MODELLING & CONTROL OF ELECTROMAGNETIC LEVITATION
SYSTEM
A Project Report submitted to NIT Durgapur
in partial fulfillment of the requirement for the
Bachelor Degree
In
Electrical Engineering
By
Srubabati Basu(13/EE/35)
Kumari Anjali(13/EE/09)
Priyanshu Sharma(13/EE/77)
Dhrubojyoti Ghosh(13/EE/42)
Tanmoy Roy(13/EE/29)
Rajeev Gupta(13/EE/47)
Department of Electrical Engineering
National Institute of Technology
Durgapur - 713209, India
May, 2017
ACKNOWLEDGEMENT
First of all, I would like to express my deep and sincere regard for my supervisor,
Prof. S. Banerjee & Prof. S. K. Dutta , who were primarily responsible for bringing out the
best in me in the area of this research work. This was made possible through endless rounds
of discussions and translating those into something concrete. Their painstaking patience in
correcting all the articles, whether submitting to a Conference, Journal or the thesis work
itself was simply superb.
I would again like to thank Prof. S. Banerjee, Head of The Department of Electrical
Engineering, for being a constant source of guidance for all round development during my
thesis period.
I would also like to thank faculty members and staff of the Department of Electrical
Engineering, for being a constant source of encouragement and co-operation during my
Project period.
Last, but not the least I would express my sincere gratitude to all family members, relatives
and friends for their love, sacrifice and moral support at a critical juncture in my career and
life.
Priyanshu Sharma(13/EE/77)
i
CERTIFICATE
This is to certify that Priyanshu Sharma(13/EE/77) has worked on
“ Modeling & Control of Electromagnetic Levitation System ” under my
supervision and have fulfilled all the requirements for regulations of the
institute relating to nature and period of work.
Prof. S. Banerjee
Head of The Department
Department of Electrical Engineering
National Institute of Technology
Durgapur-713209
ii
ABSTRACT
Magnetic Levitation is a method by which an object is suspended in air by means of
magnetic force. Earnshaw stated that static arrangements of magnet cannot levitate a
body. The exception comes in case of diamagnetic and superconducting materials and by
controlling magnetic field by control method. Diamagnetic materials or superconducting
materials when placed in magnetic field produce magnetic field in opposite direction.
Here the problem of controlling the magnetic field by control method is taken up to
levitate a metal hollow sphere. The control problem is to supply controlled current to coil
such that the magnetic force on the levitated body and gravitational force acting on it are
exactly equal. Thus, the magnetic levitation system is inherently unstable without any
control action. It is desirable to not only levitate the object but also at desired position or
continuously track a desired path.
The aim of this thesis was to investigate magnetic levitation and to design a working
system capable of levitating an object from below. The system should be able to levitate
an object from below, clear of an array of electromagnets without any form of support.
There shouldn’t be any object, structure or device assisting in levitation, on the same level
of elevation as the levitating object. The control and circuit complexities have been
investigated and recommendations for improving the designed system are made.
iii
CONTENTS
Acknowledgement
i
Certificate
ii
Abstract
iii
Table of contents
iv - vi
List of figures
vi
List of tables
vii
CHAPTER 1
INTRODUCTION AND LITERATURE STUDY
1.1
Introduction To Magnetic Levitation
2
1.2
The Earnshaw Theorem
2
1.3
Meissner Effect
3
1.4
Electromagnetic Suspension
1.5
Motivation
6
1.6
Organization of the Report
6
3-5
iv
CHAPTER 2
SYSTEM MODELLING
2.1
Introduction
8 - 10
2.2
Model Linearization
10 - 14
CHAPTER 3
CONTROLLER DESIGN
3.1
Uncompensated Maglev System
16
3.2
Phase Lead Controller
17 - 18
3.3
Proportional Plus Derivative Control
18 - 20
3.3.1 Proportional Action
3.3.2 Derivative Action
3.4
Cascaded Control
20 - 24
CHAPTER 4
POWER ELECTRONIC CONVERTERS
4.1 Introduction to Power Electronic Converters
4.2 Types of Converters
26
27 - 38
4.2.1 Buck Converter
4.2.2 Boost Converter
4.2.3 Buck-Boost Converter
4.2.4 H-Bridge Converter
4.2.5 Half Bridge Converter
v
CHAPTER 5
IMPLEMENTATION & RESULTS
5.1 Introduction
40
5.2 Feedback Magnetic Levitation Setup
5.3 Set Of Equipments
40 - 41
42
5.4 Block Diagram
42 - 43
5.5 Observation
44 - 46
5.5.1 With Optimum Parameters
5.5.2 With Decreased Integral Value
5.5.3 With Increased Proportional Gain
5.6 Complete System
46
5.7 Simulink Diagram
47 – 48
CHAPTER 6
MAJOR CONCLUSIONS & FUTURE WORK
6.1 Conclusion
50 - 51
6.2 Future Scope
51
REFERENCES
52
vi
LIST OF FIGURES
Fig.1.1 Block Diagram for Maglev System
3
Fig 1.2: Diagram Showing the Physical Model of A Magnetic Suspension System
4
Fig 1.3: Diagram Showing A Simple Phase Lead Circuit
5
Fig 1.4: Picture Showing a Magnetic Suspension System in Action
5
Fig. 2.1: Free-Body Diagram of a Levitated Object in Electromagnetic Levitation
8
Fig. 2.2: Relation between Inductance and Distance
9
Fig 2.3: Block Diagram of the Closed-Loop Maglev System
12
Fig. 2.4: Schematic View of Magnetic Levitation System Layout
13
Fig.2.5: Magnetic Levitation System Interface
14
Fig. 3.1: Root Locus For Uncompensated System
16
Fig. 3.2: Bode Plot For Uncompensated System
16
Fig. 3.3: Step Response For An Uncompensated System
16
Fig.3.4: Root Locus For Phase Lead Controlled System
17
Fig.3.5: Bode Plot For Phase Lead Controlled System
17
Fig. 3.6: Step Response For Phase Lead Controlled System
18
Fig 3.7: Root Locus For Pd Controlled System
19
Fig 3.8: Bode Plot For Pd Controlled System
19
Fig. 3.9: Step Response For Pd Controlled System
20
Fig. 3.10: Block Diagram Of Cascade Control
21
Fig. 3.11: Basic Block Diagram For The Closed Loop System Of A Maglev System.
22
Fig. 3.12: Simulink Model Of The Closed Loop System.
