A Seminar Report on

Control of Robot Using PID Controller

In partial fulfilment of the requirement for the

BACHELOR OF TECHNOLOGY
IN
ELECTRICAL ENGINEERING(EE) .

MADAN MOHAN MALAVIYA UNIVERSITY

OF TECHNOLOGY, GORAKHPUR-273010.

DEPARTMENT OF ELECTRICAL ENGINEERING

SESSION: 2022-23

SUBMITTED BY:-
ANKIT AHIRWAR
SECTION-A
ROLL NO – 2020031035 .

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 ACKNOWLEDGEMENT

I would like to place on record my deep sense of gratitude to Prof. Vinod Kumar Giri, Head
of Department, Electrical Engineering Department, Madan Mohan Malaviya University of
Technology, Gorakhpur for his generous guidance, help and useful suggestions. It would not
have been possible without the kind support and help of many individuals in this organization.
I would like to extend my sincere thanks to all of them.

I am highly indebted to Lt. Kishan Bhushan Sahay, Asst. Professor, Electrical Engineering
Department for his guidance and constant supervision as well as for providing necessary
information regarding the project & also for his support in completing the project. I express
my sincere gratitude for his stimulating guidance, continuous encouragement, and supervision
throughout the course of the report.

I would like to express my thanks towards my parents & faculty members of Madan Mohan
Malaviya University of Technology for their insightful comments, kind co-operation and
encouragement which helped me in completion of this project. My thanks and appreciations
also go to my colleagues in developing the project and people who have willingly helped me
out with their abilities and constructive criticism.

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 ABSTRACT

Today, the great development of science and technology has created a premise for scientific
research to develop to a new level in which the field of robotics has being chosen to be the
leading industry by many countries. To promote science and technology backgrounds,
intelligent robots in the industrial application are starting to prosper strongly, attracting many
research experts. To control robot moving safely to desired positions with obstacles, collision
avoidance and path planning were matters of concern. In recent years, various strategies have
been studied for collision avoidance control purpose. The basic idea behind the collision
avoidance algorithms is to design a proper controller which can result in a conflict-free
trajectory. Path selection methods are the one of several techniques to avoid obstacles. To
realize control objectives of the robots in real-life missions, simple proportional-integral-
derivative (PID) controllers are priority options due to simple design. If the proper control
gains were found, the high control outcomes could be obtained). A lot of research have been
then studied to improve the performance of the PID controllers using intelligent approaches
such as evolutionary optimization and fuzzy logic.
A PID controller calculates an error value as the difference between a measured process variable
and a desired setpoint (desired outcome). The controller attempts to minimize the error by
adjusting the process through the use of a manipulated variable. ‘P’ depends on the present
error, ‘I’ on the accumulation of past errors, and ‘D’ is a prediction of future errors, based on
the current rate of change. The weighted sum of these three actions is used to adjust the process
via a control element such as the position of a control valve, a damper, or the power supplied to
a heating element. A non-linear neural network is employed to eliminate internal/external
disturbances during the working process. To increase the adaptive robustness of the controller,
a new gain learning rule is integrated to flexible tune the PID gain for different working
conditions.

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 Contents

Acknowledgement 2
Abstract 3
1. Introduction 5
2. Control System Overview 6
3. Robotic Control 7
3.1 Omnidrive vs Differential Drive Robot 8
4. PID Controller 9
5. PID Responses 10
5.1 Proportional Response 10
5.2 Integral Response 11
5.3 Derivative Response 13
6. Tuning of Controllers 14
6.1 Manual Tuning 14
6.2 Ziegler-Nichols Method 15
6.3 Relay (Åström–Hägglund) method 15
7. Applications 16
8. Conclusion 18
9. References 19

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 CHAPTER – 1

1. Introduction
Robotics is one of the engineering branches that deal with modeling, controlling, and
utilization of robots. Robotics manipulators comprise two billion industries. Although they
have a lot of advantages; they suffer from disadvantages such as lack of mobility. The use of
various optimization strategies to fine-tune the proportional integral derivative control’s
parameters is investigated. The DC motor, which is widely used in numerous technical
applications, is the system under investigation. According to the simulation’s results, the
control’s overshoot and rising and settling times were performed satisfactorily. To fine-tune
the gains in the feedback controller, a novel fitness function with multiple objectives is
developed for advanced particle swarm optimization. The nonlinear Euler–Lagrange model is
used to validate the state-space model. The APSO technique uses the traditional Lyapunov
approach. Using the Gauss pseudo-spectral approach, parking trajectory planning is
represented as an optimum control issue that is then converted into a nonlinear programming
problem. For parking trajectory tracking, the velocity and front-wheel swing angle are
collected as control signals. To confirm the efficiency of the suggested hierarchical control
approach, actual vehicle testing is conducted.

