized state-space models from your Simscape model by adding a Timed-Based Linearization or Trigger-Based Linearization block to the model and simulating. These blocks combine time-based simulation up to specified times or internal trigger points, with state-based linearization at those times or trigger points.

For complete details about these blocks, see their respective block reference pages.

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2 Simulating Physical Models

Linearizing with Simulink Control Design Software

Note The techniques described in this section require the Simulink Control

Design product. You must use the features of this product on the Simulink lines in your model, not directly on Simscape physical network lines or blocks.

The following methods require that you start with an operating point object saved from trimming the model to an operating specification, as explained in “Using Simulink

Control Design Techniques” on page 2-26.

To linearize a model with an operating point object, use the function, customizing where necessary. The resulting state-space object contains the matrices A, B, C, D.

Additional Simulink Control Design Methods. Instead of the command line interface, you can use the associated graphical user interface, through the model menu bar: Tools > Control Design > Linear Analysis.Formore details on linearization, operating points and state-space objects, related functions, and the graphical interface, see the Simulink Control Design documentation.

linearize

References

[1] Brogan, W. L., Modern Control Theory, 2nd Ed., Englewood Cliffs, New Jersey, Prentice-Hall, 1985.

[2] The MathWorks, Control System Toolbox User Guide, www.mathworks.com/access/helpdesk/help/toolbox/control/.

2-34

Generating Code

In this section...

“About Code Generation from Simscape Models” on page 2-35

“Related Simulink Code Generation Documentation” on page 2-35

“Reasons for Generating Code” on page 2-36

“Using Code-Related Products and Features” on page 2-36

“How Simscape Code Generation Differs from Simulink” on page 2-37

About Code Generation from Simscape Mo dels

You can use Real-Time Workshop®software to generate stand-alone C code from your Physical Networks models and enhance simulation speed and portability. Certain features of Simulink software also make use of generated or external code. This section explains code-related tasks you can perform with your Simscape models.

Generating Code

Code versions of Simscape models typically require fixed-step Simulink solvers, which are discussed in the Simulink documentation. Some features of Simscape software are restricted when you translate a model into code. See “How Simscape Code Generation Differs from Simulink” on page 2-37, as well as “Limitations” on page 2-39.

Note Code generated from Simscape models is intended for rapid prototyping and hardware-in-the-loop applications. It is not intended for use as production code in e mbedded controller applications.

Add-on products based on the Simscape platform also support code generation, with some variations and exceptions described in their respective User’s Guides. Consult those User’s Guides for more information.

Reasons for Generating Code

Code generation has many purposes and methods. There are two essential rationales:

• Compiled code versions of Simulink and Simscape models run faster than

• An equally im portant consideration for Simscape models i s the sta nd-alone

Using Code-Related Products and Features

With Simulink, Real-Time Workshop, and xPC Target software, using several code-related technologies, you can link existing code to your models and generate code versions of your models.

the original block diagram models. The time savings can be dramatic.

implementation of generated and compiled code. Once you convert part or all of your model to code, you can deploy the stand-alone executable program on virtually any platform, independently of MATLAB application.

Converting a model or subsystem to code also hides the original m o del or subsystem.

2-36

Code-Related Task

Link existing code written in C or other supported languages to Simulink models

Speed up Simulink simulations Accelerator mode

Generate stand-alone fixed-step code from Simulink models

Generate stand-alone variable-step code from Simulink models

Convert Simulink model to code andcompileandrunitonatarget PC

Component or Feature

Simulink S-functions to generate customized blocks

Rapid Accelerator mode

Real-Time Workshop software

Real-Time Workshop Rapid Simulation Target (RSim)

Real-Time Workshop and xPC Target software

Generating Code

HowSimscapeCodeGenerationDiffersfrom Simulink

In general, using the code generated from Simscape models is similar to using code generated from regular Simulink models. However, there are certain differences.

Simscape and Simulink Code Are Generated Separately

Real-Time Workshop software g enerates code from the Simscape blocks separately from the Simulink blocks in your model. The generated Simscape code does not pass through the code generated from a single model resides in the same directory, however.

Compiler Support and Precompiled Libraries

Simscape software and its add-on products provide static runtime libraries precompiled for compilers supported by Real-Time Workshop software. These are the standard UNIX compilers for UNIX operating systems, LCC and Microsoft for 64-bit W indows.

Visual Studio®for 32-bit Windows®, and Microsoft Visual Studio

model.rtw or the Target Language Compiler. All

Forallothercompilers,thestaticruntime libraries needed by code generated from Simscape models are compiled once per model during the code generation build process.