23
Fig. 3.13 Root-Locus And Bode Plot For The Cascaded Controlled System
23
Fig.3.14: Step Response For Cascaded Controlled System.
24
Fig 4.1: Circuit Diagram Of Buck Converter
27
vii
Fig 4.2: Simulation Of Buck Converter
28
Fig 4.3: Inductor Current Waveform
28
Fig 4.4: Inductor Voltage Waveform
29
Fig 4.5: Gate Pulse Waveform
29
Fig 4.6: Circuit Diagram Of Boost Converter
30
Fig 4.7 Simulation Of Boost Converter
30
Fig 4.8: Inductor Current Waveform
31
Fig 4.9: Inductor Voltage Waveform
31
Fig 4.10: Gate Pulse Waveform
32
Fig 4.11: Circuit Diagram Of Buck-Boost Converter
33
Fig 4.12: Simulation Of Buck Boost Converter
33
Fig 4.13: Inductor Current Waveform
34
Fig 4.14: Inductor Voltage Waveform
34
Fig 4.15: Gate Pulse Waveform
34
Fig 4.16: Circuit Diagram Of H-Bridge Converter
35
Fig 4.17: Simulation Of H Bridge Converter
36
Fig 4.18: Inductor Current Waveform
36
Fig 4.19: Inductor Voltage Waveform
36
Fig 4.20: Gate Pulse Waveform
37
Fig 4.21: Circuit Diagram Of Half Bridge Converter
37
Fig 4.22: Simulation Of Half Bridge Converter
38
Fig 4.23: Output Voltage Waveform
38
Fig 4.24: Gate Pulse Waveform
38
Fig.5.1 Magnetic Levitation Mechanical Unit
41
Fig.5.2: Analog Control Interface Unit
41
Fig.5.3: Block Diagram For Magnetic Levitation System With Controller
42
Fig. 5.4 Schematic Diagram Of Closed Loop System
43
Fig. 5.5: Step Response With Optimum Parameters
43
Fig. 5.6: Sinusoidal Response With Optimum Parameters
44
viii
Fig. 5.7: Sinusoidal Response With Different Parameters
44
Fig. 5.8: Step Response With Different Parameters
45
Fig. 5.9: Step Response With Different Parameters
45
Fig. 5.10: Step Response With Different Parameters
46
LIST OF TABLES
Table 2.1 : Value Of Parameters For Maglev System
ix
14
CHAPTER 1
INTRODUCTION & LITERATURE STUDY
1.1
Introduction To Magnetic Levitation
1.2
The Earnshaw Theorem
1.3
Meissner Effect
1.4
Electromagnetic Suspension
1.5
Motivation
1.6
Organization of the Report
1
1.1 INTRODUCTION TO MAGNETIC LEVITATION
Magnetic levitation is the process of levitating an object by exploiting magnetic fields.
In other words, it is overcoming the gravitational force on an object by applying a
counteracting magnetic field. Either the magnetic force of repulsion or attraction can
be used. In the case of magnetic attraction, the experiment is known as magnetic
suspension. Using magnetic repulsion, it becomes magnetic levitation. In the past,
magnetic levitation was attempted by using permanent magnets. Attempts were made
to find the correct arrangement of permanent magnets to levitate another smaller
magnet, or to suspend a magnet or some other object made of a ferrous material. It
was however, mathematically proven by Earnshaw that a static arrangement of
permanent magnets or charges could not stably magnetically levitate an object Apart
from permanent magnets, other ways to produce magnetic fields can also be used to
perform levitation. One of these is an electro-dynamic system, which exploits Lenz’s
law. When a magnet is moving relative to a conductor in close proximity, a current is
induced within the conductor. This induced current will cause an opposing magnetic
field. This opposing magnetic field can be used to levitate a magnet. This means of
overcoming the restrictions identified by Earnshaw is referred to as oscillation.
Electro-dynamic magnetic levitation also results from an effect observed in
superconductors. This effect was observed by Meissner and is known as the Meissner
effect. This is a special case of diamagnetism. This thesis will mainly deal with
electromagnetic levitation using feedback techniques to attain stable levitation of a
bar magnet.
1.2
THE EARNSHAW THEOREM
Earnshaw’s theorem basically proves that a static magnet cannot be levitated by any
arrangement of permanent magnets or charges. This can be simply proved as
follows:“The static force as a function of position F(x) acting on anybody in vacuum
due to gravitation, electrostatic and magnetostatic fields will always be divergenceless
divF=0. At a point of equilibrium the force is zero. If the equilibrium is stable the force
must point in towards the point of equilibrium on some small sphere around the point.
However, by Gauss' theorem,
The integral of the radial component of the force over the volume inside which is zero.
2
1.3
MEISSNER EFFECT
A special case of diamagnetism is observed in conductors cooled to belowtheir critical
temperature (typically close to 0 K). Below this temperature, they become superconductors,
with an internal resistance of zero. They attain arelative permeability of zero, making them
the perfect diamagnetic material.This allows them to maintain their repelling magnetic field
as long as a foreign source of magnetic flux is present.
1.4
ELECTROMAGNETIC SUSPENSION
The easiest way to levitate an object electromagnetically (from a control perspective) is via
magnetic suspension. The object that is to be levitated is placed below an electromagnet
(only one is required), and the strength of the magnetic field produced by the electromagnet
is controlled to exactly cancel out the downward force on the object caused by its weight.
This method circumvents Earnshaw’s theorem by making use of feedback.
Thus, the system only has to contend with one force, the levitating object’s weight. This
system works via the force of attraction between the electromagnet and the object. Because
of this, the levitating object does not need to be a magnet; it can be any ferrous material. This
further simplifies the design considerations. To prevent the object from immediately
attaching itself to the electromagnet, the object’s position has to be sensed and this
information fedback into the control circuit regulating the current in the electromagnet. This
Produces the basic feedback arrangement depicted below.
FIG 1.1: BLOCK DIAGRAM FOR MAGLEV SYSTEM
3
If the object gets too close to the electromagnet, the current in the electromagnet must be
reduced. If the object gets too far, the current to the electromagnet must be increased. A
possible physical arrangement is shown below:
FIG 1.2: DIAGRAM SHOWING THE PHYSICAL MODEL OF A MAGNETIC SUSPENSION SYSTEM
There are various ways to sense the position of the levitating object. One way isoptically. A
beam of light is shone across the bottom of the electromagnet and detected at the other side.
