Simulation of Automatic speed control DC Drive

1
A Project Report
On
Simulation of Automatic
Speed Control of DC Drive
Submitted in partial fulfillment for award of
Bachelor of Technology
Degree
In
ELECTRICAL AND ELECTRONICS ENGINEERING
By
MUNESH KUMAR SINGH
ADITYA VIKRAM SINGH
ANITYA KUMAR SHUKLA
DEVENDRA KUMAR
Under the guidance of
Mr. Anurag Agrawal
Assistant professor
Kanpur Institute of Technology, Kanpur, INDIA
G.B. Technical University
May, 2012

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CERTIFICATE
This is to certify that project report entitled “Simulation of Automatic Speed Control of DC
Drive.” which is submitted by Munesh Kumar Singh, AdityaVikram Singh, Anitya Kumar
Shukla and Devendra Kumar in partial fulfillment of the requirement for the award of degree
B.Tech. In Department of Electrical & Electronics Engineering of G.B. Technical University
formally as UPTU, is a record of the candidate own work carried out by him under my/own
supervision. The matter embodied in this thesis is original and has not been submitted for the
award of any other degree.
Date:
Place: K.I.T., Kanpur
Head Of Department Project Supervisor
R.K.Pandey AnuragAgrawal
(Senior Lecturer) (Assistant Professor)
DepartmentOf Electrical &Electronics Engineering
K. I. T Kanpur

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DECLARATION
We hereby declare that the project work which is being presented in the project entitled
“Simulation of Automatic Speed control of DC Drive”. This submission is my own work and
that, to the best of my knowledge and belief, it contains no material previously published or
written by another person nor material which to a substantial extent has been accepted for the
award of any other degree /diploma of the university or other institute of higher learning, except
where due acknowledgement has been made in this text. In partial fulfillment of the award of the
degree of Bachelor of Technology in ELECTRICAL AND ELECTRONICS ENGINEERING
submitted in the Department of Electrical and Electronics Engineering. Kanpur Institute of
Technology, Kanpur under the guidance of Mr. AnuragAgrawal, Assistant professor,
Department of Electrical & Electronics Engineering, K. I. T. Kanpur.
The matter embodied in this report has not been submitted by us for the reward of any other
degree.
Date:
Place: K.I.T., Kanpur
Name Roll Number Signature
Munesh Kumar Singh (0816521402)
AdityaVikram Singh (0816510008)
Anitya Kumar Shukla (0816521401)
Devendra Kumar (0816521011)
B.Tech Final Year,
Department of Electrical & Electronics Engineering
K.I.T., Kanpur.

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ACKNOWLEDGEMENT
It gives us a great sense of pleasure to present the report of the B. Tech project undertaken during
B. Tech final Year. We owe special debt of gratitude to Assistant professor Mr. Anurag Agrawal,
Department of Electrical &Electronics Engineering, Kanpur Institute of Technology, Kanpur for
his constant support and guidance throughout the course of work. His sincerity, thoroughness and
perseverance have been a constant source of inspiration for us. It is only his cognizant efforts that
our endeavors have seen light of the day.
We also take the opportunity to acknowledge the contribution of professor Head Department of
Electrical &Electronics Engineering, Kanpur Institute of Technology, Kanpur for his full support
and assistance during the development of the project.
We also do not like to miss the opportunity to acknowledge the contribution of all the faculty
members of the department for their kind assistance and cooperation during the development of
our project. Last but not the least, we acknowledge our friends for their contribution in the
completion of the project.
Date: Munesh Kumar Singh
Place: K.I.T., Kanpur AdityaVikram Singh
Anitya Kumar Shukla
Devendra Kumar
(B.Tech. Final Year)
Deptt. Of Electrical & Electronics Engineering
Kanpur Institute of Technology, Kanpur

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TABLE OF CONTENTS
CHAPTER NO. TITLE PAGE NO.
ABSTRACT vii
LIST OF FIGURES
viii
LIST OF TABLES
ix
LIST OF PLOTS x
1) INTRODUCTION
1.1) CONVENTIONAL METHODS OF SPEED CONTROL
1
1.2) ADOPTED TECHNIQUE 1
1.3) BLOCK DIAGRAM
2
2) GENERALINFORMATION OF COMPONENTS
2.1) DC MOTOR
2.1.1) WORKING PRINCIPLE OF A DC MOTOR 3
2.1.2) OPERATION OF A DC MOTOR
3
2.1.3) SPEED CONTROL METHODS OF DC MOTOR
4
2.1.4) BRAKING OF DC MOTOR 4
2.1.5) WHERE IS THE MOTOR CONTROLLER?
5
2.1.5.1) SCOPE OF MOTOR CONTROLLER APPLICATIONS
2.1.5.2) DOMESTIC APPLICATIONS
2.1.5.3) OFFICE EQUIPMENT, MEDICAL EQUIPMENT, ETC
2.1.5.4) COMMERCIAL APPLICATIONS
2.1.5.5) INDUSTRIAL APPLICATIONS
2.1.5.6)POWER TOOLS
2.2) H BRIDGE
6
2.2.1) GENERAL 6
2.2.2) OPERATION 7
2.3) PWM(PULSE WIDTH MODULATION)

6
8
2.3.1) INTRODUCTION
8
2.3.2) APPLICATIONS AS VOLTAGE REGULATOR
9
2.3.3) POWERDELIVERY 9
2.4) SENSOR 10
2.4.1) VOLTAGE SENSOR 11
2.4.1.1) OVERVIEW 11
2.4.1.2) BLOCK DIAGRAM
11
2.4.2) HALL EFFECT SENSOR
12
3) SIMULINK MODEL
3.1) SPECIFICATIONS OF COMPONANT USED IN PROJECT
13
3.1.1) D.C.MOTOR BLOCK 13
3.1.2)H-BRIDGE14
3.1.3) PWM GENERATOR 16
3.1.4)SENSOR
19
3.1.4.1) IDEAL ROTATIONAL MOTION SENSOR
19
3.1.4.2) VOLTAGE SENSOR 20
3.1.4.3) HALL EFFECT SENSOR
21
3.1.5) VARIABLE LOAD TORQUE 22
3.1.6) SCOPES
23
3.2) PROJECT INFORMATION
3.2.1) PROJECT INFORMATION 24
3.2.1.1) INTRODUCTION
3.2.1.2) PROJECT SIMULATION MODEL 25
3 .3) APPLICATIONS OF THE DRIVE ON THE DOMESTIC LOAD AND
BEHAVIOUR 29
3.4) THE SIMULINK MODEL IS GIVEN ON FAN LOAD
29
3.4.1) THE SIMULATION RESULTS OF THIS MODEL
29
3.5) THE SIMULINK MODEL IS GIVEN ON AUTOMOBILE LOAD
30
3.5.1) THE SIMULATION RESULTS OF THIS MODEL
31

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3.5.2) THE SPEED COVERED IN THIS TIME INTERVAL
32
4) SIMULATION RESULTS
4.1) RESULT OF DRIVE WITHOUT LOADED CONDITION
25
4.2) RESULT OF DRIVE WITH LOADED CONDITION
26
4.3) RESULT OF DRIVE WITH FAN LOAD
29
4.4) RESULT OF DRIVE WITH AUTOMOBILE LOAD
31
5) FUTURE SCOPE
5.1) ADVANTAGES OF AUTOMATIC SPEED CONTROL DRIVE
32
5.2) CONCLUSION 33
5.3) REFERENCES 34
APPENDIX

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ABSTRACT
Automatic speed control drive describes equipment used to control the speed of machinery. The
used of the drive circuit when regulated amount of speed required as per the demanded by the load.
Sometime in many applications the required speed is high or low as per the need for that load .So
by the use of the automatic speed control drive we can regulate the speed of the motor as per the
requirement of the load which also reduce the excess amount of electricity required.
We are planning to control the speed of permanent magnet D.C. motor by using PWM inverter.
This drive is advanced in a sense that it can also be controlled easily a Hall Effect sensor and
control motor speed just by varying PWM inverter output.
The working concept is based upon principle of general D.C. motor, which may be control speed
by the variation in armature current or field current .So we are varying the current of armature
according to the load.
Where speeds may be selected from several different pre-set ranges, usually the drive is said to be
adjustable speed. If the output speed can be changed without steps over a range, the drive is usually
referred to as variable speed.
Due to efficient control methods, DC motors are widely used motors to drive the loads in
industry. Among the different control techniques for the DC motor speed control, armature
voltage control method using Pulse Width Modulation (PWM) technique is the best one.

