Simscape 3
Model and simulate multidomain physical systems
Simscape extends Simulink with tools for modeling systems spanning mechanical, electrical, hydraulic, and other physical domains as physical networks. It provides fundamental building blocks from these domains to let you create models of custom components. The MATLAB based Simscape language enables text-based authoring of physical modeling components, domains, and libraries. Simscape models can be converted to C code (with Real-Time Workshop). The C code can be used as a standalone executable, incorporated into other simulation environments, and executed in real time on hardware-in-the-loop (HIL) systems. Simscape can be used to model custom electrohydraulic valves, electromechanical actuators, inverting op-amps, heat transfer in a DC motor, and a variety of other systems. You can combine Simscape with other MathWorks physical modeling products to model complex interactions in multidomain physical systems.

Key features

ingle modeling environment for modeling and simulating S physical systems, such as mechanical, electrical, hydraulic, and thermal systems ibrary of fundamental physical modeling building blocks and L mathematical elements, for modeling custom components ATLAB based Simscape language, enabling text-based authoring M of physical modeling components, domains, and libraries bility to specify units of parameters and variables, with all A unit conversions handled automatically Connection blocks for bridging physical domains Full simulation and limited editing capabilities for models built with Simscape add-on products without requiring a license for these products Ability to convert Simscape models to C code (with Real-Time Workshop)
Cross-section illustration of an electrohydraulic servo-valve that uses a flapper-nozzle amplifier, highlighted in yellow (above). The colored blocks in the associated Simscape model (left) correspond to the colored arrows (above), which represent typical hydraulic flow paths.
Accelerating the pace of engineering and science
Modeling Multidomain Physical Systems
With Simscape, you build a model of a system just as you would assemble a physical system. Simscape employs a physical network approach, also referred to as acausal modeling, to model building: Components (blocks) corresponding to physical elements, such as pumps, motors, and op-amps, are joined by lines corresponding to the physical connections that transmit power. This approach lets you describe the physical structure of a system rather than the underlying mathematics. From your model, which closely resembles a schematic, Simscape automatically constructs the differential algebraic equations (DAEs) that characterize the systems behavior. These equations are integrated with the rest of the Simulink model, and the DAEs are solved directly. The variables for the components in the different physical domains are solved simultaneously, avoiding problems with algebraic loops.
Modeling Mechanical Components
Simscape provides mechanical building blocks for representing one-dimensional translational and rotational motion. In addition to basic elements like mass, spring, and damper, nonlinear effects such as backlash and friction are also included. Interface blocks provided with SimMechanics and SimDriveline enable you to connect Simscape models to models built using those tools.

transduction, and flow through basic fixed and variable orifices. You can define a fluid by entering its fluid properties. More elaborate hydraulic components are available in SimHydraulics.

Modeling Thermal Effects

Simscape provides thermal building blocks for modeling and simulating thermal effects in your system. You can model conductive, convective, and radiative heat transfer as well as the thermal mass of elements. Using thermal source blocks, you can specify the temperature or heat transfer; using thermal sensor blocks, you can measure the amount of heat transfer or temperature change.
Modeling Electrical Components
Simscape provides electrical building blocks for representing electrical components and circuits. In addition to basic elements like resistors, capacitors, and inductors, more complex elements such as op-amps and transformers are also included. More elaborate electronic and electromechanical components are available in SimElectronics.
Working with Physical Signals
With Simscape your models can include physical signals that have units associated with them. You specify the units and parameter values in the block dialog boxes, and Simscape performs the necessary unit-conversion operations when solving a physical network. The Physical Signals block library
Modeling Hydraulic Components
Simscape provides hydraulic building blocks that model fundamental hydraulic effects and can be combined to create more complex hydraulic components. These blocks define the pressure/flow relationship for basic physical effects, such as fluid compressibility, fluid inertia, mechanical friction, energy
Creating Custom Components
Simscape lets you create models of custom components by using the basic elements contained in its foundation libraries.
Mechanical Translational Reference

Constant Volume Chamber

Fixed Orifice

Fluid Inertia

Translational Friction

S Hydraulic Reference A B A B

Translational Damper

Linear Hydraulic Resistance
Orifice with Variable Area Round Holes
Orifice with Variable Area Slot
X A B Y Pressure Compensator

Translational Hard Stop

A B Resistive Tube

Translational Spring

C R A Translational Hydro-Mechanical Converter

Variable Volume Chamber

Variable Orifice

Inertia

Mechanical Rotational Reference
Simscape libraries of electrical, mechanical, hydraulic, and thermal building blocks for creating customized component models.