As the object obscures more and more light (indicating that the object is getting closer to the
electromagnet) the electromagnet controller limits the current more and more. As the object
drops away from the electromagnet, more light is exposed to the sensor, and the current to
the electromagnet is increased. This system can prove difficult to properly set up, as the
alignment of the light source and the light sensor is critical. Also, critical is the shape of the
levitating object, because the rate at which light is obscured or exposed should be linear as
the object rises and falls. This will produce the best results.
The circuit used to implement a solution of this nature only has to achieve linear current
control from 0 amperes to the maximum operating current. Only a single supply is required,
along with the sensor circuitry and the proper gain to the current source control. It has been
noted however, in experiments with this system, that oscillations in the levitating object exist
due to the phase lag caused by the current control circuitry and the electromagnet itself,
which is in fact a large inductive load. In physical terms, the problem is that the circuit reacts
too slowly to the changes in position of the levitating object. If the object drops it is inherently
4
accelerating. The control circuit would over compensate with a large correcting current, and
by the time it slacked off, the object would be accelerating towards the electromagnet. This
causes growing oscillations as the control circuitry constantly over compensates until
eventually levitation cannot be maintained and the object falls. Thus to counteract the phase
lag caused by the control circuitry and the electromagnet, phase lead needs to be added. In
control terms, the position of the levitating object is insufficient information to maintain
stable levitation; the rate of change of position is required as well, i.e. the speed. This can be
achieved with the basic circuit below:
FIG 1.3: DIAGRAM SHOWING A SIMPLE PHASE LEAD CIRCUIT
This circuit would be positioned between the position sensing circuitry and thecurrent
control circuitry. As a heuristic, R2 is usually one tenth of R1 (to limit AC current). C2 is
determined based on the cut-off frequency, i.e. the frequency of the oscillation that must be
eliminated. This is determined according to the equation:
FIG 1.4: PICTURE SHOWING A MAGNETIC SUSPENSION SYSTEM IN ACTION
5
1.5
MOTIVATION
MagLev is a non-contact technology, thus, finds application in high speed transportation
system as there is no friction, since there is no friction it can be applied to high precision
system, also absence of friction gives way to no wear and tear of moving parts which results
in high longevity for example MagLev bearing and also no dust pollution thus creates a clean
environment where very high purity is required example semi-conductor industry. MagLev
also creates environment separation thus one can operate from one environment to another
environment example Heart pump, in medical industry and in hazardous places. Thus,
MagLev can be said to be a future technology and it has a vast area of application to be
uncovered. All this applicability comes at the cost of either a good design of superconducting
magnet (which is inherently stable) or good controller design because fundamentally the
levitation by electromagnet is unstable. Here, we consider for designing a controller which
stabilizes the levitated object through continues monitoring of position and feed backing it.
The MagLev system is a nonlinear and open loop unstable system. Thus it provides an
exciting opportunity for controller designer to explore different control algorithm for the
system.
1.6ORGANIZATION OF THE REPORT
OBJECTIVE: The objective of the work can be directed to design controller considering the
linear model. The controller designed is validated by simulating and implementing on real
time system.
THESIS ORGANISATION: The thesis is organized into five chapters with each chapters has its
own subsection. The chapters are briefly described as below
Chapter 1: This chapter briefly introduces the magnetic levitation technology, history of
development, some application, and motivation of taking the project, literature review of
some previous works and objective of work.
Chapter 2: This chapter describes the Magnetic Levitation setup on which the controller
is tested and mathematical modeling of the system.
Chapter 3: In this chapter controller is designed based on the model achieved.
Chapter 4: simulation and design of power amplifier for current control.
Chapter 5: In this chapter, the controller design is simulated and the results are
discussed. The experiment validation is proposed controller is carried out
Chapter 6 : Conclusion discussion
6
CHAPTER 2
SYSTEM MODELING
2.1
Introduction
2.2
Model Linearization
7
2.1
INTRODUCTION
The basic components of the maglev system include a sensor (infrared emitter-detector pair),
an actuator (the electromagnet), and a controller. The sensor is a phototransistor with a
resistor and can be modeled as a simple gain element. The sensor produces a voltage, vs,
proportional to the object’s position with a gain, β, which is linear around the operating point
and can be determined experimentally. A free-body diagram for a simple maglev system
levitating an object of mass, m, is shown in fig.2.1. There are two forces acting on the ball, the
gravitational force, mg, and the magnetic force, which is given by:
Where x is gap spacing between the pole of the electromagnet and the ball, i is the current
through the inductor, and k is an electromagnetic force constant, which is dependent on the
material properties and physical structure of the magnet. The magnetic force relation is a
simplified approximation for the system; it ignores many non-ideal characteristics.
Specifically, the equation does not account for effects including finite core reluctance,
saturation of the core, magnetic hysteresis, and eddy currents in the core.
The motion of the object is constrained to the vertical axis, and it is also assumed that the
center of mass coincides exactly with the point of application of the electromagnetic forces
𝑣𝑠 = 𝛽𝑥
FIG. 2.1: FREE-BODY DIAGRAM OF A LEVITATED OBJECT IN ELECTROMAGNETIC LEVITATION
8
The magnitude of the force f (x, i, t) exerted across an air gap x (t) by an electromagnet
through which a current of magnitude i(t) flows can be obtained using Faraday’s inductive
law and Ampere’s circuit law as:
Where L(x) is the total inductance of the system
And L1 is the inductance of the coil in the absence of the levitated object, Lo is the additional
inductance contributed by its presence and xo is the air gap when the levitated object is in
equilibrium.The inductance is characterized by the geometry and construction of the
electromagnet, and can be determined experimentally as shown in fig. 2.2 From (4), the
derivative of inductance with respect to position is given by the following relation
The relation between the coil inductance and the air gap is shown in Figure 2.2.
FIG. 2.2: RELATION BETWEEN INDUCTANCE AND DISTANCE
9
Which, on combining with (3), gives:
Where
C is a constant that can be determined experimentally.
2.2MODEL LINEARIZATION
The suspension of a ball with an electromagnet is difficult because it is open-loop unstable
and there isa nonlinear relationship between force, current, and gap between the pole of the
electromagnet and ball. Equilibrium is reached when the magnetic force balances the
gravitational force. Intuitively it makes sense that the system is unstable. Imagine the ball is
sitting at the equilibrium point under a fixed magnetic field, a small deviation towards the
magnet will increase the magnetic force perturbation or a small deviation away from the
magnetic will decrease the magnetic force allowing the ball to fall, also growing the
perturbation. One effective method to stabilize a nonlinear system around an operating point
is to take the first order approximation of the system around that operating point, a
linearization, and then proceed with standard control techniques for linear systems.