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LIST OF FIGURES
FIGURE NO.
Fig 1
Fig 2.1.1
Fig 2.1.2
Fig 2.2.1
Fig 2.2.2
Fig 2.4.1
Fig 3.1.1
Fig 3.1.1.1
Fig 3.1.1.2
Fig 3.1.2
Fig 3.1.2.1
Fig 3.1.3
Fig 3.1.3.1
Fig 3.1.3.2
Fig 3.1.4.1
Fig 3.1.4.2
Fig 3.1.4.2.1
Fig 3.1.4.3
Fig 3.1.4.3.1
Fig 3.1.5
Fig 3.1.5.1
Fig 3.1.6
Fig 3.2.1
Fig 3.3.1
Fig 3.3.1.1
Fig 3.3.2
Fig 3.4
Fig A.1
Fig A.1.2.1
Fig A.1.3
Fig A.1.4.1
Fig A.1.10
Fig A.1.11
Fig A.1.11.2
Fig A.1.11.3
Fig A.1.11.4
Fig A.1.11.5
Fig A.1.11.6
Fig A.1.A.1.1
Fig A.1.A.1.2
DESCRIPTION
Block Diagram of Drive
Structure DC motor
Operation of DC motor
Block of H-Bridge
Operation of H-Bridge
Block of Voltage Sensor
Model of DC motor
Electrical parameter of DC motor
Mechanical Parameter of DC motor
Model of H-Bridge
Parameter of H- Bridge
Model of PWM
Parameter of PWM
Waveform of PWM
Ideal Rotational Sensor
Model of voltage Sensor
Parameter of voltage Sensor
Model of Hall effect Sensor
Parameter of HE sensor
Variable Load Torque
Parameter of variable Load torque
Model of Sink(scopes)
Simulink Model of Speed Drive with Variable Load
Parameter of Fan Load
Simulink model of Fan Load
ON Automobile model
Simulink Model of ON Automobile
Command Window
Simulink Library
Model building
States Block
Zero crossing
Threshold Signal
Algebraic loop
Ability of algebraic loop
Atomic Subsystem
Compile Version of system model
Error in model
Graphical user’s Debugger
Starting of Debugging
PAGE NO.
2
3
3
7
7
11
13
13
14
14
15
17
17
19
19
20
21
21
22
22
23
23
25
29
29
31
31
37
37
38
41
52
54
57
58
58
59
59
61
61

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LIST OF TABLES
TABLE No.
1
A.1.5.2
A.1.A.1.10
A.1.A.1.11
A.1.A.1
DESCRIPTION
Operation of H-Bridge
Different sample at various time
Zero Crossing Algorithm
Description of Zero Crossing
Description of Buttons
PAGE NO.
8
44
52
55
62

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LIST OF PLOTS
PLOT NO.
Plot 3.1
Plot 3.2.1
Plot 3.2.2
Plot 3.2.3
Plot 3.3
Plot3.4.1
Plot 3.4.2
DESCRIPTION
Result of Variable Load
Variation of Torque according Load
Result of Speed according Load
Graph of variation in rpm, voltage and Torque
Result of ON Fan Load
Result of ON automobile model
Speed curve of ON automobile model
PAGE NO.
24
26
27
28
30
32
32

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CHAPTER-1
INTRODUCTION
1.1: CONVENTIONAL METHODS OF SPEED CONTROL
The DC motors used in industrial applications have progressively gotten better over the
years.Along with this, the way we control these motors has continued to improve. From the old
rheostat which gave the way to solid state electronics and then the DCC and there after the PID
controller
A PID is a generic control loop feedback motor. It calculates the difference between a measured
process variable and desired set point. It tries to minimize the error by adjusting the control
inputs. As PID controllers require exact mathematical modeling, the performance is questionable
if there is any parameter variation. It does not guarantee optimal control of the system. It is a
time consuming process as we cannot get the required speed till the error produced equals to
zero. Mechanism used to control the speed of the
1.2:ADOPTED TECHNIQUE
In this project we are designing the H- Bridge and controlling the input voltage of the DC motor
by PWM technique.PWM is an effective method for adjusting the amount of power delivered to
the load. PWM technique allows smooth speed variation without reducing the starting torque and
eliminates harmonics. The H-Bridge allows the bidirectional rotation of the DC motor. In PWM
method, operating power to the motors is turned on and off to modulate the current to the motor.
The ratio of on to off time is called as duty cycle. The duty cycle determines the speed of the
motor. The desired speed can be obtained by changing the duty cycle.
1.3: BLOCK DIAGRAM

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Fig 1-Block Diagram of Drive
CHAPTER-2

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GENERAL INFORMATION OF COMPONENTS
2.1DC MOTOR
2.1.1: WORKING PRINCIPLE OF A DC MOTOR
A DC motor is an electric motor that runs on DC electricity. It works on the principle of
electromagnetism. A current carrying conductor when placed in an external magnetic field will
experience a force proportional to the current in the conductor.
Fig 2.1.1 -DC Motor
2.1.2: OPERATION OF A DC MOTOR
There are two magnetic fields produced in the motor. One magnetic field is produced by the
permanent magnets and the other magnetic field is produced by the electrical current flowing in
the motor windings. These two fields result in a torque which tends to rotate the rotor. As the
rotor turns, the current in the windings is commutated to produce a continuous
Torque output this makes the motor to run.
Fig 2.1.2 Operation Of DC Motor
2.1.3: SPEED CONTROL METHODS OF DC MOTOR

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They are various methods used to control the speed of a DC motor. Some of them are:
1. Armature control method
2. Flux control method
3. Ward Leonard system.
Armature control method:Speed can be controlled by varying the voltage. As speed is directly
proportional to the voltage. As voltage increases speed increases and vice-versa. A simple
voltage regulation would cause lots of power loss on control circuit. So we are going for PWM.
In this method the duty cycle determines the speed of the DC motor. Required speed can be
attained by changing the duty cycles. PWM also allows smooth speed variation without reducing
the torque. It also eliminates harmonics.
2.1.4: BRAKING OF DC MOTOR
When a motor is switched off it ‘coasts’ to rest under the action of frictional forces.
Braking is employed when rapid stopping is required. In many cases mechanical braking is
adopted. The electric braking may be done for various reasons such as those mentioned below:
1. To augment the brake power of the mechanical brakes.
2. To save the life of the mechanical brakes.
3. To regenerate the electrical power and improve the energy efficiency.
4. In the case of emergencies to step the machine instantly.
5. To improve the through put in many production process by reducing the stopping time.
In many cases electric braking makes more brake power available to the braking process where
mechanical brakes are applied. This reduces the wear and tear of the mechanical brakes and
reduces the frequency of the replacement of these parts. By recovering the mechanical energy
stored in the rotating parts and pumping it into the supply lines the overall energy efficiency is
improved. This is called regeneration. Where the safety of the personnel or the equipment is at
stake the machine may be required to stop instantly. Extremely large brake power is needed
under those conditions. Electric braking can help in these situations also. In processes where
frequent starting and stopping is involved the process time requirement can be reduced if braking
time is reduced. The reduction of the process time improves the throughput.
Basically the electric braking involved is fairly simple. The electric motor can be made to work
as a generator by suitable terminal conditions and absorb mechanical energy.This converted
mechanical power is dissipated/used on the electrical network suitably.
Braking can be broadly classified into:
1. Dynamic
2. Regenerative
3. Reverse voltage braking or plugging

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2.1.5-WHERE IS THE MOTOR CONTROLLER?
A motor controller is a device or group of devices that serves to govern in some predetermined
manner the performance of an electric motor. A motor controller might include a manual or
automatic means for starting and stopping the motor, selecting forward or reverse rotation,
selecting and regulating the speed, regulating or limiting the torque and protecting against over
load and fault.
2.1.5.1-SCOPE OF MOTOR CONTROLLER APPLICATIONS
The scope of motor control technology must be very wide to accommodate the wide variety of
motor applications.
2.1.5.2-DOMESTIC APPLICATIONS-
Electric motor are used domestically in the personal care products .small and large appliances
,and residential heating and cooling equipment .In most domestic applications the motor
controller functions are built in to the product .In some cases such as bathroom ventilation ,
ventilation fans ,motor is control by a switch on the wall.
2.1.5.3-OFFICE EQUIPMENT, MEDICAL EQUIPMENT, ETC-
There is a wide variety of motorized office equipment such as personal computers, computer
peripheral, photo copy machines and fax machines as well as smaller items such as electric
pencil sharpeners .Motor controller for these type equipment are built in to the equipment. Some
quite sophisticated motor controller are used to control the motor in the computer disk drive
.Medical equipment may include very sophisticated motor controllers .
2.1.5.4-COMMERCIAL APPLICATIONS-
Commercial buildings have larger heating ventilation and air conditioning (HVAC) equipment
than that found in individual residence. In addition motors are used for elevators, escalators and
other applications. In commercial applications ,the motor control functions are sometimes built
in to the motor driven equipment and some time installed separately.
2.1.5.5-INDUSTRIAL APPLICATIONS-

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Many industrial applications are dependent upon motors or machines, which range from the size
of your thumb to the size of rail road locomotive. In the motor controllers can be built in to the
driven equipment, installed separately, installed in an in closer along with the machine control
equipment or installed in motor control centers (MCC ROOM).
An electric vehicle (EV), also referred to as an electric drive vehicle, uses one or more electric
motor or traction motor forpropulsion. Three main types of electric vehicles exist, those that are
directly powered from an external power station, those that are powered by stored electricity
originally from an external power source, and those that are powered by an on-board electrical
generator, such as an internal combustion engine (a hybrid electric vehicle) or a hydrogen fuel
cell. Electric vehicles include electric cars, electric trains, electric lorries, electric airplanes,
electric boats, electric motorcycles and scooters and electric spacecraft.
2.1.5.6-POWER TOOLS
- Power tools such as drills, saws, and sanders are widely used by home
owners, hobbyists, construction and trade people and industrial workers. Both portable and
stationary power tools usually have built in motor controllers and often include adjustable speed.
2.2 H Bridge
An H bridge is an electronic circuit that enables a voltage to be applied across a load in either
direction. These circuits are often used in robotics and other applications to allow DC motors to
run forwards and backwards. H bridges are available as integrated circuits, or can be built from
discrete components.
2.2.1 GENERAL
The term H Bridge is derived from the typical graphical representation of such a circuit. An H
bridge is built with four switches (solid-state or mechanical). When the switches S1 and S4
(according to the first figure) are closed (and S2 and S3 are open) a positive voltage will be
applied across the motor. By opening S1 and S4 switches and closing S2 and S3 switches, this
voltage is reversed, allowing reverse operation of the motor.
Using the nomenclature above, the switches S1 and S2 should never be closed at the same time,
as this would cause a short circuit on the input voltage source. The same applies to the switches
S3 and S4. This condition is known as shoot-through.