Fig1. Double Q-PID algorithm for mobile robot control

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 Chapter-2
2. Control System Overview
Every robot has a controller, which continuously reads from sensors like motor encoders, force
sensors, or even vision or depth sensors, and updates the actuator commands so as to achieve
the desired robot behavior. Examples of control objectives include motion control, as when a
robot arm moves along a specified trajectory; force control, where the objective is to apply
specific forces to an object or the environment; hybrid motion-force control, as when writing
on a board: you control the motion in the plane of the board but the force into the board; and
impedance control, as when a robot is used to render a virtual environment. In this case, the
user grabs the end-effector of the robot and moves it around to explore objects in a virtual
world, which could be displayed to the user as masses, springs, or dampers.

Fig 2. Control System Analysis

It's also common to model force disturbances and sensor errors as being inserted into the
control loop. In this chapter, though, we will simplify our analysis by assuming that the
amplifiers and actuators work perfectly to generate the control forces requested by the
controller and that the sensors measure the robot's performance perfectly. We also ignore the
fact that the controller is typically implemented at a finite frequency and instead assume that
control laws are implemented in continuous time. Then our block diagram can be simplified
to this block diagram, consisting of only the controller and the dynamics blocks.

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 Chapter-3

3. Robotic Control
Robotic control is the system that contributes to the movement of robots. This involves the
mechanical aspects and programmable systems that makes it possible to control robots.
Robotics could be controlled in various ways, which includes using manual control, wireless
control, semi-autonomous (which is a mix of fully automatic and wireless control), and fully
autonomous (which is when it uses artificial intelligence to move on its own, but there could
be options to make it manually controlled). In the present day, as technological advancements
progress, robots and their methods of control continue to develop and advance.

Here, we have made use of PID controllers for the motion control of the robot. The motion is
of holonomic drive. Basically it differs in the number of degree of freedoms which we use. So,
in differential drive we use two degree of freedoms while in holonomic drive we use three
degree of freedoms

Fig3. Holonomic Drive Robot

3.1. Omnidrive vs. differential drive robot

Omnidrive robots have many advantages in terms of mobility, including the capacity to move
in confined spaces, crowded situations, and tight places, as well as the ability to turn sideways,
turn on the spot, and follow complex trajectories, thanks to their 360º movement.
Besides, these vehicles are capable of easily performing tasks in environments with static and
dynamic obstacles and narrow spaces.
A differential drive robot is a mobile robot with movement based on two separately
driven wheels which are situated on each side of the robot body, which allows the robot to
move back and forth, yet not sideways. This means that reaching every location and orientation
in a two-dimensional space requires more maneuver’s and potentially more complex path-
planning.

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On one hand, omnidrive robots appear to be the best option in situations requiring extreme
maneuverability, thanks to their versatility of 360º movement. The omnidrive system is
particularly useful when maneuverings in tight environments such as transporting long loads
sideways through standard-sized doors or narrow aisleways or parking in parallel, whereas a
differential drive robot would make more maneuvers than an omnidirectional drive robot.
Differential drive robots, on the other hand, are widely used in robotics because their motion
is simple to program and easily controlled. Many consumer robots on the market today use
differential steering, owing to its simplicity. Besides, differential drive robots make a strong
choice when it comes to pushing power. Omnidirectional wheels also require individual,
speed-controlled motors for each wheel.

Fig4. Omnidirectional Drive with three degree of freedom

First, we’ll get some nomenclature for PID controllers out of the way. In a PID context, we use
the term reference or setpoint to mean the desired state of the mechanism, and the term output
or process variable to refer to the measured state of the mechanism. Below are some common
variable naming conventions for relevant quantities.
Roughly speaking: the proportional term drives the position error to zero, the derivative term
drives the velocity error to zero, and the integral term drives the total accumulated error-over-
time to zero. All three terms are added together to produce the control signal.

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 Chapter-4
4.PID Controller
PID controller is used for the control system of the industry; it has a control loop feedback
system and the PID stands for proportional integral derivative controller. The error value is
continuously calculated by the PID controller; it is measured by the variation between the
desired and measured values. The controller is used to control errors by adjusting the control
variables such as controlling the power supplied to the heating element, varying the position
of a control valve. Kp, Ki, and Kd are the proportional coefficient, derivative, and integral
controller.