Applying Newton’s second law of motion and neglecting the effect of any drag forces, the
governing equation of thesystem can be obtained as:
Substituting Equation (6) into Equation (7) gives:
Where g is the acceleration due to gravity. For designing a linear control strategy, the nonlinear electromagnetic force in Equation (6) is linearized about an equilibrium pointx0.
10
Or
Where
Where i0and x0 are the equilibrium values and δi and δx are incremental values for the
current and position variables, respectively. In the following analysis, I and x represent only
the changes (δi and δx) from equilibrium values of current and position, respectively, and not
their absolute values. From the free body diagram in Fig. 2.1, at equilibrium the magnetic
force on the levitated object equals the gravitational force. By defining f0 as the force to
balance the weight of the object at equilibrium
Neglecting the higher order terms in Equation (10) and Equation(11), the incremental
(control) force required for maintaining equilibrium f (x, i, t) is
The governing equation for the levitated object is determined by application of Newton’s
second law:
On combination with Equation (11), Equation (14), and Equation (15), Equation (16) gives
11
Since at equilibrium, Equation (14) applies, Equation (17) becomes
Taking the Laplace transform of the above equation gives
Thus, the transfer function of the system with the change in current to the coil as the input
and the change in position of the levitated object as the output is given by:
The transfer function has two poles, one of which is in the right half plane at
which makes it unstable in open-loop. A representation of the maglev system is shown in the
block diagram in Figure 3.
FIG 2.3: BLOCK DIAGRAM OF THE CLOSED-LOOP MAGLEV SYSTEM
12
The force constant, C, can be obtained from equation (14) experimentally by levitating an
object of known mass, m, and measuring the current, 0 i and position, x0 .The value of L0 can
then be calculated from Equation (7). Another way to interpret the transfer function for the
maglev system is to consider the sensor output as the system output and the voltage to the
electromagnet as the system input. The electromagnet can be represented as a series
combination of a resistor and inductor. From Kirchoff’s voltage law, the voltage, v, in the coil
can be determined as,
Combining the Laplace transforms of the above equations, the overall transfer-function
between the voltage of the electromagnet as input and the position as the output is
determined as:
The transfer function shows that the system has no zeros and a pole in the right half plane
which makes it open-loop unstable.
A representation of the maglev system setup is shown in Figure 2.4.
FIG. 2.4: SCHEMATIC VIEW OF MAGNETIC LEVITATION SYSTEM LAYOUT
13
Finally the parameters that have been considered for this magnetic levitation system are illustrated
in the table shown below:
PARAMETERS
VALUES
.658kg
7.5cm
7.5cm
1065
7.1 ohm
.440 H
4000 v/m
Mass of the
Height of the cylinder
Diameter of the cylinder
No. of turn in the coil
Resistance of the coil
Inductance of the coil
Sensor gain
TABLE 2.1: VALUE OF PARAMETERS FOR MAGLEV SYSTEM
The physical system interface wiring diagram is shown in figure 2.5
FIG.2.5: MAGNETIC LEVITATION SYSTEM INTERFACE
14
CHAPTER 3
CONTROLLER DESIGN
3.1
Uncompensated Maglev System
3.2
Phase Lead Controller
3.3
Proportional Plus Derivative Control
3.3.1 Proportional Action
3.3.2 Derivative Action
3.4
Cascaded Control
15
3.1 UNCOMPENSATED MAGLEV SYSTEM
Given below is the equation for maglev system which shows that this system has one stable
pole, while the other is still unstable. The following plots (step response, root-locus, Bode
plot) show that the uncompensated system is unstable and cannot be stabilized simply by
changing the system gain.
4.536
G(s)=(𝑠−22.5)(𝑠+22.5)(𝑠+16)
FIG. 3.1: ROOT LOCUS FOR UNCOMPENSATED
SYSTEM
FIG. 3.2: BODE PLOT FOR UNCOMPENSATED
SYSTEM
FIG. 3.3: STEP RESPONSE FOR AN UNCOMPENSATED SYSTEM
16
3.2 PHASE LEAD CONTROLLER
The system is designed to carry out the major Function of stabilizing the working point of the
levitation system. This plot shows that the uncompensated system is unstable and cannot be
stabilized simply by changing the system gain. The simplest way to stabilize the system is to
use the phase-lead compensated controller to cancel the unstable pole. In order to pull the
root-locus into the left-hand plane, a zero needs to be added to the phase-lead compensated
controller in the left-hand plane between the first left-hand plane pole and the origin. The
necessary pole required for the phase-lead compensated controller is placed deeper into the
left-hand plane. This will minimize the impact of the pole of the compensated controller on
the root-locus. The transfer function of the phase-lead compensated controller is shown as:
It seems reasonable to attempt pole-zero cancellation by placing the compensator zero at the
system pole of -22.5. Choose Z1= -22.5 and Z2=-16 to compensate the open loop poles
(-22.5).
G(s)Gc(s)=
63621(𝑠+22.5)(𝑠+16)
(𝑠+400)(𝑠+450)
FIG.3.4: ROOT LOCUS FOR PHASE LEAD
FIG.3.5: BODE PLOT FOR PHASE LEAD
CONTROLLED SYSTEM
CONTROLLED SYSTEM
17
FIG. 3.6: STEP RESPONSE FOR PHASE LEAD CONTROLLED SYSTEM
From the above simulation results of the phase lead compensated controller it is evident that
the phase-lead controller can pull the uncompensated root locus in theright-hand plane into
the left-hand plane, which indicates that the system can be stabilized as shown in figure
above. In the transient state, the simulated result shows that the controller will cause the ball
to return to its original position whenever it is disturbed. Obviously, changes in the
electromagnet’s current occur more quickly than variations in the ball’s position, which
indicates that the controlled electromagnet current can stabilize the disturbances that
otherwise, would cause the ball to either fall or attach itself to the electromagnet.
3.3 PROPORTIONAL PLUS DERIVATIVE CONTROLLER (PD)
Proportional-Derivative control is useful for fast response controllers that do not need a
steady-state error of 0. Proportional controllers are fast. Derivative controllers are fast. The
two together is very fast.