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Fig 2.2.1 -Block diagram of H-Bridge
2.2.2-OPERATION
The H-bridge arrangement is generally used to reverse the polarity of the motor, but can also be
used to 'brake' the motor, where the motor comes to a sudden stop, as the motor's terminals are
shorted, or to let the motor 'free run' to a stop, as the motor is effectively disconnected from the
circuit. The following table summarizes operation, with S1-S4 corresponding to the diagram
below.
Fig-2.2.2:Operational diagram of H-Bridge

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Table1-Operational result of H Bridge
2.3 PWM(PULSE WIDTH MODULATION)
2.3.1INTRODUCTION
Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a commonly used
technique for controlling power to inertial electrical devices, made practical by modern
electronic power switches.
The average value of voltage (and current) fed to the load is controlled by turning the switch
between supply and load on and off at a fast pace. The longer the switch is on compared to the
off periods, the higher the power supplied to the load is.
The PWM switching frequency has to be much faster than what would affect the load, which is
to say the device that uses the power. Typically switching’s have to be done several times a
minute in an electric stove, 120 Hz in a lamp dimmer, from few kilohertz (kHz) to tens of kHz
for a motor drive and well into the tens or hundreds of kHz in audio amplifiers and computer
power supplies.
The term duty cycle describes the proportion of 'on' time to the regular interval or 'period' of
time; a low duty cycle corresponds to low power, because the power is off for most of the time.
Duty cycle is expressed in percent, 100% being fully on.
The main advantage of PWM is that power loss in the switching devices is very low. When a
switch is off there is practically no current, and when it is on, there is almost no voltage drop

20
across the switch. Power loss, being the product of voltage and current, is thus in both cases
close to zero. PWM also works well with digital controls, which, because of their on/off nature,
can easily set the needed duty cycle.
2.3.2APPLICATIONS AS VOLTAGE REGULATOR
PWM is also used in efficient voltage regulators. By switching voltage to the load with the
appropriate duty cycle, the output will approximate a voltage at the desired level. The switching
noise is usually filtered with an inductor and a capacitor.
One method measures the output voltage. When it is lower than the desired voltage, it turns on
the switch. When the output voltage is above the desired voltage, it turns off the switch
2.3.3 POWER DELIVERY
PWM can be used to control the amount of power delivered to a load without incurring the losses
that would result from linear power delivery by resistive means. Potential drawbacks to this
technique are the pulsations defined by the duty cycle, switching frequency and properties of the
load. With a sufficiently high switching frequency and, when necessary, using additional passive
electronic filters, the pulse train can be smoothed and average analog waveform recovered.
High frequencyPWM power control systems are easily realizable with semiconductor switches.
As explained above, almost no power is dissipated by the switch in either on or off state.
However, during the transitions between on and off states, both voltage and current are non-zero
and thus power is dissipated in the switches. By quickly changing the state between fully on and
fully off (typically less than 100 nanoseconds), the power dissipation in the switches can be quite
low compared to the power being delivered to the load.
Modern semiconductor switches such as MOSFETs or Insulated-gate bipolar transistors (IGBTs)
are well suited components for high efficiency controllers. Frequency converters used to control
AC motors may have efficiencies exceeding 98 %. Switching power supplies have lower
efficiency due to low output voltage levels (often even less than 2 V for microprocessors are
needed) but still more than 6.10-80 % efficiency can be achieved.
Variable-speed fan controllers for computers usually use PWM, as it is far more efficient when
compared to a potentiometer rheostat. (Neither of the latter is practical to operate electronically;
they would require a small drive motor.)
Light dimmers for home use employ a specific type of PWM control. Home-use light dimmers
typically include electronic circuitry which suppresses current flow during defined portions of
each cycle of the AC line voltage. Adjusting the brightness of light emitted by a light source is
then merely a matter of setting at what voltage (or phase) in the AC half cycle the dimmer begins
to provide electrical current to the light source (e.g. by using an electronic switch such as a triac).
In this case the PWM duty cycle is the ratio of the conduction time to the duration of the half AC
cycle defined by the frequency of the AC line voltage (50 Hz or 6.10 Hz depending on the
country).

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These rather simple types of dimmers can be effectively used with inert (or relatively slow
reacting) light sources such as incandescent lamps, for example, for which the additional
modulation in supplied electrical energy which is caused by the dimmer causes only negligible
additional fluctuations in the emitted light. Some other types of light sources such as light-
emitting diodes (LEDs), however, turn on and off extremely rapidly and would perceivably
flicker if supplied with low frequency drive voltages. Perceivable flicker effects from such rapid
response light sources can be reduced by increasing the PWM frequency. If the light fluctuations
are sufficiently rapid, the human visual system can no longer resolve them and the eye perceives
the time average intensity without flicker (see flicker fusion threshold).
In electric cookers, continuously-variable power is applied to the heating elements such as the
hob or the grill using a device known as a Simmer stat. This consists of a thermal oscillator
running at approximately two cycles per minute and the mechanism varies the duty cycle
according to the knob setting. The thermal time constant of the heating elements is several
minutes, so that the temperature fluctuations are too small to matter in practice
2.4 SENSOR
A sensor (also called detector) is a converter that measures a physical quantity and converts it
into a signal which can be read by an observer or by an (today mostly electronic) instrument. For
example, a mercury-in-glass thermometer converts the measured temperature into expansion and
contraction of a liquid which can be read on a calibrated glass tube. A thermocouple converts
temperature to an output voltage which can be read by a voltmeter. For accuracy, most sensors
are calibrated against known standards.
Sensors are used in everyday objects such as touch-sensitive elevator buttons (tactile sensor) and
lamps which dim or brighten by touching the base. There are also innumerable applications for
sensors of which most people are never aware. Applications include cars, machines, aerospace,
medicine, manufacturing and robotics.
A sensor is a device which receives and responds to a signal. A sensor's sensitivity indicates how
much the sensor's output changes when the measured quantity changes. For instance, if the
mercury in a thermometer moves 1 cm when the temperature changes by 1 °C, the sensitivity is
1 cm/°C (it is basically the slope Dy/Dx assuming a linear characteristic). Sensors that measure
very small changes must have very high sensitivities. Sensors also have an impact on what they
measure; for instance, a room temperature thermometer inserted into a hot cup of liquid cools the
liquid while the liquid heats the thermometer. Sensors need to be designed to have a small effect
on what is measured; making the sensor smaller often improves this and may introduce other
advantages. Technological progress allows more and more sensors to be manufactured on a
microscopic scale as micro sensors using MEMS technology. In most cases, a micro sensor
reaches a significantly higher speed and sensitivity compared with macroscopic approaches.

22
2.4.1 VOLTAGE SENSOR
2.4.1.1 OVERVIEW
In this project, the voltage sensor will be a voltage divider coming out of the DC-DC converter in
which it will send the output to the micro-controller. To make this a simple task, we just decided
to create a voltage divider, and by using math, the micro controller can take the output voltage
and then know how much voltage we are getting out of our power supply. The micro-controller
can only intake a maximum of 5 volts, so the voltage sensor has to step down our 25 volts to less
than 5 volts.
2.4.1.2 BLOCK DIAGRAM
Figure2.4.1: Voltage Sensor Block Diagram.

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2.4.2 HALL EFFECT SENSOR
Hall effect sensor is a transducer that varies its output voltage in response to a magnetic field.
Hall effect sensors are used for proximity switching, positioning, speed detection, and current sensing
applications.
In its simplest form, the sensor operates as an analogue transducer, directly returning a voltage. With a
known magnetic field, its distance from the Hall plate can be determined. Using groups of sensors, the
relative position of the magnet can be deduced.
Electricity carried through a conductor will produce a magnetic field that varies with current, and a Hall
sensor can be used to measure the current without interrupting the circuit. Typically, the sensor is
integrated with a wound core or permanent magnet that surrounds the conductor to be measured.
Frequently, a Hall sensor is combined with circuitry that allows the device to act in a digital (on/off)
mode, and may be called a switch in this configuration. Commonly seen in industrial applications such as
the pictured pneumatic cylinder, they are also used in consumer equipment; for example some computer
printers use them to detect missing paper and open covers. When high reliability is required, they are used
in keyboards.

24
CHAPTER-3
PROJECT SIMULATION MODEL AND ITS WORKING
3.1 SPECIFICATIONS OF COMPONANT USED IN PROJECT
3.1.1-D.C.MOTOR BLOCK-
Fig 3.1.1 Model of DC motor
LIBRARY-Actuators & Drivers
SPECIFICATION AND DESCRIPTION
Fig.3.1.1.1-Electrical parameter Of D.C. Motor

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Fig.3.1.1.2-Mechanical parameter of D.C. motor
3.1.2-H-BRIDGE
Fig 3.1.2 Model of H-Bridge
LIBRARY-Actuators & Drivers

26
Fig-3.1.2.1-Parameter of H Bridge
The H-Bridge block represents an H-bridge motor driver. The block has the following two
Simulation mode options:
PWM — The H-Bridge output is a controlled voltage that depends on the input signal at the
PWM port. If the input signal has a value greater than the Enable threshold voltage parameter
value, the H-Bridge output is on and has a value equal to the value of the Output voltage
amplitude parameter. If it has a value less than the Enable threshold voltage parameter value, the
block maintains the load circuit using one of the following two Freewheeling mode options:
A freewheeling diode and a semiconductor switch
Two freewheeling diodes

27
The signal at the REV port determines the polarity of the output. If the value of the signal atthe
REV port is less than the value of the Reverse threshold voltage parameter, the output has
positive polarity; otherwise, it has negative polarity.
Averaged — The H-Bridge output is:
Where:
 VO is the value of the Output voltage amplitude parameter.
 VPWM is the value of the voltage at the PWM port.
 APWM is the value of the PWM signal amplitude parameter.
 IOUT is the value of the output current.
 RON is the Bridge on resistance parameter.
Set the Simulation mode parameter to Average to speed up simulations when driving the H-
Bridge block with a Controlled PWM Voltage block. You must also set the Simulation mode
parameter of the Controlled PWM Voltage block to Averaged mode. This applies the average of
the demanded PWM voltage to the motor. The Averaged mode assumes that the effect of the
motor inductive term is small at the PWM frequency. To verify this assumption, run the
simulation using the PWM mode and compare the results to those obtained from using the
Averaged mode.
3.1.3 PWM
Fig 3.1.3 Model of PWM

28
LIBRARY - Extras/Control Blocks
Fig-3.1.3.1-Parameter of PWM
The PWM Generator block generates pulses for carrier-based pulse width modulation (PWM)
converters using two-level topology. The block can be used to fire the forced-commutated
devices (FETs, GTOs, or IGBTs) of single-phase, two-phase, three-phase, two-level bridges or a
combination of two three-phase bridges.
The pulses are generated by comparing a triangular carrier waveform to a reference modulating
signal. The modulating signals can be generated by the PWM generator itself, or they can be a
vector of external signals connected at the input of the block. One reference signal is needed to
generate the pulses for a single- or a two-arm bridge, and three reference signals are needed to
generate the pulses for a three-phase, single or double bridge.