U(t)=KP e(t)+KI∫τ0e(τ)d(τ)+KDde(t)dt.

In the above Equation

U(t) = Control signal
E(t) = Error signal
Kp = Proportional gain
Ki = Integral gain
Kd = Derivative gain

Fig5. the PID controller for DC Motor Speed Control.

The PID controller design should be merged into the system. the speed control of DC motor
using PID controller. The transfer function of PID controller is:

C(S)=KP+KiS+KdS.

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 Chapter-5
5.1 Proportional Response
The proportional response examines an error in the present, as it evaluates the distance error
proportionately from a given time step. In other words, if the amount of error is low, there is a
small correction. Conversely, if there is a lot of error, there is a much larger correction.

Fig6. Proportional response

Think about a pendulum that’s held in someones hand. When its not at rest, it will swing back
and forth, as gravity will ultimately always pull the pendulum back into the start position, with
a force that depends on how far it is from the start position. When it’s far from the starting
position, the pendulum will swing with a large amount of force.
The issue with using Proportional Control is overshoot, whereby an object overcorrects it’s
position. It’s akin to a pendulum swinging past the resting position. On its own, Proportional
Control can have issues when an object has mass or inertia, because they will affect the speed
of the object regardless of decreasing influence from whatever is accelerating the object, such
as gravity or a cars engine. It doesn’t anticipate it’s going back to the target position, so it tends
to overshoot and oscillate.
The proportional term is given by

A high proportional gain results in a large change in the output for a given change in the error.
If the proportional gain is too high, the system can become unstable. In contrast, a small gain
results in a small output response to a large input error, and a less responsive or less sensitive
controller. If the proportional gain is too low, the control action may be too small when
responding to system disturbances. Tuning theory and industrial practice indicate that the
proportional term should contribute the bulk of the output change

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5.2 Integral Response
The integral helps looks at data from the past as it sums past errors. Even a small error will
result in an progressive increase in the integral response, taking into account the fact that
something hasn’t been properly corrected over time.

Fig7. Integral Response

It’s useful in removing constant errors in a control system, since no matter how small the
constant error, eventually the summation of that error will be significant enough to adjust the
controller output. It has the effect of driving the steady-state error to zero.
If the gain is too large, the controller might become unstable because normal controller
fluctuations will be exaggerated. If it’s too small, it can take too long to respond to dynamic
changes. The integral term is given by

The integral term accelerates the movement of the process towards setpoint and eliminates the
residual steady-state error that occurs with a pure proportional controller. However, since the
integral term responds to accumulated errors from the past, it can cause the present value to
overshoot the setpoint value.

5.3 Derivative Response

The derivative response anticipates the future by examining the rate of the change of the error
that contributes at a given time step. The derivative response is proportional to the rate of the
change of the process variable. When the change of the error is moving is slowly, the derivative
path is small. The faster the error changes, the larger the derivative path. It is sometimes called
anticipatory control.

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 Fig8. Derivative Response

The derivative of the process error is calculated by determining the slope of the error over time
and multiplying this rate of change by the derivative gain Kd. The magnitude of the
contribution of the derivative term to the overall control action is termed the derivative
gain, Kd.
The derivative term is given by

Derivative action predicts system behavior and thus improves settling time and stability of the
system. An ideal derivative is not causal, so that implementations of PID controllers include
an additional low-pass filtering for the derivative term to limit the high-frequency gain and
noise. Derivative action is seldom used in practice though – by one estimate in only 25% of
deployed controller – because of its variable impact on system stability in real-world
applications.

Fig8. PID Controllers

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 Chapter-6
6. Tuning of Controllers
6.1 Manual Tuning
If the system must remain online, one tuning method is to first set Ki and Kd values to zero.
Increase the Kp until the output of the loop oscillates; then set Kp to approximately half that
value for a "quarter amplitude decay"-type response. Then increase Ki until any offset is
corrected in sufficient time for the process, but not until too great a value causes instability.
Finally, increase Kd, if required, until the loop is acceptably quick to reach its reference after
a load disturbance. Too much Kd causes excessive response and overshoot. A fast PID loop
tuning usually overshoots slightly to reach the setpoint more quickly; however, some systems
cannot accept overshoot, in which case an overdamped closed-loop system is required, which
in turn requires a Kp setting significantly less than half that of the Kp setting that was causing
oscillation.