Simscape Code Reuse Is Not Supported

Reusable subsyste ms in Simulink reuse code that is generated once from the subsystem. You cannot generate reusable code from subsystems containing Simscape blocks.

Tunable Parameters Are Not Supported

A tunable parameter is a Simulink run-time parameter that you can change while the simulation is running. Simscape blocks do not support tunable parameters in either simulations or generated code.

2-37

2 Simulating Physical Models

Simscape Run-Time Parameter Inlining Ignores Global Exceptions

If you choose to enable parameter inlining for code generated from a Simscape model, the software inlines all its run-time parameters. If you choose to make some of the global Simscape block parameters exceptions to inlining, the exceptions are ignored. You can change global tunable parameters only by regenerating code from the model.

2-38

Limitations

In this section...

“SampleTimeandSolverRestrictions”onpage2-39

“Algebraic Loops” on page 2-39

“Restricted Simulink Tools” on page 2-40

“Unsupported Simulink Tools” on page 2-42

“Simulink Tools Not Compatible with Simscape Blocks” on page 2 -4 2

“Code Generation” on page 2-42

Sample Time and Solver Restrictions

The default sample times of Simscape blocks are continuous. You cannot simulate Simscape blocks with discrete solvers using the default sample times.

IfyouswitchtoalocalsolverintheSolverConfigurationblock,theassociated states become discrete. If there are no continuous Simulink or Simscape states elsewhere in the model, you should use a discrete solver to simulate such a model.

You cannot override the sample time of a nonvirtual subsystem containing Simscape blocks.

Algebraic Loops

A Simscape physical network should not exist within a Simulink algebraic loop. This means that you should not directly connect an output of a PS-Simulink Converter block to an input of a Simulink-PS Converter block of the same physical network.

For example, the following model contains a direct feedthrough between the PS-Simulink Converter block and the Simulink-PS Converter block (highlighted in magenta). To avoid the algebraic loop, you can insert a Transfer Function block anywhere along the highlighted loop.

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2 Simulating Physical Models

A better way to avoid an algebraic loop without introducing additional dynamics is shown in the modified model below.

2-40

Restricted Simulink Tools

Certain Simulink tools are restricted for use with Simscape software:

• You can use the Simulink

get Simscape block parameters. The MathWorks does not recommend that you use these commands for this purpose.

If you make changes to block parameters at the command line, run your model first before saving it. Otherwise, you might save invalid block parameters. Any block p aram eter changes that you make with are not validated unless you run the model.

set_param and get_param commands to set or

set_param

• Enabled subsystems can contain Simscape blocks . Always set the States

when enabling parameter in the Enable dialog to

Enable port.

held for the subsystem’s

Limitations

Setting States when enabling to to fatal simulation errors.

• You can place Simscape blocks within nonvirtual subsystems that support

continuous states. Nonvirtual subsystems that support continuous states include Enabled subsystems and Atomic subsystems. However, physical connections and physical signals must not cross nonvirtual boundaries. When placing Simscape blocks in a nonvirtual subsystem, make sure to place all block s belonging to a given Physical Network in the same nonvirtual subsystem.

• Simulink configurable subsystems work with Simscape blocks only if all of

the block choices have consistent port signatures.

• For Iterator, Function-Call, Triggered, and While Iterator nonvirtual

subsystems cannot contain Simscape blocks.

• An atomic subsystem with a user-specified (noninherited) sample time

cannot contain Simscape blocks.

• You can use the Simulink Save As command only to rename Simscape

models within the current version. Saving in a previous version format is not supported for models containing Simscape blocks.

• Linearization with the Simulink

Simulink Control Design functions and graphical interfaces is not supported with Simscape models if you use local solvers.

reset is not supported and can lead

linmod function or with equivalent

• Model referencing is supported, with some restrictions:

- All Physical connection lines must be contained within the referenced

model. Such lines cannot cross the boundary of the referenced model subsystem in the referencing model.

- The referencing model and the referenced model must use the same

solver.

For further information, consult the Simulink documentation on referencing models.