29
The amplitude (modulation), phase, and frequency of the reference signals are set to control the
output voltage (on the AC terminals) of the bridge connected to the PWM Generator block.
The two pulses firing the two devices of a given arm bridge are complementary. For example,
pulse 4 is low (0) when pulse 3 is high (1). This is illustrated in the next two figures.
The following figure displays the two pulses generated by the PWM Generator block when it is
programmed to control a one-arm bridge.
Fig-3.1.3.2-Wave form of PWM generation(Triangular wave and sinusoidal wave comparison)

30
3.1.4 SENSORS
3.1.4.1 IDEAL ROTATIONAL MOTION SENSOR
Fig-3.14.1 Ideal Rotational Motion Sensor
LIBRARY-Mechanical Sensors
Fig-3.1.4.1- Parameter of Ideal Rotational Motion Sensor
3.1.4.2 VOLTAGE SENSOR
Fig-3.1.4.2 Voltage Sensor

31
LIBRARY- Mechanical Sensors
Fig-3.1.4.2 Parameter of voltage sensor
3.1.4.3HALL EFFECT SENSOR
Fig 3.1.4.3 Model of Hall Effect Sensor
LIBRARY-Mechanical Sensors
This linear actuator consists of a DC motor driving a worm gear which in turn
drives a lead screw to produce linear motion. The actuator is controlled with an inner-loop
current controller, and outer-loop speed controller. This is a detailed model that includes
quantization effects of the Hall-effect sensor and the implementation of the control in analog
electronics. Optionally, the implementation detail of the PWM & H-Bridge subsystem can be
included by right clicking on the block and selecting the Implementation option from the Block
Choice menu. The model will run slowly in this case due to the 10KHz PWM waveform and is
intended for validation only. The Linear Electric Actuator (System- Level Model) shows an
equivalent system-level model suitable for tasks where simulation speed is important.

32
Fig-3.1.4.3.1 Parameter of Hall effect sensor
3.1.5 VARIABLE LOAD TORQUE-
Fig 3.1.5 Model of Variable Load Torque
LIBRARY- Mechanical Sensors
SPECIFICATIONS AND DESCRIPTION

33
Fig-3.1.5.1 -Parameter of variable torque
3.1.6 SCOPES-
We can get the output in scope at different parameter such as loadtorque ,speedmeasurement,
voltage and PWM waveform.
Fig 3.1.6 Model of Load Torque

34
Plot -3.1. Result of variable load torque
3.2 PROJECT INFORMATION
3.2.1 INTRODUCTION
In our project we control the motion of the D.C. motor (permanent magnet type).In this motor
the armature voltage is controlled to control the motion.
We provided the H-bridge to control the motion in bi-direction in many applications we
required the bi-direction control. The mechanical load is connected to the motor at the various
time interval which gives us various loading condition. The speed sensors are required to control
the speed of the speed of the motor .The speed sensor in our project is Hall sensor. The drive
output is tested on the various loading conditions and saw the behavior on these loading
conditions. As we want the constant speed through-out the various loading conditions.
We taken the two domestic loading condition. On the drive these load are-
(1) On fan loading
(2) On automobile model

35
3.2.2PROJECT SIMULATION MODEL
Fig.3.2.1 Simulink model of automatic speed drive with variable load
In the above shown model the input is given to the form of speed demanded and the hole given
model reached to the value described by the load .
There are two blocks used in the feedback
(1)-speed controller
(2)-current controller
Speedcontroller- speed controller is block which controls the motion according to the set
value to the speed. If the output speed is varies from the set value then there is an error and this

36
error can controlled
The output of the current controlled voltage source.
current controller- this given the output controlled voltage. Which controlled by the error signal
of the speed controller. When there is a difference between the set speed and the demanded speed
there is an error signal generate which given to the controlled voltage source which varies it
speed output according to load.
VARIATION IN THE LOAD APPLIED
Plot -3.2.1 variation of torque according load
As seen from the graph the load torque applied to the various time intervals are different .but the
speed output cannot be change because we need constant speed at the output. So the variation in
the output with respect to the time shown below.

37
Plot -3.2.2 Result of speed according load

38
Plot -3.2.3 Graph of the variation in rpm, voltage ,Torque

39
3.3 APPLICATIONS OF THE DRIVE ON THE DOMESTIC LOAD AND
BEHAVIOUR
Now we see the drive behavior on the various domestic applications.
The fan load is given as below.
3.3.1On fan load model
The total fan load = fan inertia load + fan air friction(aero drag)
Fig-3.3.1 Parameter of on load
3.3.1.1THE SIMULINK MODELIS GIVEN ON FAN LOAD AS BELOW
Fig-3.3.1.1 Simulink model of on fan load
As speed demanded in the above model is 2500rpm. now we seen the Simulink result of this
model.

40
3.3.1.2THE SIMULATION RESULTS OF THIS MODELIS GIVEN AS BELOW
Plot 3.3.1 Result of on fan load
as we seen from this model the speed is pick up to the 2500 rpm at the fan load.

41
3.3.2On automobile model–Automobile model is given as below.
Fig-3.3.2 ON automobile model
Block parameters-
 Rear Wheels radius 0.20m
 FrontWheels radius 0.20m
 Rear-Wheels Inertia 0.30 kg*m*m
 Front-Wheels Inertia 0.10 kg*m*m
 Total mass 15Kg
3.4 THE SIMULINK MODEL IS GIVEN ON AUTOMOBILE LOAD AS
BELOW
Fig-3.4.1 Simulink model of ON automobile LOAD
Project - Automatic speed control drive
By - Aditya vikram singh
Munesh kumar singh
Anitya kumar shukla
Devendra kumar
voltage1
voltage
speed m/s
-K-
rpm2volts
V
+
-
Voltage Sensor1
V
+
-
Voltage Sensor
R
C
V
P Velocity
Sensor
Total-vehicle
mass
500
Speed Demand
(rpm)
Y
R
Vi_r
Speed
Controller
f(x)=0
Solver
Configuration
SLV
SL2V_2
SLV
SL2V_1
Rear-wheel
inertia
A P
Rear wheels
and axle
RPM
PWM
PS S
PS-Simulink2
PS S
PS-Simulink1
PS S
PS S
PS-Simulink
Mechanical
Rotational
Reference
Measured & actual
speeds (rpm)
SLV
R
C
W
A
Ideal
Rotational
Motion
Sensor
rpm
V
R
Hall Effect
Sensor
PWM
REF
REV
BRK
+
-
H-Bridge
Front-wheel
inertia
AP
Front wheels
and axle
Electrical Reference
Distance m
1
s
Distance
travelled
integrator
+-
RC
DC Motor
Vi_1
Vi_r
Vr
REV
Current
Controller
+ref
-ref
PWM
REF
Controlled PWM
Voltage

42
3.4.1THE SIMULATION RESULTS OF THIS MODEL IS GIVEN AS
BELOW
Plot-3.5.1 Result of on automobile model
In this model the speed is stable near the 500 rpm (demanded load) but after some time it goes
out of limit. which is not controlled in this model.
6.5.2THE SPEED COVERED IN THIS TIME INTERVAL
Plot-3.5.2 Speed curve for on automobile load with time

43
ADVANTAGE OF THE AUTOMATIC SPEED
CONTROL DRIVE:
(1) The load got the mechanical power as per the requirement of its need so there is
no waste of energy.
(2) The motor works on its rated capacity so the motor operation of time is high.
(3) Optimum utilization of machinery (motor and load combinations).

44
CONCLUSION
The used of the drive circuit when regulated amount of speed required as per the
demanded by the load. Sometime in many applications the required speed is high or low
as per the need for that load .So by the use of the automatic speed control drive we can
regulate the speed of the motor as per the requirement of the load which also reduce the excess
amount of electricity required

45
REFERENCES
·G.K. Dubey, “Fundamentals of Electric Drives”, Narosa publishing House
· . S.K.Pillai, “A First Course on Electric Drives”, New Age International.
· Cowie, Charles J. (2001). Adjustable Frequency Drive Application Training . PowerPoint
presentation.
· Phipps, Clarence A. (1997). Variable Speed Drive Fundamentals.The Fairmont Press, Inc.
ISBN 0- 88173 -258-3
· Spitzer, David W. (1990). Variable Speed Drives. Instrument Society of America.ISBN 1 -
55617-242 - 7.
· Campbell, Sylvester J. (1987). Solid-State AC Motor Controls. New York: Marcel Dekker,
Inc..ISBN 0 8247-7728- X.
· Jaeschke, Ralph L. (1978). Controlling Power Transmission Systems. Cleveland, OH: Pen
ton/IPC.
· Siskin, Charles S. (1963). Electrical Control Systems in Industry. New York: McGraw -Hill,
Inc.ISBN 0- 07 057746 -3
· Variable Speed Pumps Explained
· David Finney Variable frequency AC motor drive systems IET, 1988 ISBN 0 - 86341-
114-2, chapter 10
· Drury, Bill (2009). The Control Techniques Drives and ControlsHandbook (2nded.). London:
Institution of Engineering and Technology. ISBN 978 -1-84919 -013-8