Fig 10. Effects of varying PID parameters (Kp,Ki,Kd) on the step response of a system

6.2 Ziegler–Nichols method

Another heuristic tuning method is known as the Ziegler-Nichols Method, introduced by John
G. Ziegler and Nathaniel B. Nichols in the 1940s. As in the method above, the Ki and Kd
gains are first set to zero. The proportional gain is increased until it reaches the ultimate gain,
Ku, at which the output of the loop starts to oscillate constantly. Ku and the oscillation period
Tu are used to set the gains as follows:

Control Type Kp Ki Kd

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 P 0.50Ku --- ---

PI 0.45Ku 0.54Ku/Tu ---

PID 0.60ku 1.2Ku/Tu 3KuTu/40

These gains apply to the ideal, parallel form of the PID controller. When applied to the
standard PID form, only the integral and derivative gains Ki and Kd are dependent on the
oscillation period.

6.3 Relay (Åström–Hägglund) method

Published in 1984 by Karl Johan Astrom and Tore Hägglund, the relay method temporarily
operates the process using bang-bang control and measures the resultant oscillations. The
output is switched (as if by a relay, hence the name) between two values of the control variable.
The values must be chosen so the process will cross the setpoint, but they need not be 0% and
100%; by choosing suitable values, dangerous oscillations can be avoided.
As long as the process variable is below the setpoint, the control output is set to the higher
value. As soon as it rises above the setpoint, the control output is set to the lower value. Ideally,
the output waveform is nearly square, spending equal time above and below the setpoint. The
period and amplitude of the resultant oscillations are measured, and used to compute the
ultimate gain and period, which are then fed into the Ziegler–Nichols method.
Specifically, the ultimate period Tu is assumed to be equal to the observed period, and the
ultimate gain is computed as Ku= 4b/pi*a, where a is the amplitude of the process variable
oscillation, and b is the amplitude of the control output change which caused it.

Fig11. Tuning Procedures

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 Chapter-7
7. Applications
7.1 Space exploration
Space missions involve sending robots into space in the goal of discovering more of the
unknown. The robots used in space exploration have been controlled semi-autonomously. The
robots that are sent to space have the ability to maneuver itself, and are self-sustaining. To
allow for data collection and a controlled research, the robot is always in communications with
scientists and engineers on Earth. For the National Aeronautics and Space Administration’s
(NASA) Curiosity rover, which is part of their Mars exploration program, the communication
between the rover and the operators are made possible by “an international network of antennas
that…permits constant observation of spacecraft as the Earth rotates on its own axis”.

Fig12. The Martian Robot

7.2 Boston Dynamics Robot
Boston Dynamics “Spot” is an autonomous robot that uses four sensors and allows the robot
to map where it is relative to its surroundings. The navigational method is called simultaneous
localization and mapping or “SLAM” for short. Spot has several operating modes and
depending on the obstacles in front of the robot, it has the ability to override the manual mode
of the robot and perform actions successfully. This is similar to other robots made by Boston
Dynamics, like the “Atlas”, which also has similar methods of control. When the “Atlas” is
being controlled, the control software doesn’t explicitly tell the robot how to move its joints,
but rather it employs mathematical models of the underlying physics of the robot’s body and
how it interacts with the environment”. Instead of inputting data into every single joint of the
robot, the engineers programmed the robot as a whole, which makes it more capable to adapt
to its environment. The information in this source is dissimilar to other sources, except the
second source, because robots vary so much depending on the situation.
7.3 Military
The earliest robots used in the military dates back to the 19th Century, where automatic
weapons were on the rise due to developments in mass production. The first automated
weapons were used in World War I, including radio-controlled, unarmed aerial vehicles Since
the invention, the technology of ground and aerial robotic weapons continues to develop, it
transitioned to become part of modern warfare. In the transition phase of the development, the
robots were semi-automatic, being able to be controlled remotely by a human controller. The
advancements made in sensors and processors lead to advancements in capabilities of military

