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Table of contents
Difference between Classical Control and state space
methods
Classical control vs modern control
Advantages and disadvantages of classical control
system
Advantages and disadvantages of modern control systems
Limitations of classical control system
Controlling of torque in induction motors
Manipulation control of robots
Controlling of smart grid system
Removing total
harmonic distortion in inverters
Classical
control method in robust control
In this report, there is complete
information about the use of classical control method used in modern industry.
It can be noted that in classical control there is single input and single
output. Due to this control method researchers are able to make changes and
make new ones for the modern era. This report is discussing about classical
control methods in detail. The main thing is that control is quite a main thing
for the checking the behaviour of the whole system and work according to it. In
classical control, there are some parameters that are playing a major role it
this system. The first one is PID that is also known as proportional, integral
differential controller. It is also known as a foundational control technology
used for process technology in the 20th century. Then after this, there is
brief information about the history of the classical control method used in the
past. It will also discuss some important parameters of the control system in
detail like root locus, frequency response and PID controller.
Then after this, there is
complete information about the difference between state space and classical
control. It can be noted that classical control method is better than state
space control. The best thing is that classical control is quite easy rather
than state space control. Furthermore, there is some information about the
difference between the classical control and modern control. The main
difference is that classical control is using only single input and single
output. On the other hand, in modern control system there is multiple input and
multiple output. For analysing the system in classical control time domain is
used and performed through differential equations. The next thing is that
modern control is carried out in complex-s domain and frequency domain. Due to
this it will become easy to deal with the MIMO systems. The modern control
system is comprehensively described through digital system. The difference
between these control strategies will be explained in detail in the given section.
Moreover, in the next section,
there is complete information about the pros and cons of classical and modern
control systems with complete explanation. Then after this, there is some
information about the limitations of classical control system is presented. For
that case, there is need to overcome these problems in the system. This is can
be done through applying artificial intelligence techniques.
In the last section of the report
there will be complete information about the use of classical control method in
the modern industry. It will discuss how classical control is playing an
important role in solving control related problems in the industry. The
classical control is also used for controlling induction motors through the
help of indirect field-oriented control system. This will show how classical
control method is used to solve the problem of the induction motor. There is
another use and it is related to the field of robotics. It can be noted that
for controlling the manipulation problem of the robot by classical control
method. It shows that if artificial intelligence is used in the robots then it
will become easy to manipulate robot and solve its problem. The next
application that will be discussed is related to the smart grid system. It
shows that classical control system is also used for controlling the smart
grid. This is because, smart grid is considered as a future of technology.
Another use of this control system is related to increase quality of the
inverter. Due to classical control method, total harmonic distortion problem is
removed from the three phase inverter. The complete method is explained in the
section below.
Control is used to alter
the behavior of a society so that it can acts in appropriate manner. For
example, we ought the speed of car on high hills way to be 60 miles per hour
despite of all hindrances or we may demand aircraft to obey a required
altitude, heading, and velocity profile free of any wind gusts or we desire
that the temperature and pressure in a chemical process should be maintained.
All these requirements are being accomplished today by control measures. And
above mentioned are examples of what control are forced to do, without human
interruption. Control is used for quantities such as speed, temperature or voltage
to behave in orderly manner
To understand, how an
automatic control system works, we shall explain the speed control mechanism in
a car. It is maybe informative to consider first how a normal driver may
control the car speed over uneven terrain. The driver, by carefully noticing
the speedometer, and adequately increasing or decreasing the fuel flow to the
engine, using the gas pedal, can balance the speed quite accurately. Higher
level of perfection can perhaps be achieved by looking ahead to antedate road
gradients. An automatic speed control system, also called cruise control, works
on the difference, or error, between the actual and desired speeds and
knowledge of the car’s response to fuel increases and decreases to calculate
via some algorithm an appropriate gas pedal position, so to drive the speed
error to zero. This is called a control law and it is applicable in the
controller. The car dynamics of interest are captured in the plant. Controller
collect information about actual speed by sensors. and the control decisions
are applied through a device, the actuator, that changes the position of the
gas pedal. The knowledge of the car’s response to fuel increases and decreases
is most often captured in a mathematical model. Definitely in an automobile
today there are many more automatic controls systems such as the antilock brake
system (ABS), emission control, and tracking control. The use of feedback
control preceded control theory, explained in the following sections, by over
2000 years. The first feedback device on record is the famous Water Clock of
Ktesibios in Alexandria, Egypt, from the third century BC
The
concept of control systems began fundamentally in the ancient world. Early
civilizations, especially the Greeks and the Arabs were highly concerned with
the precise time measurement, the consequence of which was many "water
clocks" that were constructed and introduced.