Rotational Damper

Rotational Friction

Rotational Hard Stop

Rotational Spring
component lossy_ultracapacitor % Lossy Ultracapacitor % Models an ultracapacitor with resistive losses. nodes p = foundation.electrical.electrical % +:top n = foundation.electrical.electrical; % -:bottom end parameters C0 = { 1, F }; % Nominal capacitance C0 at V=0 Cv = { 0.2, F/V}; % Rate of change of C with voltage V R = {2, Ohm }; % Effective series resistance Rd = {500, Ohm }; % Self-discharge resistance V0 = { 0, V }; % Initial voltage end variables i = { 0, A }; % Current through variable v = { 0, V }; % Voltage across variable vc = { 0, V }; % Internal variable end function setup if R <= { 0, Ohm} error( Resistance must be greater than zero ) end through( i, p.i, n.i ); % Through variable i across( v, p.v, n.v ); % Across variable v vc = V0; end equation i == (C0 + Cv*v)*vc.der + vc/Rd; % Equation 1 v == vc + i*R; % Equation 2 end end
Using the Simscape language to create a custom model of an ultracapacitor with losses. The equation shown (bottom) is implemented in the Simscape language (left). The Simulink block (top right) and dialog box (center) are created automatically from the Simscape file.
lets you perform math operations on physical signals and graphically enter equations inside the physical network. Physical signal ports are used in Simscape block diagrams to better integrate physical signals into your physical system, which increases computational speed. Using the elements contained in these foundation libraries, you can create more complex components that span different physical domains. As with Simulink, you can then group this assembly of blocks into a subsystem and parameterize it to reuse and share these components. You can use the sensor blocks in Simscape to measure values for different physical quantities such as mechanical (force/torque, velocity), hydraulic (pressure, flow rate),

or electrical (voltage, current) variables, and then pass these signals into standard Simulink blocks. Source blocks enable Simulink signals to assign values to any of these variables. Sensor and source blocks let you connect a control algorithm developed in Simulink to a Simscape network.
DAEs. You can also use MATLAB to analyze the parameter values, perform preliminary computations, and initialize system variables. The Simulink block and dialog box for the component are automatically created from the Simscape file. The components you create can reuse the physical domain definitions provided with Simscape to ensure that your components are compatible with the standard Simscape components. You can also add your own physical domains. You can automatically build and manage Simulink libraries of your Simscape components and domains, enabling you to share these models across your organization. You can also generate C code from Simulink models that contain your custom components.
Using the Simscape Language
The Simscape language enables you to add new physical domains and to create your own physical modeling components and libraries. It is based on the MATLAB programming language, well-known by engineers. Using this object-oriented modeling language, you can define custom components, complete with parameterization, physical connections, and equations represented as acausal implicit
w w w. m a t h w o r k s. c o m
Sharing Models Using Simscape Editing Modes
The Simscape Editing Modes let you perform physical modeling and simulation using Simscape and its add-on products: SimDriveline, SimElectronics, SimHydraulics, and SimMechanics. You can open, simulate, tune parameters for, and save models that contain blocks from add-on products with only a Simscape license, as long as the add-on products are installed on your machine. You can share your models across your organization without purchasing additional licenses.
Multidomain Physical Modeling in MATLAB and Simulink
Simscape provides expanded capabilities for modeling physical systems. You can create your physical plant model using physical connections and connect it directly to your control model built using signal flows in Simulink. Simscape models can also be connected directly to other MathWorks application- and domain-specific physical modeling tools, enabling you to model complex interactions in multidomain physical systems. You can use MATLAB to parameterize your model, automate simulation tests, analyze output data, and optimize system performance. As a result, you can test your entire system (multidomain physical plant and controller) within the MATLAB and Simulink environment.