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robots. Since the mid-20th century, the technology of artificial intelligence began to
develop and in the 21st century, the technology transferred to warfare, and the weapons that
were semi-automatous is developing to become lethal autonomous weapon systems, LAWS
for short.
7.4 Artificial Intelligence
Artificial Intelligence(AI) is used in robotic control to make it able to process and adapt to its
surroundings. It is able to be programmed to do a certain task, for instance, walk up a hill. The
technology is relatively new, and is being experimented in several fields, such as the military.
7.5 Medical and surgical
In the medical field, robots are used to make precise movements that are humanly difficult.
Robotic surgery involves the use of less-invasive surgical methods, which are “procedures
performed through tiny incisions”. Currently, robots use the da Vinci surgical method, which
involves the robotic arm (which holds onto surgical instruments) and a camera. The surgeon
sits on a console where he controls the robot wirelessly. The feed from the camera is projected
on a monitor, allowing the surgeon to see the incisions. The system is built to mimic the
movement of the surgeon’s hands and has the ability to filter slight hand tremors. But despite
the visual feedback, there is no physical feedback. In other words, as the surgeon applies force
on the console, the surgeon won’t be able to feel how much pressure he or she is applying to
the tissue.

Fig13. The surgeon who operates from 400km away

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 Chapter-8 Conclusion
In this report, it had been shown that various works can be done quickly by the use of mobile
robots and for that proper stabilization of robots is very necessary to perform a particular task.
The PID controllers a hue and a critical role which can: (i) adaptively drive the parameter
selection of the low-level PID controllers of mobile robots, thus improving the adaptability
and the real-time performance;(ii) make a controlled exploration through the most promising
regions of the state and action spaces by means of an sparse incremental. This can provide a
better understanding of the performance of different optimization techniques for PID controller
design in mobile. Overall, the findings of this study highlight the importance of optimization
techniques in PID controller design for mobile robot control and pave the way for further
research in this field. A PID controller relies only on the measured process variable, not on the
knowledge of the underlying process, making it a broadly useful controller. By tuning the three
parameters in the PID controller algorithm, the controller can provide control action designed
for specific process requirements. The response of the controller can be described in terms of
the responsiveness of the controller to an error, the degree to which the controller overshoots
the setpoint, and the degree of system oscillation. Note that the use of the PID algorithm for
control does not guarantee optimal control of the system or system stability. Some applications
may require using only one or two actions to provide the appropriate system control. This is
achieved by setting the other parameters to zero. A PID controller will be called a PI, PD, P or
I controller in the absence of the respective control actions. PI controllers are fairly common,
since derivative action is sensitive to measurement noise, whereas the absence of an integral
term may prevent the system from reaching its target value due to the control action.A PID
controller relies only on the measured process variable, not on the knowledge of the underlying
process, making it a broadly useful controller. By tuning the three parameters in the PID
controller algorithm, the controller can provide control action designed for specific process
requirements. The response of the controller can be described in terms of the responsiveness
of the controller to an error, the degree to which the controller overshoots the setpoint, and the
degree of system oscillation. Note that the use of the PID algorithm for control does not
guarantee optimal control of the system or system stability. Some applications may require
using only one or two actions to provide the appropriate system control. This is achieved by
setting the other parameters to zero. A PID controller will be called a PI, PD, P or I controller
in the absence of the respective control actions. PI controllers are fairly common, since
derivative action is sensitive to measurement noise, whereas the absence of an integral term
may prevent the system from reaching its target value due to the control action.

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 9.References

1. https://www.academia.edu/82126732/Design_and_Analysis_of_Robot_PID_Controll
er_Using_Digital_Signal_Processing_Techniques
2. https://stemrobotics.cs.pdx.edu/node/7268.html
3. https://www.sciencedirect.com/science/article/abs/pii/S0957417419304749
4. https://en.wikipedia.org/wiki/PID_controller
5. https://www.codeproject.com/Articles/36459/PID-process-control-a-Cruise-Control-
example
6. https://web.archive.org/web/20140513162717/http://www.ee.hacettepe.edu.tr/~solen/
ELE356/exp1.pdf
7. https://books.google.co.in/books?id=iwbWCgAAQBAJ&q=%22Centrifugal+Govern
or%22+Huygens&pg=PA36&redir_esc=y#v=snippet&q=%22Centrifugal%20Govern
or%22%20Huygens&f=false
8. https://docs.wpilib.org/en/stable/docs/software/advanced-controls/controls-
glossary.html
9. https://medium.com/autonomous-robotics/pid-control-
85596db59f35#:~:text=Conclusion%3A,designed%20for%20specific%20process%20
requirements.
10. https://ctms.engin.umich.edu/CTMS/index.php?example=Introduction&section=Cont
rolPID
11. https://www.frontiersin.org/articles/10.3389/frobt.2022.975850/full

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