However,
before the onset of the Renaissance in Europe there was still little in the way
of practical development in the engineering industry. Leonhard Euler (whom
Euler's Theorem is named for) invented a effective integral transform, but
Pierre-Simon Laplace used the transformation (later called the Laplace
Transform) to solve complex probability theoretical questions.
Around
1910-1945 there existed the "golden age" of control technologies,
where mass communication techniques were developed and two world wars were
battled. Two of the most famous names in the control engineering did their work
during this period: Bode and Nyquist.
Hendrik
Wade Bode and Harry Nyquist developed the majority of what we now consider
"Classical Control Techniques," particularly during the 1930s while
working with Bell Laboratories. Such techniques were cantered on the effects of
the previously known Laplace and Fourier Transforms, but made famous around the
end of the century by Oliver Heaviside. The transforms had not been commonly
used, nor valued mathematical devices, prior to Heaviside
Bode
is accredited with the "discovery" of the closed-loop feedback system
and the logarithmic plotting method (bode plots) that still carries his name.
Harry Nyquist has done significant work on system stability and the theory of
information. He developed a powerful criterion of stability, named after him
(The Criterion of Nyquist).
In
the early 1950s, new methods of management were adopted as a way to overcome
some of the drawbacks of classical processes. Rudolf Kalman is known for his
work in modern control theory, and in his honour, an adaptive controller called
the Kalman Filter was named. With the electronic revolution, and the launch of
the space program, new control methods became increasingly common after 1957.
Computers generated the need for modern control methodologies, and certain
"advanced" control methods such as "optimal control,"
"robust control" and "nonlinear control" were demanded by
the space program. These latter subjects, and many more, are still popular
study areas among research engineers
This controller was developed in
the early of 20th century by Elmer Sperry. Then after this in the
next decade its theoretical analysis is presented by the Nicolas Minorsky. Then
he had worked on this controller in a proper way and designed automatic
steering system for the US navy. Later on, there are two categories of this
controller is presented. The first one is related to model free and next on is
model based. On the other hand, the model based PID controller was the first
one applied for the tuning of controller. In the model based PID control there are
two main examples of this approach that include Ziegler Nichols and manual
tuning
The next thing is that in manual tuning the
derivative and integral actions are removed by just setting the integral time
to infinity and derivative time to zero. Then after this, it can be observed
that proportional gain Kp is increased. Now in the next case during decay type
response the proportional gain is half and its value will be decreased.
Moreover, integral time is adjusted until certain corrections are made in the
loop operation.
Furthermore, in Ziegler Nichols
there is a loop that will go towards oscillatory state with constant amplitude.
It is measured by setting the parameters with same values. then after some decades,
the two scientists were working on the problems present in these approaches and
also some risks that are related to it. They had presented relay-oscillation
auto-tuning for overcoming these drawbacks
The frequency response is used to
analyse the main response of the whole control system. If there is need to
analyse the response of the system then different methods are applied on it. Moreover,
frequency response is analysed through the help of sinusoidal wave of the
system. Then after thus bode plot is presented of the wave and it will show its
frequency response. Through this plot it is easy to tune the whole system by
applying changes.
In classical control methods when
there is need to predict the behaviour of the closed loop system then for that
case there is use of root locus plots. It can easily predict the graphs of the
system and produces results according to the closed loop system. This shows
that if the value of gain is changed constantly then what will be the effect of
the system in the future. For getting such information about the closed loop
system root locus plots are used. Such plots are designed in the twenty first
century when there is need to analyse the future behaviour of the system
properly
It
is becoming difficult to represent the systems in terms of differential
equation as the systems complexity is growing. We can emphasize on this more of
the system comprises many inputs and outputs. State space method is introduced
in this document which greatly alleviates this problem. With the single first
order differential equation, the state space is representing the nth order
differential equation of the system. Two equations are given for the state
space representation of the system;
Note:
vector or matrix are the bold face characters. In textbooks the variable X is
used more commonly and when state variables are discussed then other references
are variable 1. The variable q will get in use here instead of variable x to
represent the position.