3.3.1 Proportional Action
Proportional action provides an instantaneous response to the control error. This is useful for
improving the response of a stable system but cannot control an unstable system by itself.
Additionally, the gain is the same for all frequencies leaving the system with a nonzero
steady-state error.
3.3.2 Derivative Action
Derivative action acts on the derivative or rate of change of the control error. This provides a
fast response, as opposed to the integral action, but cannot accommodate constant errors (i.e.
the derivative of a constant, nonzero error is 0). Derivatives have a phase of +90 degrees
leading to an anticipatory or predictive response. However, derivative control will produce
18
large control signals in response to high frequency control errors such as set point changes
(step command) and measurement noise.
In order to use derivative control the transfer functions must be proper. This often requires a
pole to be added to the controller (this pole is not present in the equations below).
With proportional controller alone the shape of the open loop transfer function will be the
same as the plant but the overall magnitude of the plant will be higher. With derivative
control the open loop transfer function above the frequency fTo the derivative (zero) will
have a +20 dB/decade slope. The phase will gain +90 degrees above the zero as well.
Integral control drives the system to a steady-state error of zero by averaging the noise and
disturbances. Thus only correcting for the slower error signals such as a step command.
Proportional control will follow the noise and amplify it by the magnitude of the controller.
Derivative control will amplify noise by following the difference between 2 noisy error
signals.
For the given magnetic levitation system:
Transfer function=
4.46
(𝑠+22.5)(𝑠−22.5)(𝑠+150)
Controller,C(s)=
63621(𝑠+20)
(𝑠+100)
FIG 3.7:ROOT LOCUS FOR PD CONTROLLED SYSTEM
19
(27)
(28)
FIG 3.8:BODE PLOT FOR PD CONTROLLED SYSTEM
FIG. 3.9: STEP RESPONSE FOR PD CONTROLLED SYSTEM
3.4 CASCADED CONTROL
When single loop control does not provide acceptable control performance then an
enhancement such as cascade control becomes necessary. In single-loop control, the
controller’s set point is set by an operator, and its output drives a final control element. For
example: a level controller driving a control valve to keep the level at its set point. In a
cascade control arrangement, there are two (or more) controllers of which one controller’s
output drives the set point of another controller. For example: a level controller driving the
set point of a flow controller to keep the level at its set point. The flow controller, in turn,
drives a control valve to match the flow with the set point the level controller is requesting.
The controller driving the set point (the level controller in the example above) is called the
primary, outer, or master controller. The controller receiving the set point (flow controller in
the example) is called the secondary, inner or slave controller.
What are the Advantages of Cascade Control?
There are several advantages of cascade control, and most of them boil down to isolating a
slow control loop from nonlinearities in the final control element. In the example above the
relatively slow level control loop is isolated from any control valve problems by having the
fast flow control loop deal with these problems.
Cascade control design criteria
Cascade control is desired when:
1. Single-loop control does not provide satisfactory control performance.
20
2. A measured secondary variable is available.
A secondary variable must satisfy the following criteria:
1. The secondary variable must indicate the occurrence of an important disturbance.
2. There must be a causal relationship between the manipulated and secondary variables.
3. The secondary variable dynamics must be faster than the primary variable dynamics.
FIG. 3.10:BLOCK DIAGRAM OF CASCADE CONTROL
Taking into account all advantages of cascaded control, it is applied to magnetic levitation
system where inner loop is the current control loop which utilizes Proportional plus Integral
controller in order to reduce steady state error. While the outer loop makes use of
PID(Proportional plus integral plus derivative controller) or Lead-Lag controller to improve
the transient response.
Design should be such that the time constant of the inner current loop becomes around ten
times faster than the outer position loop. After modeling of the inner loop is done it can be
considered as unity as it is ten times faster and the rest modeling is finished on that
assumption.
21
The basic schematic diagram of the entire closed loop system is shown below.
FIG. 3.11: BASIC BLOCK DIAGRAM FOR THE CLOSED LOOP SYSTEM OF A MAGLEV SYSTEM.
The given system has one stable pole at s=-22.5 and one instable pole at s=22.15 for an
operating air-gap of 40mm.The closed loop system has been stabilized by a cascade lead
compensation technique utilizing inner current loop and outer position control loop.
The transfer function of the designed lead controller for an operating air-gap of 40mm is
given by
2.5(𝑠+20)
G(s)=
(29)
(𝑠+192)
The phase-lead compensator design procedure in this case is to place the zero of the
compensator between 0 and -22.5 on the real axis of the s-plane, while the pole of the
compensator is placed ten times to the left of the zero position. Simulation studies are carried
out to find a pole-zero and gain combination so that the system is stable as well as acceptable
performance is obtained. It must be mentioned that since the system is inherently unstable.
In general, both stability and good performance cannot be achieved by using a single
controller.
The root-locus plot of the overall closed loop system with the lead controller is shown in the
fig shown below.
The transfer function of the designed current controller is given by:
Gc(s)=
12𝑠+4000
(30)
𝑠
22
FIG. 3.12: SIMULINK MODEL OF THE CLOSED LOOP SYSTEM.
FIG. 3.13 ROOT-LOCUS AND BODE PLOT FOR THE CASCADED CONTROLLED SYSTEM
23
FIG.3.14: STEP RESPONSE FOR CASCADED CONTROLLED SYSTEM.
24
CHAPTER 4
POWER ELECTRONIC CONVERTERS
4.1 Introduction to Power Electronic Converters
4.2 Types OfConverters
4.2.1 Buck Converter
4.2.2 Boost Converter
4.2.3 Buck-Boost Converter
4.2.4 H-Bridge Converter
4.2.5 Half Bridge Converter
25
4.1 INTRODUCTION TO POWER ELECTRONIC CONVERTERS
The primary task of power electronics is to process and control the flow of electric energy by
supplying voltages and currents in a form that is optimally suited for user loads. Modern
power electronic converters are involved in a very broad spectrum of applications like
switched-mode power supplies, active power filters, electrical-machine-motion-control,
renewable energy conversion systems distributed power generation, flexible AC transmission
systems, and vehicular technology, etc.
Power electronic converters can be found wherever there is a need to modify the electrical
energy form with classical electronics in which electrical currents and voltage are used to
carry information, whereas with power electronics, they carry power. Some examples of uses
for power electronic systems are DC/DC converters used in many mobile devices, such as cell
phones or PDAs, and AC/DC converters in computers and televisions. Large scale power
electronics are used to control hundreds of megawatt of power flow across our nation.
