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248 Appendix D: The SIMSCAPE Modeling Environment Tutorial

D.3.3 Mechanical Library

This section is an introduction to the Mechanical Library of SIMSCAPE. We will

illustrate the components included in this library (fig. D.18).

Fig. D.18 The SIMSCAPE Mechanical Library

The Mechanical Library is composed by four sub-libraries, termed the

Translational Elements, Rotational Elements, Mechanical Sensors and Sources,

and Mechanism libraries.

The Translational Elements library contains some of the common elements

which constitute the translational mechanical systems (mass, spring, damper,…)

(fig. D.19), while the Rotational Elements library contains some of the common

elements which constitute the rotational mechanical systems (inertia, spring,

damper,…) (fig. D.20).

Fig. D.19 The SIMSCAPE Mechanical Translational Elements sub-library

Fig. D.20 The SIMSCAPE Mechanical Translational Elements sub-library

D.3 SIMSCAPE Libraries 249

The Mechanical Sensors and Sources library contains both translational and

rotational position/velocity sensors as well as force/torque sensors. Besides,

contains force/torque sources in order to actuate over the mechanical circuit

elements, as well as velocity sources (fig. D.21).

Fig. D.21 The SIMSCAPE Mechanical Sensors and Sources sub-library

Additionally, a Mechanism library where mechanical transformers (gear and

lever) and ideal pulleys can be found, is included (fig. D.22).

Fig. D.22 The SIMSCAPE Mechanisms sub-library

D.3.4 Thermal Library

This section is an introduction to the Thermal Library of SIMSCAPE. We will

illustrate the components included in this library (fig. D.23).

Fig. D.23 The SIMSCAPE Thermal Library

250 Appendix D: The SIMSCAPE Modeling Environment Tutorial

The Thermal Library is composed of two sub-libraries, termed the Thermal

Elements, and Thermal Sensors and Sources libraries.

The Thermal Elements library contains some of the common elements which

constitute the thermal systems (mass and heat trasnfer mechanism) (fig. D.24).

Fig. D.24 The SIMSCAPE Thermal Elements sub-library

The Thermal Sensors and Sources library contains both tempearture and heat

flow sensors and sources in order to measure or actuate over the thermal circuit

elements (fig. D.25).

Fig. D.25 The SIMSCAPE Thermal Sensors and Sources sub-library

D.3.5 Physical Signal Library

This section is an introduction to the Physical Signal Library of SIMSCAPE,

which is utilized to create equations, by using linear and nonlinear operators,

functions, lookup tables, etc. These equations are solved simultaneously with

physical system, and unit conversions are handled automatically.

We will illustrate the blocks included in this library and its function (fig. D.26).

These blocks are similar to those described in the SIMULINK Libraries, and

perform the same function, by using physical signal instead of dimensionless

variables as SIMULINK. In this way, it includes linear blocks (adder, gain,

integrator,…) and nonlinear also (divider, math function, table lookup,

saturation,…) as it is shown in fig. D.27.

D.3 SIMSCAPE Libraries 251

Fig. D.26 The SIMSCAPE Physical Signals Library

Fig. D.27 Blocks included into the SIMSCAPE Physical Signals Library

D.3.6 Utilities Library

This section is an introduction to the Utilities Library of SIMSCAPE, which

contains general purpose blocks as the PSS and SPS converters from SIMSCAPE

to SIMULINK or vice versa respectively, together with the input/output ports to

define subsystems in SIMSCAPE. Additionally, the solver block, which is

necessary to be attached to the physical components diagram is included, thus the

solver can be applied with the numerical methods to integrate the dynamic system

equations (fig. D.28).

252 Appendix D: The SIMSCAPE Modeling Environment Tutorial

Fig. D.28 The SIMSCAPE Utilities Library

Index

actuators, 137

block diagrams, 76

reduction rules, 79

compensator. See gain

control systems

proportional control, 108

Control systems, 137

bang-bang control, 140

closed loop systems, 138

controller, 138

integral control, 146

open loop systems, 139

PID Control, 142

Proportional control, 144

Control Systems

Derivative control, 148

damping ratio, 100

Electrical Systems, 19

error, 5, 107

position constant, 133

steady-state error, 131

velocity constant, 134

gain, 89, 158

Hydraulic Systems, 30

initial conditions, 62

Laplace transform, 51

Final value theorem, 54

inverse transform, 55

properties, 52

Matlab commands

ginput, 155

initial, 88

lsim, 88

residue, 94

rlocus, 117

rltool, 158

roots, 127

step, 88

Mechanical Systems, 24

natural frequency, 100

Perturbations, 138

poles, 63, 93

dominance of, 106

254 Index

Response, 85

forced response, 86

natural response, 86

steady-state response, 85

transient response, 85

root locus technique, 107

angle condition, 110

asymptotes, 113

magnitude condition, 110

rupture points, 114

sensors, 137

Simulink Blocks

Abs, 227

Add, 226

Backlash, 230

Constant source, 221

Dead Zone, 230

Demux, 232

Derivative, 219

Digital clock, 222

Dispaly, 224

Divide, 226

Fcn, 234

From, 232

From file block source, 222

From workspace block source, 222

Gain, 226

Goto, 232

Inport, Outport, Subsystem, 234

Integrator, 219

Look table nD, 229

Lookup table, 228

Lookup table 2D, 228

Math function, 227

Matlab Fcn, 235

MinMax, 227

Mux, 231

PID controller, 237

PID controller (approximate

derivative), 237

Product, 226

Pulse Generator, 221

Ramp, 221

Rate Limiter, 230

Relay, 230

Saturation, 230

Scope, 223

Sign, 227

Signal builder, 222

Signal Generator, 223

Sine wave source, 221

State-Sapce (initial outputs), 236

State-Space, 219

Step, 221

Stop simulation, 224

Sum, 226

Switch, 232

To file block sink, 224

To workspace block sink, 224

Transfer Fcn (initial outputs), 236

Transfer Fcn (initial states), 236

Transfer function, 219

Transport Delay, 219

Trigonometric function, 227

XY Graph, 224

Zero-Pole, 219

Zero-Pole (initial outputs), 236

Zero-Pole (initial states), 236

stability, 126

Routh-Hürwitz theorem, 128

State Space, 67

state, 67

state equations, 69

system, 1

closed loop systems, 4, 138

continuous systems, 3

control systems, 5

critically damped systems, 101

deterministic system, 3

discrete systems, 3

dynamic systems, 3

event discrete systems, 4

First-order systems, 87

High-order systems, 105

Linear and Invariant Time systems,

linear and time invariant (LTI), 43

modeling, 13

multi-input multi-output systems, 67

multi-input, multi-output systems, 44

open loop systems, 4, 139

overdamped systems, 101

Second-order systems, 92

static systems, 2

stochastic systems, 3

type of a, 132

System identification, 121

First-order system identification, 121

Overshoot, 123

Index 255

Peak time, 123

Rise time, 123

Second-order system identification,

122

Settling time, 123

Steady state value, 124

System Simulation, 167

SIMSCAPE, 167

SIMULINK, 167

Systems description, 5

external description, 6

internal description, 8

Systems linearization, 46

Thermal Systems, 33

time constant, 90

transfer function, 62

zeros, 63

Ziegler-Nichols techniques, 150

closed loop, 153

open loop, 151