Related Products

SimDriveline Model and simulate mechanical driveline systems SimElectronics Model and simulate electronic and electromechanical systems SimHydraulics Model and simulate hydraulic systems SimMechanics Model and simulate mechanical systems SimPowerSystems Model and simulate electrical power systems
Converting Simscape Models to C Code
With Simscape you can convert your models into C code, enabling you to use the accelerator modes of Simulink to reduce simulation time. You can also convert Simscape models into C code using Real-Time Workshop, which lets you: un your model in real time, enabling you R to perform HIL testing ntegrate your model into other simulation I environments ompile your Simscape model for standC alone simulations, which accelerate analyses like parameter studies and Monte Carlo simulations
Platform and System Requirements
For platform and system requirements, visit www.mathworks.com/products/simscape

Required Products

MATLAB Simulink

Learn More

www.mathworks.com/products/simscape

Resources

visit www.mathworks.com Technical Support www.mathworks.com/support Online User Community www.mathworks.com/matlabcentral Demos www.mathworks.com/demos Training Services www.mathworks.com/training Simscape model (above) representing a fullwave bridge rectifier that converts 120 volts AC to 12 volts DC. This model can be used to size the capacitor for a specific load. The graph (left) shows the ripple on the DC voltage. Third-Party Products and Services www.mathworks.com/connections Worldwide CONTACTS www.mathworks.com/contact e-mail info@mathworks.com
2008 The MathWorks, Inc. MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders.

91439v02 10/08

Simscape 3 Getting Started Guide

How to Contact MathWorks

Web Newsgroup www.mathworks.com/contact_TS.html Technical Support
www.mathworks.com comp.soft-sys.matlab suggest@mathworks.com bugs@mathworks.com doc@mathworks.com service@mathworks.com info@mathworks.com
Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information
508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098
For contact information about worldwide offices, see the MathWorks Web site. Simscape Getting Started Guide COPYRIGHT 20072011 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathWorks, Inc. FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation by, for, or through the federal government of the United States. By accepting delivery of the Program or Documentation, the government hereby agrees that this software or documentation qualifies as commercial computer software or commercial computer software documentation as such terms are used or defined in FAR 12.212, DFARS Part 227.72, and DFARS 252.227-7014. Accordingly, the terms and conditions of this Agreement and only those rights specified in this Agreement, shall pertain to and govern the use, modification, reproduction, release, performance, display, and disclosure of the Program and Documentation by the federal government (or other entity acquiring for or through the federal government) and shall supersede any conflicting contractual terms or conditions. If this License fails to meet the governments needs or is inconsistent in any respect with federal procurement law, the government agrees to return the Program and Documentation, unused, to The MathWorks, Inc.

Trademarks

MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders.

Patents

MathWorks products are protected by one or more U.S. patents. Please see www.mathworks.com/patents for more information.

Revision History

September 2007 March 2008 October 2008 March 2009 September 2009 March 2010 September 2010 April 2011
Online Online Online Online Online Online Online Online
only only only only only only only only
New for Version 2.0 (Release 2007b) Revised for Version 2.1 (Release 2008a) Revised for Version 3.0 (Release 2008b) Revised for Version 3.1 (Release 2009a) Revised for Version 3.2 (Release 2009b) Revised for Version 3.3 (Release 2010a) Revised for Version 3.4 (Release 2010b) Revised for Version 3.5 (Release 2011a)

Contents

Introduction to Simscape Software
Product Overview. Product Definition. Simscape Block Libraries. Physical Modeling Product Family. Simscape Language. Prerequisites. Background Knowledge. Required Products. Opening Simscape Libraries. Creating a New Simscape Model. Working with a Simscape Demo Model. About This Tutorial. Exploring the Model. Running the Model. Modifying the Model. Learning More. Next Steps. Product Help. MathWorks Online. 1-2 1-2 1-2 1-4 1-5 1-6 1-6 1-6 1-7 1-8 1-11 1-11 1-12 1-14 1-15 1-21 1-21 1-21 1-22
Product Overview on page 1-2 Prerequisites on page 1-6 Opening Simscape Libraries on page 1-7 Creating a New Simscape Model on page 1-8 Working with a Simscape Demo Model on page 1-11 Learning More on page 1-21