In the electromagnetic levitation system electromagnets are driven either by AC or DC source.
Although several experimental systems using AC sources have been built, these methods are
considered to be suited for applications where mass of the suspended object is small. The
severe constraints imposed by eddy-current losses in the magnet and the rather complex
control circuitry for power modulation makes the AC method of stabilization inappropriate
for heavy payloads .The use of a switching converter with pulsewidth modulation (PWM).
Switched-mode power supplies (SMPSs) have largely replaced linear power supplies because
of improved efficiencies. The heat sink in the system is less than one tenth by volume of its
linear counterpart. Switches are nonlinear devices. Averaged models are needed to study the
steady-state behaviour of switching converters. Moreover, linearized models are needed to
study dynamic behaviour, for control-loop analysis and for compensation in an unstable
system. The magnets used in EMLS are generally large and have large time constants (L/R
ratio). The working air-gap between the magnet pole face and the fixed iron guide rails are
small. The electro-magnetic forces are generally large and unless there is fast control of the
magnet current the levitating object will either be falling on the ground structure or will be
hitting the guide rails above. The magnet current needs to rise and fall in accordance with the
control signal generated by the position controller. The expected variation in the magnet
demand current (small signal component), over its nominal DC value, is expected to be band
limited to around 10 Hz but it is better to have a current tracking capability in the range of up
to 100Hz. The electrical time constant of the EMLS magnet being large, the amplifier needs to
apply considerably large instantaneous voltages to the magnet coil (larger in comparison to
the DC voltage required to maintain just the nominal for allowing quick control of the coil
current.
26
4.2 TYPES OF CONVERTERS
4.2.1 BUCK CONVERTER
A buck converter (step-down converter) is a DC-to-DC power converter which steps down
voltage (while stepping up current) mode power supply (SMPS) typically containing at least
two semiconductors (a diode and a transistor, although modern buck converters frequently
replace the diode with a second transistor used for synchronous rectification) and at least
one energy storage element, a capacitor, inductor, or the two in combination. To reduce
voltage ripple, filters made of capacitors (sometimes in combination with inductors) are
normally added to such a converter's output and input. An essential requirement of the
power circuit is to have quick control over the magnet current and this calls for application of
bipolar voltage (positive as well as negative) across the coil. In other words, not only the
current build up through the magnet coil needs to be fast, current decay must also be quite
fast. The simple circuit proposed here achieves both these objectives. With a fixed duty ratio
of the chopper switch, the mean DC voltage across the capacitor is controlled by the discharge
resistor value. Selection of the resistor must be such that, Coil voltage and coil current during
levitation of electromagnet the nominal operating condition, the capacitor voltage (and hence
coil voltage during OFF state) is nearly equal to the supply voltage (ON state coil voltage). The
capacitor voltage magnitude also affects the maximum switch and diode voltage ratings and
controls the rate of current decay through the coil during OFF state. The capacitor should be
able to handle a ripple current equal to the nominal coil current and hence, a DC capacitor
having required ripple current rating should be used. As the Magnetic Levitation system
requires equal amount of voltage in the both halves so this type of converters are not used.
FIG 4.1: CIRCUIT DIAGRAM OF BUCK CONVERTER
27
FIG 4.2: SIMULATION OF BUCK CONVERTER
FIG 4.3: INDUCTOR CURRENT WAVEFORM
28
FIG 4.4: INDUCTOR VOLTAGE WAVEFORM
FIG 4.5: GATE PULSE WAVEFORM
4.2.2 BOOST CONVERTER
A boost converter (step-up converter) is a DC-to-DC power converter that steps up voltage
(while stepping down current) from its input (supply) to its output (load). It is a class of
switched-mode power supply (SMPS) containing at least two semiconductors (a diode and a
transistor) and at least one energy storage element: a capacitor, inductor, or the two in
combination. To reduce voltage ripple, filters made of capacitors (sometimes in combination
with inductors) are normally added to such a converter's output (load-side filter) and input
29
(supply-side filter).The electrical time constant of the EMLS magnet being large, the amplifier
needs to apply considerably large instantaneous voltages to the magnet coil (larger in
comparison to the DC voltage required to maintain just the nominal current) for allowing
quick control of the coil current .Though boost converter can amplify the voltage nearly 10
times the input voltage still this type of converters are not used as the voltage is not equally
fed to magnetic levitation system in positive and negative half.
FIG 4.6: CIRCUIT DIAGRAM OF BOOST CONVERTER
FIG 4.7 SIMULATION OF BOOST CONVERTER
30
FIG 4.8: INDUCTOR CURRENT WAVEFORM
FIG 4.9: INDUCTOR VOLTAGE WAVEFORM
31
FIG 4.10: GATE PULSE WAVEFORM
4.2.3 BUCK- BOOST CONVERTER
A Buck-Boost converter is a type of switched mode power supply that combines the
principles of the Buck Converter and the Boost converter in a single circuit. Like other SMPS
designs, it provides a regulated DC output voltage from either an AC or a DC input.There are
many applications however, such as battery-powered systems, where the input voltage can
vary widely, starting at full charge and gradually decreasing as the battery charge is used up.
At full charge, where the battery voltage may be higher than actually needed by the circuit
being powered, a buck regulator would be ideal to keep the supply voltage steady. However
as the charge diminishes the input voltage falls below the level required by the circuit, and
either the battery must be discarded or re-charged, at this point the ideal alternative would
be the boost regulator. This type of converter are capable of amplifying voltage to large
extent still we cannot implement this type of converter as the voltage fed in both positive and
negative half of the cycle are not equal. So, they cannot be used in the magnetic levitation
system.