46
APPENDIX
A.1-INTRODUCTION-
Simulink, developed by Math Works, is a commercial tool for modeling, simulating and
analyzing multidomain dynamic systems. Its primary interface is a graphical block diagramming
tool and a customizable set of block libraries. It offers tight integration with the rest of the
MATLAB environment and can either drive MATLAB or be scripted from it. Simulink is widely
used in control theory and digital signal processing for multidomain simulation and Model-Based
Design
The Simulink® Control Design™ software provides tools for linearization and compensator
design for control systems and models. Linearized models often simplify compensator design
and system analysis. This is useful in many industries and applications, including
Aerospace: flight control, guidance, navigation Automotive: cruise control, emissions control,
transmission Equipment manufacturing: motors, disk drives, servos The Simulink Control
Design software works with the Simulink® linearization engine and the Control System
Toolbox™ SISO Design Tool. Use it to Compute operating points of models using specifications
or simulation. Extract linear models from models. Tune compensator blocks in models with
either single or multi-loop configurations.
The Simulink Control Design software provides a graphical user interface (GUI) for performing
linearization and compensator design for Simulink models. This chapter introduces a Quick Start
guide for using this GUI. The remaining chapters give more details on the linearization and
compensator design tasks.
A.1.2 SIMULINK AND ITS RELATION TO MATLAB
The MATLAB® and Simulink ® environments are integrated in to one entity, and thus we can
analyze, simulate, and revise our models in either environment at any point. We invoke
Simulink from within MATLAB. We begin with a few examples and we will discuss generalities
in subsequent chapters. Throughout this text, a left justified horizontal bar will denote the
beginning often example, and a right justified horizontal bar will denote the end of the example.
These bars will not be shown whenever an ex ample begins at the top of a page or at the bottom
of a page. Also, when one example follows immediately after a previous example, the right
justified bar will be omitted.

47
Starting Simulink Software
To start the Simulink software, you must first start the MATLAB® technical computing
environment. Consult your MATLAB documentation for more information. You can then start
the Simulink software in two ways:
On the toolbar, click the Simulink icon. Enter the simulink command at the MATLAB prompt.
The Library Browser appears. It displays a tree-structured view of the Simulink block libraries
installed on your system. You build models by copying blocks from the Library Browser into a
model window (see Editing Blocks). The Simulink library window displays icons representing
the pre-installed block libraries. You can create models by copying blocks from the library
model window.
FigA.1.2-Command window
A.1.2.1 SIMULINK LIBRARY- The simulink library wbrowser window now appear on the
screen most of the blocks neede for the modeling of the system .

48
figA.1.2.1 -Simulink library browser
A.1.3 BASIC ELEMENTS-There is two major classes of element in simulink; Block and lines.
Block are generally used to generate modify, combined, output and display the signal .Lines are
use to connect the blocks and transfer signal from one block to another.
BLOCK-The description of block are as follows-
1-Continuous: Linear, continuous, time system elements (Integrator transfer function state space
models.etc)
2-Discrete: Linear, discrete time system elements (Integrator transfer function state space
models.etc)
3-Functions and tables: User defined functions and tables for interpolating function values .
4-Math: Mathematical operator (Sum, gain, dot product etc.)
5-Nonlinear:Nonlinear operator (coulomb/viscous friction, switches, relays,etc.)
A.1-Signal and system: Block for controlling/monitoring signals and for creating subsystem.
A.1-Sinks-Sinks are used to output or display signals (Display, scopes, graph, etc.)
8-Source-Sources are used to generate various signals (Step, Ramp, Sinusoidal, etc)
LINES-
Lines are used to connect the various blocks and transmit signal in the direction of
arrow. Lines must have always transmit signals from the output terminal of one block to the
input terminal of another block.

49
BUILDING A MODEL-To demonstrate how a system is represented using simulink .We will
build the block diagram for a simple model consists of sinusoidal input multiplied by a constant
gain. Which is shown below-?
Fig A.1.3-model building diagram
A.1.4 HOW SIMULINK WORKS-
Simulink is a software package that enables you to model, simulate, and analyze systems whose
outputs change over time. Such systems are often referred to as dynamic systems. The Simulink
software can be used to explore the behavior of a wide range of real-world dynamic systems,
including electrical circuits, shock absorbers, braking systems, and many other electrical,
mechanical, and thermodynamic systems. This section explains how Simulink works.
Simulating a dynamic system is a two-step process. First, a user creates a block diagram, using
the Simulink model editor, that graphically depicts time-dependent mathematical relationships
among the system's inputs, states, and outputs. The user then commands the Simulink software to
simulate the system represented by the model from a specified start time to a specified stop time.
Modeling Dynamic Systems
Block Diagram Semantics
A classic block diagram model of a dynamic system graphically consists of blocks and lines
(signals). The history of these block diagram models is derived from engineering areas such as
Feedback Control Theory and Signal Processing. A block within a block diagram defines a
dynamic system in itself. The relationships between each elementary dynamic system in a block
diagram are illustrated by the use of signals connecting the blocks. Collectively the blocks and
lines in a block diagram describe an overall dynamic system.
The Simulink product extends these classic block diagram models by introducing the notion of
two classes of blocks, nonvirtual blocks and virtual blocks. Nonvirtual blocks represent
elementary systems. Virtual blocks exist for graphical and organizational convenience only: they
have no effect on the system of equations described by the block diagram model. You can use

50
virtual blocks to improve the readability of your models.
In general, blocks and lines can be used to describe many "models of computations." One
example would be a flow chart. A flow chart consists of blocks and lines, but one cannot describe
general dynamic systems using flow chart semantics.
The term "time-based block used to distinguish block diagrams that describe dynamic systems
from that of other forms of block diagrams, and the term block diagram (or model) is used to
refer to a time-based block diagram unless the context requires explicit distinction.diagram" is
A.1.4.1 To summarize the meaning of time-based block diagrams:
Simulink block diagrams define time-based relationships between signals and state variables.
The solution of a block diagram is obtained by evaluating these relationships over time, where
time starts at a user specified "start time" and ends at a user specified "stop time." Each
evaluation of these relationships is referred to as a time step.
Signals represent quantities that change over time and are defined for all points in time between
the block diagram's start and stop time.
The relationships between signals and state variables are defined by a set of equations
represented by blocks. Each block consists of a set of equations (block methods). These
equations define a relationship between the input signals, output signals and the state variables.
Inherent in the definition of a equation is the notion of parameters, which are the coefficients
found within the equation.
A.1.4.2 Creating Models
The Simulink product provides a graphical editor that allows you to create and connect instances
of block types (see Creating a Model) selected from libraries of block types (see Blocks —
Alphabetical List) via a library browser. Libraries of blocks are provided representing elementary
systems that can be used as building blocks. The blocks supplied with Simulink are called built-
in blocks. Users can also create their own block types and use the Simulink editor to create
instances of them in a diagram. User-defined blocks are called custom blocks.
A.1.4.3 Time
Time is an inherent component of block diagrams in that the results of a block diagram
simulation change with time. Put another way, a block diagram represents the instantaneous
behavior of a dynamic system. Determining a system's behavior over time thus entails repeatedly
solving the model at intervals, called time steps, from the start of the time span to the end of the
time span. The process of solving a model at successive time steps is referred to as simulating the

51
system that the model represents.
A.1.4.5 States
Typically the current values of some system, and hence model, outputs are functions of the
previous values of temporal variables. Such variables are called states. Computing a model's
outputs from a block diagram hence entails saving the value of states at the current time step for
use in computing the outputs at a subsequent time step. This task is performed during simulation
for models that define states.
Two types of states can occur in a Simulink model: discrete and continuous states. A continuous
state changes continuously. Examples of continuous states are the position and speed of a car. A
discrete state is an approximation of a continuous state where the state is updated (recomputed)
using finite (periodic or aperiodic) intervals. An example of a discrete state would be the position
of a car shown on a digital odometer where it is updated every second as opposed to
continuously. In the limit, as the discrete state time interval approaches zero, a discrete state
becomes equivalent to a continuous state.
Blocks implicitly define a model's states. In particular, a block that needs some or all of its
previous outputs to compute its current outputs implicitly defines a set of states that need to be
saved between time steps. Such a block is said to have states.
The following is a graphical representation of a block that has states:
Fig A.1.4 Graphical Representation of state Block
Blocks that define continuous states include the following standard Simulink blocks:
Integrator
State-Space
Transfer Function
Variable Transport Delay
Zero-Pole
The total number of a model's states is the sum of all the states defined by all its blocks.
Determining the number of states in a diagram requires parsing the diagram to determine the
types of blocks that it contains and then aggregating the number of states defined by each
instance of a block type that defines states. This task is performed during the Compilation phase
of a simulation.

52
A.1.4.5.1 Working with States
The following facilities are provided for determining, initializing, and logging a model's states
during simulation:
The model command displays information about the states defined by a model, including the
total number of states defined by the model, the block that defines each state, and the initial
value of each state.
The Simulink debugger displays the value of a state at each time step during a simulation, and
the Simulink debugger's states command displays information about the model's current states
(see Simulink Debugger).
The Data Import/Export pane of a model's Configuration Parameters dialog box (see Importing
and Exporting Data) allows you to specify initial values for a model's states, and to record the
values of the states at each time step during simulation as an array or structure variable in the
MATLAB workspace. The Block Parameters dialog box (and the ContinuousStateAttributes
parameter) allows you to give names to states for those blocks (such as the Integrator) that
employ continuous states. This can simplify analyzing data logged for states, especially when a
block has multiple states.
The Two Cylinder Model with Load Constraints demo illustrates the logging of continuous
states.
A.1.4.5.2 Continuous States
Computing a continuous state entails knowing its rate of change, or derivative. Since the rate of
change of a continuous state typically itself changes continuously (i.e., is itself a state),
computing the value of a continuous state at the current time step entails integration of its
derivative from the start of a simulation. Thus modeling a continuous state entails representing
the operation of integration and the process of computing the state's derivative at each point in
time. Simulink block diagrams use Integrator blocks to indicate integration and a chain of blocks
connected to an integrator block's input to represent the method for computing the state's
derivative. The chain of blocks connected to the integrator block's input is the graphical
counterpart to an ordinary differential equation (ODE).
In general, excluding simple dynamic systems, analytical methods do not exist for integrating the
states of real-world dynamic systems represented by ordinary differential equations. Integrating
the states requires the use of numerical methods called ODE solvers. These various methods
trade computational accuracy for computational workload. The Simulink product comes with
computerized implementations of the most common ODE integration methods and allows a user
to determine which it uses to integrate states represented by Integrator blocks when simulating a
system.