The state equation is the first equation, second equation is output equation. For an nth order system (i.e., it can be represented by an nth order differential equation) with r inputs and m outputs the size of each of the matrices is as follows:
Several
features of the system
It can be noted that the state equation contains only single first order derivative of the state vector and given on the left side of the vector. It is also showing the q(t) as a state vector, u(t) as an input of the system given on right side. Moreover, it shows no derivative on the right hand side of the equation. Moreover, this is the reason why it is written as like this
Advantages of this representation
include;
·
The notation is quite compact. Even two simple
equations are required for a large system.
·
It is very easy to establish general techniques
in order to solve these systems, as all the systems have the same notation.
It is considered as a branch of
the control theory that is involved in dealing with the behaviour of dynamical
systems. It will analyse the behaviour of the input and then it will modified
it by feedback system and also Laplace transform. The main aim of these method
is to control the behaviour of the system. The main control system is also
known as plant. The output of the plant is following the main input of the
system. This input point is also called as reference. The reference point of
the plant can be fixed or variable. For that case, a controller is deign for
the plant. It is involved in analysing the system and also monitors its output
and change according to the reference point. If the output is not matching with
the reference point then its difference is known as error signal
This signal is applied on the
feedback. Another thing is that these
systems are dealing with the time invariant and linear systems. On the other
hand, classical control method is also using array of tools for designing and
analysing the controller for particular system. These tools are quite valuable
for the system. These tools include, Nyquist stability, root locus, gain
margin, and bode plot and phase margin. There are also some advance tools that
include bode integrals. These tools are involved in analysing the nonlinear
behaviour of the control system
Control theory consists of two important division
which are termed as classical and modern, which impact directly on the
applications of control engineering. The theory of classical control has a
boundary of single-input and single output (SISO) system design, differential
equations are used to carry out in the wider domain of system analysis. Domains
with complex Laplace transform or by transforming domain from the
complex domains. All the systems are considered to have the applications of
second order and single variable, and system response of higher-order and
effects of multivariable are ignored. A controller structured with the help of
classical theory mostly needs on-site tuning because of the approximations of
designs. Yet because of the less hard physical connectivity process of
classical controller structures as compared to the design of systems using the
theory of modern control, most industrial application relies on these types of
controllers. The most widely used controllers which are structured with the
help of classical controllers’ theory are PID controllers
Classical and Modern control literature and theories
are elaborated in a way which misleads, due to the reason that group or set of techniques
which is known as Classis were actually created or designed after the
techniques which are known as “Modern”. But in terms of structuring control
systems. The methods of modern controllers have been in usage to bring great
effect in recent times. In the meantime, the classical methodology has been
increasing falling out of favour. In the latest it has been acknowledged that
classical and modern methods can be connected to show their altogether strength
and weaknesses
Classical Methods, which is considered at first
priority in this book will includes method which involves Laplace Transform
domain. In the so-called “time domain” systems physical systems are modelled,
where the response given by the system is function of multiple inputs, the time
and the values of the previous systems. As time moves forward, the position of
the system and its response take a change. However time-domain model for
systems are mostly structured with the help of differential equations of
higher-order which can make it turn out to be highly difficult and near to
impossible for humans to sort out and there can be some which are even at a
state of impossible for modern computers systems to solve in a efficient
manner. The counter this issue, integral transforms, which includes the Laplace
Transform and the Fourier Transform can be put into action to change on
Ordinary Differential Equations (ODE) in the domain of time into a common
algebraic polynomial in the domain of transform. Once a provided system has
been changed into the transform domain it further is capable to be manipulated
with larger spectrum of ease and measured quickly by humans and computers.
In light of the theory of modern control it is
carried out strictly in the complex or in the domain of frequency, and can
further handle the multi-input and multi-output (MIMO) systems, this takes
control the boundaries of classical control method in more analysed and
structed design problems. For an example a fighter aircraft control. In a
modern design, the representation of the system is a set of first order of the
differential equations which is elaborated using the help of other variables.
Multivariable, nonlinear, adaptive and robust control methodologies come under
the banner of this division, as for being new, the theory of modern control has
many places yet to be studied.