32
FIG 4.11: CIRCUIT DIAGRAM OF BUCK-BOOST CONVERTER
FIG 4.12: SIMULATION OF BUCK BOOST CONVERTER
33
FIG 4.13: INDUCTOR CURRENT WAVEFORM
FIG 4.14: INDUCTOR VOLTAGE WAVEFORM
FIG 4.15: GATE PULSE WAVEFORM
34
4.2.4 H-BRIDGE CONVERTER
It consists of two controlled switches placed along one diagonal corners of the H-bridge and
two diodes along the other diagonal corners. It can be seen that when both the controlled
switches are ON, the entire input DC voltage is applied to the load. The load voltage polarity
supports the build-up of current through the load. Next, when the switches are turned OFF
the current through the highly inductive coil does not change immediately and starts flowing
back to the source through the diagonal diodes. This allows application of negative voltage to
the coil, which in magnitude is equal to the source voltage. The chopping frequency is kept
high and this keeps the coil current continuous. By proper duty ratio control of the chopper
switches, the average voltage applied to the coil, during any high frequency cycle, can vary
from full positive to full negative of the supply voltage. A full bridge circuit having four
controlled switches can apply equal amount of positive and negative voltage to the load while
allowing coil current to be bi-directional. Electromagnetic attraction force is, however,
independent of the coil-current direction and hence one may as well go for a cheaper
asymmetrical bridge circuit that allows only one direction of load (coil) current. The input DC
voltage to the chopper must have the required magnitude to meet the instantaneous voltage
demand of the magnet coil during dynamic condition. The chopper switches need to be rated
for this voltage and for the worst case coil current.
FIG 4.16: CIRCUIT DIAGRAM OF H-BRIDGE CONVERTER
35
FIG 4.17: SIMULATION OF H BRIDGE CONVERTER
FIG 4.18: INDUCTOR CURRENT WAVEFORM
FIG 4.19: INDUCTOR VOLTAGE WAVEFORM
36
FIG 4.20: GATE PULSE WAVEFORM
4.2.5 HALF BRIDGE CONVERTER
A half-bridge converter is a type of DC-DC converter that, like flyback and forward
converters, can supply an output voltage either higher or lower than the input voltage and
provide electrical isolation via a transformer. Although more complex than
a flyback or forward converter, the half-bridge converter design can yield higher output
power (potentially up to 500W) and use parts that are smaller and less expensive.The main
problem occurs in this kind of converters in designing two equal capacitors for voltage
balancing. As a capacitor is a passive electronic component that stores energy in the form of
an electric field. As part of an electrical circuit, capacitors "oppose" changes in voltage by
supplying (or drawing) current. An ideal capacitor is characterized simply by its capacitance
value, the device's ability to store charge. However, a real-world capacitor has many
additional characteristics, such as tolerance rating, working voltage, leakage current,
temperature coefficient, and equivalent series resistance (ESR) – it is very difficult to obtain
to exactly equal capacitor.
.
FIG 4.21: CIRCUIT DIAGRAM OF HALF BRIDGE CONVERTER
37
FIG 4.22: SIMULATION OF HALF BRIDGE CONVERTER
FIG 4.23: OUTPUT VOLTAGE WAVEFORM
FIG 4.24: GATE PULSE WAVEFORM
38
CHAPTER 5
IMPLEMENTATION & RESULTS
5.1 Introduction
5.2 Feedback Magnetic Levitation Setup
5.3 Set Of Equipments
5.4 Block Diagram
5.5 Observation
5.5.1 With Optimum Parameters
5.5.2 With Decreased Integral Value
5.5.3 With Increased Proportional Gain
5.6 Complete System
5.7 Simulink Diagram
39
5.1 INTRODUCTION
This chapter gives an idea of the magnetic levitation system provided by “Feedback”
company and other set of equipment required to perform the experiment. The later part of
chapter deals with modelling of a magnetic levitation system. In modelling a linear and
nonlinear model of the MagLev system is derived. Here magnetic force causing the levitation
is also derived.
5.2FEEDBACK MAGNETIC LEVITATION SETUP
Magnetic levitation setup plant consists of three important parts:
a) Electromagnetic coil
b) Infrared light sensors
c) Metal object
d) Analogue and Digital interface
e) Controller from computer
a) Electromagnetic coil: The electromagnetic coils gives necessary magnetic field
when current is passed through it. The produced field interacts with the metallic
object to produce the necessary lifting force. A heat sink is provide to regulate the
temperature of coil after prolong current supply is provided.
b) Infrared light Sensor: There are two parts in IR sensor. One is the transmitter of IR
light and other is receiver of IR light. Base on the amount of light fall on the receiver
voltage is produced. When object is in levitation position then the some part of the
lights are blocked and correspondingly voltage is produced. The amount of the
voltage produced gives the position of the object.
c) Metal Object: Here, a hollow metallic ball is considered as object. The weight of the
ball is around 20 grams.
d) Analogue and Digital interface: The Maglev plant is the interface with a computer
via Analogue and Digital interface as the plant is in continuous time domain whereas
the computer works in the digital domain. Thus to couple both an interface is needed.
Sensor output is feed to analogue to digital converter pin and the control input from
the controller in computer feed to digital to analogue converter pin.
e) Controller: The maglev plant is open loop unstable. Thus to perform levitation a
controller is needed. The necessary controller is designed in MATLAB or 14 Simulink
and connected to MagLev system via Advantech PCI1711 card. The control output is
bounded to be within +5V and -5V .
40
FIG.5.1 MAGNETIC LEVITATION MECHANICAL UNIT.
FIG.5.2:ANALOG CONTROL INTERFACE UNIT
41
5.3 SET OF EQUIPMENTS
Set of equipment required for experiment are as follows
i) Feedback Magnetic Levitation setup
ii) Hollow metallic ball
iii) Feedback Analogue control interface
iv) PC with Windows 2000 or Window XP
v) MATLAB V7.3(R2006b) or later version
vi) MATLAB Toolbox required:

Real Time Workshop with real time target
 System Identification tool box
 Control tool box
vii)Advantech PCI17111 card
viii) Installation software
5.4 BLOCK DIAGRAM
The block diagram of whole system is given as:
FIG.5.3:BLOCK DIAGRAM FOR MAGNETIC LEVITATION SYSTEM WITH CONTROLLER
42
FIG. 5.4 SCHEMATIC DIAGRAM OF CLOSED LOOP SYSTEM
Given below are the simulation results for various considered parameters.
5.5 OBSERVATION
5.5.1 WITH OPTIMUM PARAMETERS
Considering the optimum parameters as (KP=4, Ki=2 , KD=0.2) we see that output signal is
following the reference signal. As evident from the step response and sinusoidal response the
system shows output signal completely tracks input reference signal.
FIG. 5.5: STEP RESPONSE WITH OPTIMUM PARAMETERS
43
FIG. 5.6: SINUSOIDAL RESPONSE WITH OPTIMUM PARAMETERS
5.5.2 WITH DECREASED INTEGRAL(KI) VALUE:
KP=4, KI=0 ,
KD=0.2
For the validation of theoretical results we decreased the value of integral constant, as
expected the error is quite attenuated as we can see the difference between reference and
output signal is more pronounced.