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2 Simulating Physical Models

Unsupported Sim

Certain Simulin

• The Simulink Pr

• Physical sign

different fro tool and the si

Simulink Too

Some Simulin

• Execution o

• Simscape bl

• You cannot

• Reusable s

• You canno

• The Repor

Code Gen

Code gen family from Si

eration is supported for Simscape physical modeling software and its

of add-on products. How ever, there are restrictions on code generated

mscape models.

k tools and features do not work with Simscape softw are:

ofiler tool does not work with Simscape models.

als and physical connection lines between conserving ports are

m Simulink signals. Therefore, the Signal and Scope Manager

gnal label functionality are not supported.

lsNotCompatiblewithSimscapeBlocks

k tools and features do not work with Simscape blocks:

rder tags do not appear on Simscape blocks.

ocks do not invoke user-defined callbacks.

set breakpoints on Simscape blocks.

ubsystems cannot contain Simscape blocks.

t use the Simulink Fixed-Point Tool with Simscape blocks.

t Generator reports Simscape block properties incompletely.

eration

ulink Tools

2-42

• Code r

• C++ co

• Tunab

• Run-

• Simu

• Blo

if y con

• Co

S-

euse is no t supported.

de generation is not supported.

le parameters are not supported.

time parameter inlining ignores global exceptions.

lation of Simscape models on fixed-point processors is not supported.

ck diagnostics in error messages are not supported. This means that ou get an error message from simulating generated code, it does not tain a list of blocks involved.

nversion of models or subsystems containing Simscape blocks to

functions is not supported.

Limitations

• Simulation-in-the-loop (SIL) is not supported.

• Code generation respects the Linear Algebra setting in the Solver

Configuration block, but only when you choose the local solver option. Otherwise, code generation uses full linear algebra.

“Generating Code” on page 2-35 describes Simscape code generation features. “Restricted Simulink Tools” on page 2-40 describes limitations on model referencing.

There are variations and exceptions as well in the code generation features of the a dd-on products based on Simscape platform. For details, see the User’s Guides for individual add-on products.

Code Generation and Fixed-Step Solvers

Most code generation options for Simscape models require the use of fixed-step Simulink solvers. This table summarizes the available solver choices, depending on how you generate code.

Code Generation Optio n Solver Choices

Accelerator mode Rapid Accelerator mode

Real-Time Workshop software: RSim Target*

Real-Time Wo rks ho p software: Targets other than RSim

* For the R Sim Target, Simscape software supports only the Simulink solver module. In the model Configuration Parameters dialog box, see the Real-Time Workshop: RSim Target: Solver selection menu. T he default is automatic selection, whichmightfailtochoosetheSimulinksolvermodule.

Variable-step o r fixed-step

Fixed-step only

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2 Simulating Physical Models

2-44

Mathworks SIMSCAPE 3 user guide

Specifications and Main Features

Frequently Asked Questions

User Manual

Modeling Physical Systems

Basic Principles of Modeling Physical Networks

Variable Types

Building the Mathematical Model

Direction of Variables

Physical Conserving Ports

Physical Signal Ports

Connecting Simscape Diagrams to Simulink Sources and Scopes

Introducing the Simscape Block Libraries

Library Structure Overview

Using the Simulink Library Browser to Access the Block Libraries

Using the Command Prompt to Access the Block Libraries

Essential Steps to Building a Physical Model

Building Your Model

Using the Conserving Ports

Creating a Simple Model

Building a Simscape Diagram

Modifying Initial Settings

Running the Simulation

Adjusting the Parameters

Changing the Force Profile

Changing the Model Parameters

Changing the Mass Position Output Units

Modeling Best Practices

Grounding Rules

Each Domain Requires at Least One Reference Block

Each Circuit Requires at Least One Reference Block

Avoiding Numerical Simulation Issues

Modeling Pneumatic Systems

Intended Applications

Assumptions and Limitations

Fundamental Equations

Network Variables

Connection Constraints

References

Simulating Physical Models

How Simscape Simulation Works

Simscape Simulation Phases

Model Validation

Network Construction

Equation Construction

Computing Initial Conditions

Performing Transient Initialization

Transient Solve

Working with Solvers

Selecting a Solver

Input Filtering

Troubleshooting Simulation Errors

Troubleshooting Tips and Techniques

System Configuration Errors

Missing Solver Configuration Block

Extra Fluid Block or Gas Properties Block

Missing Reference Block

Basic Errors in Physical System Representation

Numerical Simulation Issues

Dependent Dynamic States

Parameter Discontinuities

Transient Simulation Issues

Transient Initialization Not Converging

Step-Size-Related Errors

Finding an Operating Point

What Is an Operating Point?

Using Operating Points for Linearization

Example

How to Find Operating Points

Time-Based Search

State-Based Search

Checking Discrete System States

Simulating in Time to Search for an Operating Point

Using the Simscape Steady-State Solver

Using Simulink Control Design Techniques

Using Sources to Find Operating Points Not Recommended

Simulink trim Function Not Supported with Simscape Models

Linearizing at an Operating Point

What Is Linearization?

Choosing a Good Operating Point for Linearization