53
Computing the value of a continuous state at the current time step entails integrating its values
from the start of the simulation. The accuracy of numerical integration in turn depends on the
size of the intervals between time steps. In general, the smaller the time step, the more accurate
the simulation. Some ODE solvers, called variable time step solvers, can automatically vary the
size of the time step, based on the rate of change of the state, to achieve a specified level of
accuracy over the course of a simulation. The user can specify the size of the time step in the
case of fixed-step solvers, or the solver can automatically determine the step size in the case of
variable-step solvers. To minimize the computation workload, the variable-step solver chooses
the largest step size consistent with achieving an overall level of precision specified by the user
for the most rapidly changing model state. This ensures that all model states are computed to the
accuracy specified by the user.
A.1.4.5.3 Discrete States
Computing a discrete state requires knowing the relationship between its value at the current
time step and its value at the previous time step. This is referred to this relationship as the state's
update function. A discrete state depends not only on its value at the previous time step but also
on the values of a model's inputs. Modeling a discrete state thus entails modeling the state's
dependency on the systems' inputs at the previous time step. Simulink block diagrams use
specific types of blocks, called discrete blocks, to specify update functions and chains of blocks
connected to the inputs of discrete blocks to model the dependency of a system's discrete states
on its inputs.
As with continuous states, discrete states set a constraint on the simulation time step size.
Specifically, the step size must ensure that all the sample times of the model's states are hit. This
task is assigned to a component of the Simulink system called a discrete solver. Two discrete
solvers are provided: a fixed-step discrete solver and a variable-step discrete solver. The fixed-
step discrete solver determines a fixed step size that hits all the sample times of all the model's
discrete states, regardless of whether the states actually change value at the sample time hits. By
contrast, the variable-step discrete solver varies the step size to ensure that sample time hits
occur only at times when the states change value.
A.1.4.5.4 Modeling Hybrid Systems
A hybrid system is a system that has both discrete and continuous states. Strictly speaking, any
model that has both continuous and discrete sample times are treated as a hybrid model,
presuming that the model has both continuous and discrete states. Solving such a model entails
choosing a step size that satisfies both the precision constraint on the continuous state integration
and the sample time hit constraint on the discrete states. The Simulink software meets this
requirement by passing the next sample time hit, as determined by the discrete solver, as an
additional constraint on the continuous solver. The continuous solver must choose a step size that
advances the simulation up to but not beyond the time of the next sample time hit. The
continuous solver can take a time step short of the next sample time hit to meet its accuracy

54
constraint but it cannot take a step beyond the next sample time hit even if its accuracy constraint
allows it to.
A.1.5 Block Parameters
Key properties of many standard blocks are parameterized. For example, the Constant value of
the Simulink Constant block is a parameter. Each parameterized block has a block dialog that lets
you set the values of the parameters. You can use MATLAB expressions to specify parameter
values. Simulink evaluates the expressions before running a simulation. You can change the
values of parameters during a simulation. This allows you to determine interactively the most
suitable value for a parameter.
A parameterized block effectively represents a family of similar blocks. For example, when
creating a model, you can set the Constant value parameter of each instance of the Constant
block separately so that each instance behaves differently. Because it allows each standard block
to represent a family of blocks, block parameterization greatly increases the modeling power of
the standard Simulink libraries.
A.1.5.1 Tunable Parameters
Many block parameters are tunable. A tunable parameter is a parameter whose value can be
changed without recompiling the model (see Model Compilation for more information on
compiling a model). For example, the gain parameter of the Gain block is tunable. You can alter
the block's gain while a simulation is running. If a parameter is not tunable and the simulation is
running, the dialog box control that sets the parameter is disabled.
Note You can not change the values of source block parameters through either a dialog box or
the Model Explorer while a simulation is running. Opening the dialog box of a source block with
tunable parameters causes a running simulation to pause. While the simulation is paused, you can
edit the parameter values displayed on the dialog box. However, you must close the dialog box to
have the changes take effect and allow the simulation to continue.
It should be pointed out that parameter changes do not immediately occur, but are queued up and
then applied at the start of the next time step during model execution. Returning to our example
of the constant block, the function it defines is signal(t) = ConstantValue for all time. If we were
to allow the constant value to be changed immediately, then the solution at the point in time at
which the change occurred would be invalid. Thus we must queue the change for processing at
the next time step.
You can use the Inline parameters option on the Optimization pane of the Configuration
Parameters dialog box to specify that all parameters in your model are nontunable except for
those that you specify. This can speed up execution of large models and enable generation of
faster code from your model. See Configuration Parameters Dialog Box for more information.

55
A.1.5.2 Block Sample Times
Every Simulink block has a sample time which defines when the block will execute . Most
blocks allow you to specify the sample time via a SampleTime parameter. Common choices
include discrete, continuous, and inherited sample times.
Table A.1.5.2 Table of different Sample with sample time
For discrete blocks, the sample time is a vector [Ts, To] where Ts is the time interval or period
between consecutive sample times and To is an initial offset to the sample time. In contrast, the
sample times for no discrete blocks are represented by ordered pairs that use zero, a negative
integer, or infinity to represent a specific type of sample time (see How to View Sample Time
Information). For example, continuous blocks have a nominal sample time of [0, 0] and are used
to model systems in which the states change continuously (e.g., a car accelerating). Whereas you
indicate the sample time type of an inherited block symbolically as [–1, 0] and Simulink then
determines the actual value based upon the context of the inherited block within the model.
Note that not all blocks accept all types of sample times. For example, a discrete block cannot
accept a continuous sample time.
For a visual aid, Simulink allows the optional color-coding and annotation of any block diagram
to indicate the type and speed of the block sample times. You can capture all of the colors and the
annotations within a legend (see How to View Sample Time Information).
For a more detailed discussion of sample times, see
A.1.5.3 Custom Blocks
You can create libraries of custom blocks that you can then use in your models. You can create a
custom block either graphically or programmatically. To create a custom block graphically, you
draw a block diagram representing the block's behavior, wrap this diagram in an instance of the
Simulink Subsystem block, and provide the block with a parameter dialog, using the Simulink
block mask facility. To create a block programmatically, you create an M-file or a MEX-file that
contains the block's system functions (see Writing S-Functions). The resulting file is called an S-
function. You then associate the S-function with instances of the Simulink S-Function block in
your model. You can add a parameter dialog to your S-Function block by wrapping it in a

56
Subsystem block and adding the parameter dialog to the Subsystem block. See Creating Custom
Blocks for more information.
A.1.A.1 Simulating Dynamic Systems
A.1.A.1.1 Model Compilation
The first phase of simulation occurs when you choose Start from the Model Editor's Simulation
menu, with the system's model open. This causes the Simulink engine to invoke the model
compiler. The model compiler converts the model to an executable form, a process called
compilation. In particular, the compiler
Evaluates the model's block parameter expressions to determine their values.
Determines signal attributes, e.g., name, data type, numeric type, and dimensionality, not
explicitly specified by the model and checks that each block can accept the signals connected to
its inputs.
A process called attribute propagation is used to determine unspecified attributes. This process
entails propagating the attributes of a source signal to the inputs of the blocks that it drives.
Performs block reduction optimizations.
Flattens the model hierarchy by replacing virtual subsystems with the blocks that they contain
(see Solvers).
Determines the block sorted order (see Controlling and Displaying the Sorted Order for more
information).
Determines the sample times of all blocks in the model whose sample times you did not
explicitly specify (see How Propagation Affects Inherited Sample Times)
A.1.A.1.2 Link Phase
In this phase, the Simulink Engine allocates memory needed for working areas (signals, states,
and run-time parameters) for execution of the block diagram. It also allocates and initializes
memory for data structures that store run-time information for each block. For built-in blocks,
the principal run-time data structure for a block is called the SimBlock. It stores pointers to a
block's input and output buffers and state and work vectors.

57
A.1.A.1.3 Method Execution Lists
In the Link phase, the Simulink engine also creates method execution lists. These lists list the
most efficient order in which to invoke a model's block methods to compute its outputs. The
block sorted order lists generated during the model compilation phase is used to construct the
method execution lists.
Block Priorities
You can assign update priorities to blocks (see Assigning Block Priorities). The output methods
of higher priority blocks are executed before those of lower priority blocks. The priorities are
honored only if they are consistent with its block sorting rules.
A.1.A.1.4 Block Priorities
You can assign update priorities to blocks (see Assigning Block Priorities). The output methods
of higher priority blocks are executed before those of lower priority blocks. The priorities are
honored only if they are consistent with its block sorting rules.
A.1.A.1.5 Simulation Loop Phase
Once the Link Phase completes, the simulation enters the simulation loop phase. In this phase,
the Simulink engine successively computes the states and outputs of the system at intervals from
the simulation start time to the finish time, using information provided by the model. The
successive time points at which the states and outputs are computed are called time steps. The
length of time between steps is called the step size. The step size depends on the type of solver
(see Solvers) used to compute the system's continuous states, the system's fundamental sample
time (see Managing Sample Times in Systems), and whether the system's continuous states have
discontinuities (see Zero-Crossing Detection).
The Simulation Loop phase has two sub phases: the Loop Initialization phase and the Loop
Iteration phase. The initialization phase occurs once, at the start of the loop. The iteration phase
is repeated once per time step from the simulation start time to the simulation stop time.
At the start of the simulation, the model specifies the initial states and outputs of the system to be
simulated. At each step, new values for the system's inputs, states, and outputs are computed, and
the model is updated to reflect the computed values. At the end of the simulation, the model
reflects the final values of the system's inputs, states, and outputs. The Simulink software
provides data display and logging blocks. You can display and/or log intermediate results by
including these blocks in your model.