Product Overview

In this section. Product Definition on page 1-2 Simscape Block Libraries on page 1-2 Physical Modeling Product Family on page 1-4 Simscape Language on page 1-5

Product Definition

Simscape software extends the Simulink product line with tools for modeling and simulating multidomain physical systems, such as those with mechanical, hydraulic, pneumatic, thermal, electrical, and electromagnetic components. Unlike other Simulink blocks, which represent mathematical operations or operate on signals, Simscape blocks represent physical components or relationships directly. With Simscape blocks, you build a model of a system just as you would assemble a physical system. Simscape models employ a Physical Network approach to model building: components (blocks) corresponding to physical elements such as pumps, motors, and op-amps, are joined by lines corresponding to the physical connections that transmit power. This approach lets you describe the physical structure of a system rather than the underlying mathematics. From your model, which closely resembles a schematic, Simscape technology automatically constructs equations that characterize the behavior of the system. These equations are integrated with the rest of the Simulink model. Simscape software runs within the Simulink environment and interfaces seamlessly with the rest of Simulink product family and with the MATLAB technical computing environment.

Simscape Block Libraries

Simscape Foundation libraries contain a comprehensive set of basic elements and building blocks, such as:
Mechanical building blocks for representing one-dimensional translational and rotational motion Electrical building blocks for representing electrical components and circuits Magnetic building blocks that represent electromagnetic components Hydraulic building blocks that model fundamental hydraulic effects and can be combined to create more complex hydraulic components Pneumatic building blocks that model fundamental pneumatic effects based on the ideal gas law Thermal building blocks that model fundamental thermal effects Physical Signals block library that lets you perform math operations on physical signals, and graphically enter equations inside the physical network Using the elements contained in these Foundation libraries, you can create more complex components that span different physical domains. You can then group this assembly of blocks into a subsystem and parameterize it to reuse and share these components. Shown below is a Simscape model of a DC motor that accounts for friction and includes electrical and mechanical components. You can easily match the model to the motor illustration on the right. The model contains two electrical ports, corresponding to the V+ and V- electric terminals of the motor, and two mechanical rotational ports, C and R, corresponding to the motor case and rotor, respectively. It is built of Simscape foundation blocks. You can use this model to create a masked subsystem of a DC motor, to reuse and share in electric diagrams.

In addition to Foundation libraries, there is also a Simscape Utilities library, which contains utility blocks, such as: Solver Configuration block, which contains parameters relevant to numerical algorithms for Simscape simulations. Each Simscape diagram (or each topologically distinct physical network in a diagram) must contain a Solver Configuration block. Simulink-PS Converter block and PS-Simulink Converter block, to connect Simscape and Simulink blocks. Use the Simulink-PS Converter block to connect Simulink outports to Physical Signal inports. Use the PS-Simulink Converter block to connect Physical Signal outports to Simulink inports. For examples of using these blocks in a Simscape model, see the following section, Working with a Simscape Demo Model on page 1-11.
Physical Modeling Product Family
Simscape functions and utilities support functionality common to other Simulink products that use physical connections between their blocks. Simscape serves as the platform product for these add-on products of the Physical Modeling family: SimHydraulics, for modeling and simulating hydraulic systems
SimDriveline, for modeling and simulating powertrain systems SimMechanics, for modeling and simulating general mechanical systems SimElectronics, for modeling and simulating electromechanical and electronic systems The Physical Modeling product family also contains SimPowerSystems, for modeling and simulating electrical power systems. Use these products together to model physical systems in the Simulink environment.

Simscape Language

The Simscape language extends the Simscape modeling environment by enabling you to create new components that do not exist in the Foundation library or in any of the add-on products. Simscape block libraries contain a comprehensive selection of blocks that represent engineering components such as valves, resistors, springs, and so on. These prebuilt blocks, however, may not be sufficient to address your particular engineering needs. When you need to extend the existing block libraries, use the Simscape language to define customized components, or even new physical domains, as textual files. Then convert your textual components into libraries of additional Simscape blocks that you can use in your model diagrams. For more information on how to do this, see the Simscape Language Guide.