The tracking performance of the system also deteriorated as seen in the sinusoidal tracking
figure.These both results validates the necessity of integral control for minimizing the error
and improving the system steady state performance.
FIG. 5.7: SINUSOIDAL RESPONSE WITH DIFFERENT PARAMETERS
44
FIG. 5.8: STEP RESPONSE WITH DIFFERENT PARAMETERS
5.5.3 WITH INCREASED PROPORTIONAL GAIN(KP=6)
KP=6, KI=0 ,
KD=0.2
As KP increases the transient performance of system improves in terms of response time but
at the same time oscillation increases and stability of system is compromised.so it is expected
that the oscillation should be high during transiesnt period which is clearly depicted in the
given figure.
FIG. 5.9: STEP RESPONSE WITH DIFFERENT PARAMETERS
45
5.5.4 WITH DECREASED (KD=0.1)
KP=6, KI=0 ,
KD=0.2
As differential controller is mainly applied for the transient performance improvement as it
damps out the oscillation and gives stability to the system but at the same time system
becomes more sluggish and response time increases so it is well expected that if we decrease
the differential constant the oscillation will be pronounced and rise time will be decreased
which is clearly shown below.
FIG. 5.10: STEP RESPONSE WITH DIFFERENT PARAMETERS
5.6 COMPLETE-SYSTEM
46
5.7 SIMULINK DIAGRAM
In a PID system, the proportional (Kp), derivative (Kd), and integral (Ki) terms all contribute
to the total controller output (the three terms are added together).
A proportional controller ( ) will have the effect of reducing the rise time and will reduce
but never eliminate the steady-state error. An integral control ( ) will have the effect of
eliminating the steady-state error for a constant or step input, but it may make the transient
response slower. A derivative control ( ) will have the effect of increasing the stability of
the system, reducing the overshoot, and improving the transient response.
The effects of each of controller parameters,
summarized in the table below.
47
,
, and
on a closed-loop system are
CL RESPONSE
RISE TIME
OVERSHOOT
SETTLING TIME
S-S ERROR
Kp
Decrease
Increase
Small Change
Decrease
Ki
Decrease
Increase
Increase
Eliminate
Kd
Small Change
Decrease
Decrease
No Change
Although these correlations may not be exactly accurate, because
, , and
are
dependent on each other. In fact, changing one of these variables can change the effect of the
other two. For this reason, the table should only be used as a reference when you are
determining the values for ,
and .
48
CHAPTER 6
MAJOR CONCLUSIONS & FUTURE WORK
6.1 Conclusion
6.2 Future Scope
49
6.1 CONCLUSION
Magnetic levitation is an exciting technology with the potential to change the world. Its
applications are far ranging from transportation to household fixtures and decorations. While
the technology is currently expensive to implement, its potential merits continued research.
In the future cost-effective and practical applications of magnetic levitation will change the
dynamics of business and life. A reduction in pollution and waste in business systems will
improve the environment and the bottom-line of corporations.Already there are examples of
this technology in action and proof of its ability to optimize systems and alter paradigms.
Such examples are bullet trains, magnetic bearings, flywheels and levitation melting and
household fixtures and decorations.
Any practical and commercial use of maglev has to be examined for technical & financial
feasibility.
The technical feasibility has been established by status of Japanese MLU002 prototype
system currently being run in yamanshi test line & by German transrapid system at Emsland
test facility. Both test systems have supplemented Maglev as the promise of a faster,
smoother, clean and safer ride.
The other aspect of financial feasibility is subjective to a country. To judge its financial
feasibility its cost and revenue estimates have to be extensively studied in context of the
geography, demography and existing transportation systems. Studies in America were
carried out by National Maglev Initiative (NMI) evaluated Maglev potential and in short their
conclusion was that a 300 mph ( 483 kmph ) is entirely feasible. Various commercial projects
in America, Germany, China and Japan should leave no room of doubt for its economical
viability. The need to upgrade this technology for a nation can be summed up in one sentence
that high mobility is linked with economic growth and productivity of nation.
India has the most complex, widespread rail network which is now bogged down by
congestion. Maglev provides the flexibility to equip existing steel tracks with magnetic
levitation (based on EDS) and propulsion system. This will help in operating both maglev and
conventional trains on same track. The possible incorporation of both steel track and maglev
guideway is hinted in figure. By this we can replace the conventional trains with maglev
trains in phased manner.
The space launch systems based on maglev are also feasible as indicated by NASA. Various
test models have proved its technical feasibility and cost studies by NASA clearly indicate
cheaper launching in future.
Over the years India has developed strong infrastructure for space exploration and has its
own array of launch vehicles and a reusable vehicle ‘Avataar’ on the cards. With NASA in
50
pursuit of low cost maglev launch its time that India too must venture into this field so that it
can compete, in the growing billion dollar market of satellite launch, in future.
6.2 FUTURE SCOPE
The future application of magnetic levitation could optimize business systems and
conventional operating models. Perhaps the most obvious impact would be on modes of
personal and commercial transportation. Infrastructures within and between countries
would have to change to facilitate the technology. This shift would impact the dynamics
between businesses, supply chains and governments. Contemporary transportation and the
related infrastructure are dependent on oil and gas.
Gas stations and oil refineries could see a tremendous drop in sales and production if
magnetic levitation became the predominant means of transportation. Civil engineers,
construction companies and conventional roadways would need to evolve to support the
technology. Currently it is expensive to create and maintain magnetic levitation railway
systems. It will take some time and major innovations for the technology to become practical
on a wide scale.
The global economy runs on gas and oil. Magnetic levitation not only has the potential to
make systems more efficient, but also to change the dynamics of energy use and production.
Current economic powers in the Middle East thrive on oil production. Magnetic levitation
could lead to a shift in the supply and demand of oil. Turbines are one means to create the
electricity needed for magnetic levitation, and many turbines burn fuels other than oil or gas.
Conventional means of transportation, such as vehicles driven by internal combustion
engines, create waste and are not environmentally friendly. Carbon dioxide emissions pollute
the environment and damage the ozone layer. Drilling and transporting oil can have
disastrous impacts on human beings and environmental systems. Magnetic levitation has the
potential to reduce the waste and undesirable byproducts of contemporary personal and
commercial transport.
51
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