58
A.1.A.1.A.1 Simulation Loop Phase
Once the Link Phase completes, the simulation enters the simulation loop phase. In this phase,
the Simulink engine successively computes the states and outputs of the system at intervals from
the simulation start time to the finish time, using information provided by the model. The
successive time points at which the states and outputs are computed are called time steps. The
length of time between steps is called the step size. The step size depends on the type of solver
(see Solvers) used to compute the system's continuous states, the system's fundamental sample
time (see Managing Sample Times in Systems), and whether the system's continuous states have
discontinuities (see Zero-Crossing Detection).
The Simulation Loop phase has two subphases: the Loop Initialization phase and the Loop
Iteration phase. The initialization phase occurs once, at the start of the loop. The iteration phase
is repeated once per time step from the simulation start time to the simulation stop time.
At the start of the simulation, the model specifies the initial states and outputs of the system to be
simulated. At each step, new values for the system's inputs, states, and outputs are computed, and
the model is updated to reflect the computed values. At the end of the simulation, the model
reflects the final values of the system's inputs, states, and outputs. The Simulink software
provides data display and logging blocks. You can display and/or log intermediate results by
including these blocks in your model.
Loop Iteration
At each time step, the Simulink Engine:
A.1.A.1.A.1 Computes the model's outputs.
The Simulink Engine initiates this step by invoking the Simulink model Outputs method. The
model Outputs method in turn invokes the model system Outputs method, which invokes the
Outputs methods of the blocks that the model contains in the order specified by the Outputs
method execution lists generated in the Link phase of the simulation (see Solvers).
The system Outputs method passes the following arguments to each block Outputs method: a
pointer to the block's data structure and to its SimBlock structure. The SimBlock data structures
point to information that the Outputs method needs to compute the block's outputs, including the
location of its input buffers and its output buffers.
A.1.A.1.8 Computes the model's states.
The Simulink Engine computes a model's states by invoking a solver. Which solver it invokes
depends on whether the model has no states, only discrete states, only continuous states, or both
continuous and discrete states.
If the model has only discrete states, the Simulink Engine invokes the discrete solver selected by

59
the user. The solver computes the size of the time step needed to hit the model's sample times. It
then invokes the Update method of the model. The model Update method invokes the Update
method of its system, which invokes the Update methods of each of the blocks that the system
contains in the order specified by the Update method lists generated in the Link phase.
If the model has only continuous states, the Simulink Engine invokes the continuous solver
specified by the model. Depending on the solver, the solver either in turn calls the Derivatives
method of the model once or enters a subcycle of minor time steps where the solver repeatedly
calls the model's Outputs methods and Derivatives methods to compute the model's outputs and
derivatives at successive intervals within the major time step. This is done to increase the
accuracy of the state computation. The model Outputs method and Derivatives methods in turn
invoke their corresponding system methods, which invoke the block Outputs and Derivatives in
the order specified by the Outputs and Derivatives methods execution lists generated in the Link
phase.
Optionally checks for discontinuities in the continuous states of blocks.
A technique called zero-crossing detection is used to detect discontinuities in continuous states.
See Zero-Crossing Detection for more information.
Computes the time for the next time step.
Steps 1 through 4 are repeated until the simulation stop time is reached.
A.1.A.1.9 Solvers
A dynamic system is simulated by computing its states at successive time steps over a specified
time span, using information provided by the model. The process of computing the successive
states of a system from its model is known as solving the model. No single method of solving a
model suffices for all systems. Accordingly, a set of programs, known as solvers, are provided
that each embody a particular approach to solving a model. The Configuration Parameters dialog
box allows you to choose the solver most suitable for your model (see Choosing a Solver Type).
Fixed-Step Solvers Versus Variable-Step Solvers
The solvers provided in the Simulink software fall into two basic categories: fixed-step and
variable-step.
Fixed-step solvers solve the model at regular time intervals from the beginning to the end of the
simulation. The size of the interval is known as the step size. You can specify the step size or let
the solver choose the step size. Generally, decreasing the step size increases the accuracy of the
results while increasing the time required to simulate the system.
Variable-step solvers vary the step size during the simulation, reducing the step size to increase

60
accuracy when a model's states are changing rapidly and increasing the step size to avoid taking
unnecessary steps when the model's states are changing slowly. Computing the step size adds to
the computational overhead at each step but can reduce the total number of steps, and hence
simulation time, required to maintain a specified level of accuracy for models with rapidly
changing or piecewise continuous states.
Continuous Versus Discrete Solvers
The Simulink product provides both continuous and discrete solvers.
Continuous solvers use numerical integration to compute a model's continuous states at the
current time step based on the states at previous time steps and the state derivatives. Continuous
solvers rely on the individual blocks to compute the values of the model's discrete states at each
time step.
Mathematicians have developed a wide variety of numerical integration techniques for solving
the ordinary differential equations (ODEs) that represent the continuous states of dynamic
systems. An extensive set of fixed-step and variable-step continuous solvers are provided, each
of which implements a specific ODE solution method (see Choosing a Solver Type).
Discrete solvers exist primarily to solve purely discrete models. They compute the next
simulation time step for a model and nothing else. In performing these computations, they rely
on each block in the model to update its individual discrete states. They do not compute
continuous states.
Two discrete solvers are provided: A fixed-step discrete solver and a variable-step discrete solver.
The fixed-step solver by default chooses a step size and hence simulation rate fast enough to
track state changes in the fastest block in your model. The variable-step solver adjusts the
simulation step size to keep pace with the actual rate of discrete state changes in your model.
This can avoid unnecessary steps and hence shorten simulation time for multi rate models (see
Managing Sample Times in Systems for more information).
A.1.A.1.10Minor Time Steps
Some continuous solvers subdivide the simulation time span into major and minor time steps,
where a minor time step represents a subdivision of the major time step. The solver produces a
result at each major time step. It uses results at the minor time steps to improve the accuracy of
the result at the major time step.
A.1.A.1.10.1 Shape Preservation
Usually the integration step size is only related to the current step size and the current integration
error. However, for signals whose derivative changes rapidly more accurate integration results
can be obtained by including the derivative input information at each time step. This is done by
activating the Shapes Preservation option in the Solver pane of the Configuration Parameter
dialog.

61
A.1.A.1.10.2 Zero-Crossing Detection
A variable-step solver dynamically adjusts the time step size, causing it to increase when a
variable is changing slowly and to decrease when the variable changes rapidly. This behavior
causes the solver to take many small steps in the vicinity of a discontinuity because the variable
is rapidly changing in this region. This improves accuracy but can lead to excessive simulation
times.
The Simulink software uses a technique known as zero-crossing detection to accurately locate a
discontinuity without resorting to excessively small time steps. Usually this technique improves
simulation run time, but it can cause some simulations to halt before the intended completion
time.
Two algorithms are provided in the Simulink software: Nonadaptive and Adaptive. For
information about these techniques, see Zero-Crossing Algorithms.
Demonstrating Effects of Excessive Zero-Crossing DetectionThe Simulink software comes with
two demos that illustrate zero-crossing behavior.Run the bounce demo to see how excessive zero
crossings can cause a simulation to halt before the intended completion time.Run the double
bounce demo to see how the adaptive algorithm successfully solves a complex system with two
distinct zero-crossing requirements.
A.1.A.1.10.3 The Bounce Demo.
Load the demo by typing bounce at the MATLAB command prompt.Once the block diagram
appears, navigate to the Configuration Parameters dialog box. Confirm that the Algorithm is set
to No adaptive.Run the model for a simulation time of 20 seconds.After the simulation
completes, click on the scope to display the results.You may need to click on Auto scale to get a
clear display.Use the scope zoom controls to closely examine the last portion of the simulation.
You can see that the velocity is hovering just above zero at the last time point.Change the
simulation run time to 25 seconds, and run the simulation again.This time the simulation halts
with an error shortly after it passes the simulated 20 second time point.
Excessive chattering as the ball repeatedly approaches zero velocity has caused the simulation to
exceed the default limit of 1000 for the number of consecutive zero crossings allowed. Although
this limit can be increased by adjusting the Number of consecutive zero crossings parameter in
the Configuration Parameters dialog box, doing so in this case does not allow the simulation to
simulate for 25 seconds.Navigate to the Configuration Parameters dialog box and select the
Adaptive Algorithm from the Algorithm pull down.
Change the simulation time to 25 seconds, and run the simulation again.This time the simulation
runs to completion because the adaptive algorithm prevented an excessive number of zero
crossings from occurring.