Prerequisites

In this section. Background Knowledge on page 1-6 Required Products on page 1-6

Background Knowledge

This Getting Started guide requires that you have some experience with modeling physical systems, as well as with building and running models in the Simulink environment.

Required Products

Simscape software requires these products: MATLAB Simulink
Opening Simscape Libraries
Simscape software is part of your MATLAB installation. To open Simscape block libraries, type simulink in the MATLAB Command Window to display the Simulink Library Browser, and then expand the Simscape entry in the contents tree.
Creating a New Simscape Model
Simscape models require certain blocks to be present in the model configuration, such as a Solver block, or domain-specific reference blocks. Other blocks, although not required, are highly likely to be needed, such as Simulink-PS Converter and PS-Simulink Converter blocks. An easy way to start a new Simscape model is by using the ssc_new command. When you type ssc_new at the MATLAB Command prompt, the software opens the main Simscape library and creates a new model prepopulated with certain blocks, as shown in the following illustration.
By default, the model name is not specified, the model contains a Solver Configuration block with the default solver set to ode15s, a Simulink-PS Converter block, and a PS-Simulink Converter block connected to a Scope block. You can use the ssc_new command arguments to specify the model name, add a domain-specific reference block, and change the default solver. See the ssc_new command reference page for details. For example, typing
ssc_new('rotor1','rotational','ode23t')
creates the following model.
After using ssc_new, continue developing your model by copying the blocks, as needed, and adding other blocks from the Simscape libraries. For electrical models, you can also use the Creating A New Circuit demo as a template for a new model. This demo also opens an Electrical Starter Palette, which contains links to the most often used electrical components. Open the demo by typing ssc_new_elec in the MATLAB Command Window and use File > Save As to save it under the desired model name. Then delete the
unwanted components and add new ones from the Electrical Starter Palette and from Simscape libraries.
Working with a Simscape Demo Model
In this section. About This Tutorial on page 1-11 Exploring the Model on page 1-12 Running the Model on page 1-14 Modifying the Model on page 1-15

About This Tutorial

This tutorial provides you with hands-on experience of using Simscape software. You will open a demo model, examine how it is built, and run the simulation. You will then perform simple modifications of the demo and view their effect on the simulation results. The Permanent Magnet DC Motor demo shows how Simscape models can simulate systems that span electrical and mechanical domains. In this demo, you learn how to model physical components with Simscape blocks, connect them into a realistic model, use Simulink blocks as well, and then simulate and modify a motor model. The model is based on a Faulhaber Series 0615 DC-Micromotor. For the 1.5V variant, equivalent circuit parameters are given as:
Rotor resistance R=3.9 Ohms Rotor inductance L=12mH Back emf constant K=0.072mV/rpm Rotor inertia J=0.01gcm^2 Friction torque Mr=0.02mNm
The model uses these parameters to verify manufacturer-quoted no-load speed, no-load current, and stall torque, which are:
No-load speed = 19,100rpm No-load current = 0.03A Stall torque = 0.24mNm
You can use the model to assess motor performance in a given application by adding the requisite mechanical load model.

Exploring the Model

1 To open the Permanent Magnet DC Motor demo, type ssc_dcmotor in
the MATLAB Command Window.

Main Model Window

The main model window contains a DC Motor subsystem with two electrical and two mechanical rotational ports. The electrical ports connect to the electrical circuit, which consists of an Electrical Reference block, representing an electrical ground, a 1.5 V DC voltage source, and a current sensor. The current sensor connects, through a PS-Simulink Converter block, to a Simulink scope labeled Motor Current.
On the mechanical side, a Mechanical Rotational Reference block represents a reference point for the other elements. An ideal rotational motion sensor connects, through a PS-Simulink Converter block, to a Simulink scope labeled RPM. The motor load is represented by an Ideal Torque Source block, which on one side connects to a Mechanical Rotational Reference block, and on the other side to the motor shaft. A regular Simulink Step source provides the control signal. A Simulink-PS Converter block converts the control signal into a physical signal and applies it to the control port of the Ideal Torque Source block. The diagram also contains a Solver Configuration block, which is required in any Simscape model. It contains parameters relevant to numerical algorithms for Simscape simulations.
2 Double-click the DC Motor subsystem to open it.