Scholars including Rudolf E. Kalman and Aleksandr Lyapunov are well
acknowledged in the society of people who have designed modem control theory
Modern
Methods of Controls, in place of taking alternate domains to avoid the
complexities brought by time-domain ODE mathematics, overrides the differential
equation into a lower-order of system time domain equation called as State
Equations, which can further be changed with the help of techniques present in
linear algebra. The book will have contents regarding Modern Method second
The
third level that is mostly developed in the realm of controls systems is to
separate methods of analogy from the methods of digital. Digital control
methodologies were structured to try and incorporate with the upcoming power of
computers systems into the methodologies of previous controls. A transform
exclusively was developed which was called out as Z- Transform which were able
to describe digital systems in manner full way.
·
The main advantage of classical control method
is that it is intuitive and easy method for implementing.
·
It is also considered as basic and simple method
of controlling systems
·
There will be low initial cost required for
implementing the system
·
It also contain plain structure in which there
are different parameters are present.
·
The response time of this method is quite fast.
This is because less number of variables are present.
·
It is also easy to implement feedback
controlling by the help of this method.
·
The main disadvantage is that it is not able to
control moving process with certain time delays. This is because it is not
supporting multiple outputs.
·
The next thing is that it lacks accuracy in the
system
·
The quality of the output is not reliable for
the system
·
There is need of a PID controller for removing
fluctuation from the controller
·
It is only involved in accepting binary inputs
from the user. It also contains some stability problems in the system
·
It gives the advantage to analyse time-varying
or time-invariant, linear or non-linear, single or multiple input-output
systems.
·
It is possible to confirm the state of the
system parameters also and not merely input-output relations.
·
It is possible to optimize the systems and
useful for optimal design.
·
It is possible to include initial conditions.
·
It is operated through applying different
complex techniques
·
For implementing this control method there is
need of many computations.
There is some limitation in
classical control theory because of those perceptions that are made for the
control system for example time invariance or linearity etc. Artificial
intelligence- based control techniques can get in use for solving these
problems. We can use such techniques even when the analytic models are not
understandable or known. So as compared to the classical control such control
system is less sensitive with regards to parameter variation.
The torque control for induction
motor is analysed through linear approximation lying under the scheme of IFOC
or indirect field-oriented control that think rotor resistance perturbations.
There are many characters of IFOC that are mentioned, that lead us to design
the linear robust and the torque that will be performance based, as well the
control of speed and position will be in it. Specifically, the resulting
controllers comprise of the low order, robust for the rotor resistance
perturbations and thus they are designed for the classical performance
specification. These are particularly the characters that are difficult to
achieve if look toward the history. There is a presentation for general control
design guidelines that could get valid for many induction motors. Moreover, the
minimum phase condition as well as the stability of IFOC torque controller are
designed in many induction motors. So well designing the position controller as
well as the linear fixed design, these conditions have their prime importance
in it. There is also a presentation for a case study that is about the typical
motor, which also comprise the robust designs controller and the results of the
real time experiments. The approach here makes us well understood about the
classical control methods that allows improvements of the results here by the
use of linear single-input-output controller design tool for example the theory
of H∞ and quantitative feedback
The
robot manipulator control is the most important one challenge in the robotics
field if talking about the acceptable performance as these systems have the
characteristics of multiple inputs and multiple outputs, some chances of
uncertainty and nonlinear. Robot manipulators can be use in many various
situations that could be known or even unknown that resulting provide
complicated systems. This is the reason that we will use a strong mathematical
theory in new emerging control methodologies in order to design a nonlinear
robust controller that also have the acceptable performance like less error
possibilities, good trajectory and disturbance rejection. In robot manipulators
control there are two main categories that is classical and non-classical
methods. The conventional or the classical control theory will use classical
methodology and on the other hand artificial intelligence methods will be used
in non-classical theory control like fuzzy logic, neuro fuzzy or neural
network. But we can say that both of these theories, conventional as well as
artificial intelligence methods have their uses in many areas but with some
limitations in it. Fuzzy logic control is more emphasized in this paper and is
applied to PUMA robot manipulator (Piltan & SH Tayebi Haghighi, 2011).
The
focus is always on meeting the demands under the constraints of application
specific. So, smart city research as well as Smart Grid at the high level is
all about making the good use of already present resources. It can be thought
as the classical consideration of Control Theory. In such application areas
classical control have a lot to offer like in the angles of contemporary
applications which also have chances for practitioners in Control Theory in
order to explore more and new challenges.
Regulating
the single system is a first and typical concern of classical control so that
the system will approach toward the desirable behaviour in an optimal level, on
the opposite side, Smart City application the aggregate effect of the
actions of an ensemble of (often human) agents is also a variable of
considerable interest. Moreover, the classical control is all about the control
system whose structure and design will not change with time.