62
A.1.A.1.10.4 The Double bounce Demo.
Load the demo by typing double bounce at the MATLAB command prompt.In the demo, click
the No adaptive button. This causes the demo to run with the Nonadaptive Algorithm. This is the
default setting used by the Simulink software for all models.Notice that the two balls hit the
ground and recoil at different times.The simulation halts after 14 seconds because the ball on the
left has exceeded the number of zero crossings limit. The ball on the right is left hanging in mid
air.
Click on the error message to clear it.
Click on the Adaptive button to run the simulation with the Adaptive Algorithm.
Notice that this time the simulation runs to completion, even when the ground shifts out from
underneath the ball on the left after 20 seconds.
How the Simulator Can Miss Zero-Crossing Events
The bounce and double-bounce demos show that high-frequency fluctuations about a
discontinuity ('chattering') can cause a simulation to prematurely halt.
It is also possible for the solver to entirely miss zero crossings if the solver error tolerances are
too large. This is possible because the zero-crossing detection technique checks to see if the
value of a signal has changed sign after a major time step. A sign change indicates that a zero
crossing has occurred, and the zero-crossing algorithm will then hunt for the precise crossing
time. However, if a zero crossing occurs within a time step, but the values at the beginning and
end of the step do not indicate a sign change, the solver steps over the crossing without detecting
it.
The following figure shows a signal that crosses zero. In the first instance, the integrator steps
over the event because the sign has not changed between time steps. In the second, the solver
detects change in sign and so detects the zero-crossing event.
Fig A.1.A.1.10 zero crossing detection

63
Preventing Excessive Zero CrossingsUsethie following table to help you prevent excessive zero-
crossing errors in your model.
TABLEA.1.A.1.10.-Zero-Crossing Algorithms
The Simulink software includes two zero-crossing detection algorithms: Nonadaptive and
Adaptive.
To choose the algorithm, either use the Algorithm option in the Solver pane of the Configuration
Parameter dialog box, or use the ZeroCrossAlgorithm command. The command can either be set
to 'No adaptive' or 'Adaptive'.
The No adaptive algorithm is provided for backwards compatibility with older versions of
Simulink and is the default. It brackets the zero-crossing event and uses increasingly smaller
time steps to pinpoint when the zero crossing has occurred. Although adequate for many types of
simulations, the No adaptive algorithm can result in very long simulation times when a high
degree of 'chattering' (high frequency oscillation around the zero-crossing point) is present.
The Adaptive algorithm dynamically turns the bracketing on and off, and is a good choice when:
The system contains a large amount of chattering.

64
You wish to specify a guard band (tolerance) around which the zero crossing is detected.
The Adaptive algorithm turns off zero-crossing bracketing (stops iterating) if either of the
following are satisfied:
The zero crossing error is exceeded. This is determined by the value specified in the Signal
threshold option in the Solver pane of the Configuration Parameters dialog box. This can also be
set with the ZCThreshold command. The default is Auto, but you can enter any real number
greater than zero for the tolerance.
The system has exceeded the number of consecutive zero crossings specified in the Number of
consecutive zero crossings option in the Solver pane of the Configuration Parameters dialog box.
Alternatively, this can be set with the MaxConsecutiveZCs command.
A.1.A.1.11 Understanding Signal Threshold
The Adaptive algorithm automatically sets a tolerance for zero-crossing detection. Alternatively,
you can set the tolerance by entering a real number greater than or equal to zero in the
Configuration Parameters Solver pane, Signal threshold pull down. This option only becomes
active when the zero-crossing algorithm is set to Adaptive.
This graphic shows how the Signal threshold sets a window region around the zero-crossing
point. Signals falling within this window are considered as being at zero.
Fig A.1.A.1.11 Threshold Signal
The zero-crossing event is bracketed by time steps Tn-1 and Tn. The solver iteratively reduces
the time steps until the state variable lies within the band defined by the signal threshold, or until
the number of consecutive zero crossings equals or exceeds the value in the Configuration
Parameters Solver pane, Number of consecutive zero crossings pull down.
It is evident from the figure that increasing the signal threshold increases the distance between
the time steps which will be executed. This often results in faster simulation times, but could
reduce accuracy.
How Blocks Work with Zero-Crossing Detection

65
A block can register a set of zero-crossing variables, each of which is a function of a state
variable that can have a discontinuity. The zero-crossing function passes through zero from a
positive or negative value when the corresponding discontinuity occurs. The registered zero-
crossing variables are updated at the end of each simulation step, and any variable that has
changed sign is identified as having had a zero-crossing event.
If any zero crossings are detected, the Simulink software interpolates between the previous and
current values of each variable that changed sign to estimate the times of the zero crossings (that
is, the discontinuities).
Blocks That Register Zero Crossings. The following table lists blocks that register zero
crossings and explains how the blocks use the zero crossings:
Table A.1.A.1.11 Description of Zero Crossing
A.1.A.1.11.1 Implementation Example: Saturation Block. An example of a Simulink block
that registers zero crossings is the Saturation block. Zero-crossing detection identifies these state
events in the Saturation block:
The input signal reaches the upper limit.
The input signal leaves the upper limit.
The input signal reaches the lower limit.

66
The input signal leaves the lower limit.
Simulink blocks that define their own state events are considered to have intrinsic zero crossings.
Use the Hit Crossing block to receive explicit notification of a zero-crossing event. See Blocks
That Register Zero Crossings for a list of blocks that incorporate zero crossings.
The detection of a state event depends on the construction of an internal zero-crossing signal.
This signal is not accessible by the block diagram. For the Saturation block, the signal that is
used to detect zero crossings for the upper limit is zcSignal = UpperLimit - u, where u is the
input signal.
Zero-crossing signals have a direction attribute, which can have these values:
rising — A zero crossing occurs when a signal rises to or through zero, or when a signal leaves
zero and becomes positive.
falling — A zero crossing occurs when a signal falls to or through zero, or when a signal leaves
zero and becomes negative.
either — A zero crossing occurs if either a rising or falling condition occurs.
For the Saturation block's upper limit, the direction of the zero crossing is either. This enables the
entering and leaving saturation events to be detected using the same zero-crossing signal.
A.1.A.1.11.2 Algebraic Loops
Some Simulink blocks have input ports with direct feedthrough. This means that the output of
these blocks cannot be computed without knowing the values of the signals entering the blocks at
these input ports. Some examples of blocks with direct feedthrough inputs are as follows:
Math Function block
Gain block
Integrator block's initial condition ports
Product block
State-Space block when there is a nonzero D matrix
Sum block
Transfer Fcn block when the numerator and denominator are of the same order

67
Zero-Pole block when there are as many zeros as poles
An algebraic loop generally occurs when an input port with direct feedthrough is driven by the
output of the same block, either directly, or by a feedback path through other blocks with direct
feedthrough. An example of an algebraic loop is this simple scalar loop
Mathematically, this loop implies that the output of the Sum block is an algebraic state z
constrained to equal the first input u minus z (i.e., z = u - z). The solution of this simple loop is z
= u/2, but most algebraic loops cannot be solved by inspection.
It is easy to create vector algebraic loops with multiple algebraic state variables z1, z2, etc., as
shown in this model.
Fig Algebraic Loop
A.1.A.1.11.3Eliminating Algebraic Loops
The Simulink software can eliminate some algebraic loops that include any of the following
types of blocks:
Atomic Subsystem
Enabled Subsystem
Model
To enable automatic algebraic loop elimination for a loop involving a particular instance of an
Atomic Subsystem or Enabled Subsystem block, select the Minimize algebraic loop occurrences
parameter on the block's parameters dialog box. To enable algebraic loop elimination for a loop
involving a Model block, select the Minimize algebraic loop occurrences parameter on the
Model Referencing Pane of the Configuration Parameters dialog box (see Model Referencing

68
Pane) of the model referenced by the Model block. If a loop includes more than one instance of
these blocks, you should enable algebraic loop elimination for all of them, including nested
blocks.
Algebraic loop minimization is off by default because it is incompatible with conditional input
branch optimization in Simulink (see Optimization Pane ) and with single output/update function
optimization in Real-Time Workshop®. If you need these optimizations for an atomic or enabled
subsystem or referenced model involved in an algebraic loop, you must eliminate the algebraic
loop yourself.
The Minimize algebraic loop solver diagnostic allows you to specify the action Simulink should
take, for example, display a warning, if it is unable to eliminate an algebraic loop involving a
block for which algebraic loop elimination is enabled. See Diagnostics Pane: Solver for more
information.
As an example of the ability of the Simulink software to eliminate algebraic loops, consider the
following model.
Fig A.1.A.1.11.3 Ability Of Software
Simulating this model with the solver's Algebraic Loop diagnostic set to error (see Diagnostics
Pane: Solver for more information) reveals that this model contains an algebraic loop involving
its atomic subsystem.Fig A.1.A.1.11.4 Atomic Subsystem

69
Checking the atomic subsystem's Minimize algebraic loop occurrences parameter eliminates the
algebraic loop from the compiled version of the model.
Fig A.1.A.1.11.5 Compile Version of model
As a result, the model now simulates without error.
Fig A.1.A.1.11.A.1 Error of the Model

70
Note that the Simulink software is able to eliminate the algebraic loop involving this model's
atomic subsystem because the atomic subsystem contains a block with a port that does not have
direct feed through, i.e., the Integrator block.
If you remove the Integrator block from the atomic subsystem, the algebraic loop cannot be
eliminated. Hence, attempting to simulate the model results in an error.
Fig A.1.A.1.11.A.1 Elimination Of Error
A.1.A.1 SIMULINK DEBUGGER
With the debugger you run your simulation method by method. You can stop after each method
to examine the execution results. In this way you can pinpoint problems in your model to
specific blocks, parameters, or interconnections.
The debugger has both a graphical and a command-line user interface. The
graphical interface allows you to access the most commonly used features of the debugger. The
command-line interface gives you access to all of the capabilities in the debugger. If you can use
either to perform a task, the documentation shows you first how to use the graphical interface,
then the command-line interface.

71
A.1.A.1.1 Debugger's Graphical User Interface :
Pull down the tool menu from the model window and select the simulink debugger it displayes
the simulinkdebuggers’s GUI as shown below-
Fig A.1.A.1.1 Graphical User’s Debugger
Start the simulation all buttons in tool bar gets enabled as following-
Fig A.1.A.1.2Starting of debugging

72
From left to right, the toolbar contains the following command buttons
Table A.1.A.1.1 Description of Buttons

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