DC Motor Subsystem

The motor consists of an electrical circuit and a mechanical circuit, connected by the Rotational Electromechanical Converter block. The electrical circuit consists of a Rotor Resistance block and an Inductance block L. It contains two electrical ports, corresponding to the V+ and
V- electric terminals of the motor. The mechanical circuit contains a Rotational Friction block, Motor Inertia J, and two mechanical rotational ports, C and R, corresponding to the motor case and rotor, respectively. Notice how the C and R ports of the Friction block and the Rotational Electromechanical Converter block are connected to the C and R ports of the motor, to preserve the correct direction of variables in the Physical Network.

Running the Model

After you have reviewed the block diagram of the demo model, you can run the simulation.
1 Double-click the Motor Current and RPM scopes to open them. During
simulation, these windows display the motor current and shaft speed, respectively, as functions of time.
2 In the toolbar of the model window, click
to start the simulation. The Simscape solver evaluates the model, calculates the initial conditions, and runs the simulation. This process might take a few seconds. The message in the bottom-left corner of the model window provides the status.
3 Examine the simulation results in the Motor Current and RPM scope

windows.

For the first 0.1 seconds, the motor has no external load, and the speed builds up to the no-load value. Then at 0.1 seconds, the stall torque is applied as a load to the motor shaft. Zooming in on the RPM and Motor Current scopes shows that the model matches the manufacturer parameters for no-load speed, no-load current, and stall torque.

Modifying the Model

After running the initial simulation, you can experiment with adjusting various inputs and block parameters. Try the following adjustments:
1 Change the supply voltage. 2 Change the motor load.
Changing the Supply Voltage
Reduce the supply voltage to 1.25 volts (to simulate the battery running down) and vary the load torque to find the maximum torque at this reduced voltage.
1 Double-click the 1.5V DC Voltage Source block. Set Constant voltage to

1.25 V.

2 Run the simulation. Note the effect of reduced voltage on the no-load speed.
3 Try varying the load torque to find the maximum torque at this reduced
voltage. Double-click the Step source block, enter different final values for the input signal, and rerun the simulation. The next illustration shows the simulation results for Final value set to -0.2e-3, which corresponds to (1.25/1.5)*0.24mNm, as the magnitude of the torque-speed curve is proportional to voltage for a DC motor.

Changing the Motor Load

Replace the torque source with a simple mechanical load, for example, a fan, for which the torque is defined by alpha*speed^2, where alpha is -1e-10 Nm/(rad/s)^2.
1 Delete the Step source and the Simulink-PS Converter block from the

model.

2 In the Simscape block library, open Foundation Library > Physical

Signals > Functions.

3 Drag the PS Product block and the PS Gain block to the model window. 4 Connect the blocks as shown in the following illustration. To rotate a block,
select it and press Ctrl+R.
5 Double-click the Gain block to open its dialog box. Enter Gain value of

-1e-10 and click OK.

6 Run the simulation and assess motor performance with the new load.

Learning More

In this section. Next Steps on page 1-21 Product Help on page 1-21 MathWorks Online on page 1-22

Next Steps

To take the next lesson on using the product, follow the steps in Creating a Simple Model in the Simscape Users Guide. Also see the following topics to continue your exploration: For. Rules of building models with physical components Variables available with each domain Block orientation in a model Overview of the simulation process Code generation Writing and compiling code to create additional custom blocks See. Basic Principles of Modeling Physical Networks Variable Types Direction of Variables How Simscape Simulation Works Generating Code Simscape Language Guide

Product Help

More information is available with your product installation. In the MATLAB desktop, click pane. For. List of blocks Advanced tutorials for help, and then click the product name in the Contents
See. Block Reference Examples
For. More product demonstrations Whats new in this product
See. Simscape Demos Release Notes

MathWorks Online

Point your Internet browser to the MathWorks Web site for additional information and support at http://www.mathworks.com/products/simscape/.