While looking toward the
other side, in Smart City applications, the concern is about controlling and
influencing the attitudes of large scale population where the population of
agents can vary or be uncertain with time. Thirdly, data sets can get through
the closed loop fashion. Which mean that operator decision is on the data sets
reflection. So finally, the most basic difference between classical control,
smart grid and smart city applications control is the requirement for studying
the effects of signals that are controlled on the level of statistical
characteristics of the populations that we wish to have the impact. Between all
of these basic differences, the last problem is the need of ergodic system of
feedback that could be most in level with classical control theorists and this
is the issue that influence more in real life applications therefore, there is
requirement of predictability, on the level of infidel agents that underpins on
the ability of operator to write the contract (André R. Fioravanti, Mareček, & Robert N. Shorten, 2017)..
While determining the quality of inventor output
waveform, total harmonic distortion plays an important role. The sinusoidal
voltage with less harmonic distortion is generator with the help of inventor
having the output LC filter. For the control of three phase inventor there are
may control schemes that are introduced. A new and a very simple control scheme
is described in this paper that use the predictive control. The controller uses
the model of discrete time of the system in order to guess the behavior of
output voltage for all the switching state possible that are generator by the
invertor. In power electronics, the control of three phase inverter is one of
the major classical subjects and has been extensively in subject study from
last ten years. Many control schemes are introduced for the converter like
nonlinear methods, linear methods which also include proportional-integral
controllers using pulse-width modulation (PWM)) (Mohamed & Sherif A. Zaid, 2013).
Because of the high level of simplicity, DOB among all
has the most popular robust control tolls. They have the efficacy and are
flexible. In DOB-based robust control, internal and external disturbances are
determined through the use of dynamics identification and with measurable
conditions of the plants and the robustness of systems is simply achieved by
feedbacking the estimations of disturbances. The main objective of this paper
is to give the overview for the DOPB based robust control and the applications
it has in engineering. (Sariyildiz & Roberto Oboe, 2019)
Summing up all the discussion
from above, it is concluded that classical control is considered as the main
wheel of the control system. In this paper, there is complete information about
the use of classical control methods in modern industry. It can be noted that
in classical control there is single input and single output. Due to this
control method researchers are able to make changes and make new ones for the
modern era. This report is discussing about classical control methods in
detail. The best thing is that classical
control is quite easy rather than state space control. Furthermore, there is
some information about the difference between the classical control and modern
control.
All these requirements are
being accomplished today by control measures. And above mentioned are examples
of what control are forced to do, without human interruption. The driver, by
carefully noticing the speedometer, and adequately increasing or decreasing the
fuel flow to the engine, using the gas pedal, can balance the speed quite
accurately. However, before the
onset of the Renaissance in Europe there was still little in the way of
practical development in the engineering industry. Leonhard Euler (whom Euler's
Theorem is named for) invented a effective integral transform, but Pierre-Simon
Laplace used the transformation (later called the Laplace Transform) to solve
complex probability theoretical questions.
Hendrik
Wade Bode and Harry Nyquist developed the majority of what we now consider
"Classical Control Techniques," particularly during the 1930s while
working with Bell Laboratories. In the model based PID control
there are two main examples of this approach that include Ziegler Nichols and manual
tuning. In classical control methods when there is need to predict the
behaviour of the closed loop system then for that case there is use of root
locus plots. It can easily predict the graphs of the system and produces
results according to the closed loop system.
The main control system is also
known as plant. The output of the plant is following the main input of the
system. This input point is also called as reference. The reference point of
the plant can be fixed or variable. This signal is applied on the
feedback. Another thing is that these
systems are dealing with the time invariant and linear systems. On the other
hand, classical control method is also using array of tools for designing and
analysing the controller for particular system. Domains with complex Laplace
transform or by transforming domain from the complex domains. All the systems
are considered to have the applications of second order and single variable,
and system response of higher-order and effects of multivariable are ignored.
Classical and Modern control literature and theories
are elaborated in a way which misleads, due to the reason that group or set of
techniques which is known as Classis were actually created or designed after
the techniques which are known as “Modern”. But in terms of structuring control
systems. Artificial intelligence- based control techniques can
get in use for solving these problems. We can use such techniques even when the
analytic models are not understandable or known. This shows that classical
control system is extremely important and it is involved in solving different
modern world problems in an efficient way.
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