Depth, Linear Speed and Attitude Control Using Gyro and Thrust Propeller of an Underwater Robot

Akhila Madhushan Jayasekara

A thesis submitted in partial fulfillment of the requirement for the degree of Master of Engineering in Mechatronics

Examination Committee: Prof. Manukid Parnichkun (Chairperson) Dr. A. M. Harsha S. Abeykoon Dr. Mongkol Ekpanyapong

Nationality: Sri Lankan Previous Degree: Bachelor of Science in Engineering in Mechatronics Asian Institute of Technology Thailand

Scholarship Donor: AIT Fellowship

Asian Institute of Technology School of Engineering and Technology Thailand December 2017

ACKNOWLEDGMENTS

This research study would have been impossible without the guidance of everyone around me. Special thanks goes to Prof. Manukid Parnichkun, Dr. A. M. Harsha S. Abeykoon, and for Dr. Mongkol Ekpanyapong advising for my research. I also be thankful to all the lectures and staff from ISE department who taught me very inestimable lessons and for their commitments that made me insightful in this field.

My parents, Dr. Dayananda Jayasekara and Seetha Ranasinghe, always have been my pillar of strength and guidance for my studies, I am truly grateful for their support. I am thankful for my colleagues for the help and for all the moral support I received throughout the two years of masters. There were many who help me in Sri Lanka and Thailand to finish this research, I am truly grateful for all your support and guidance.

ABSTRACT

A number of researches have been conducted to date on various methods and techniques to make underwater vehicles better and risk free. The ocean is a vast 3-D environment and it follows that an ocean research tool, such as the underwater vehicle, should ideally be able to move freely in any direction within its surroundings. Most underwater robots uses rudders, propellers and many numbers of water pumps to create its motion, changes its altitude and keep its stability. Actuators that deflect fluid momentum, such as fins and rudders, lose control authority at low velocities. Although actuators that generate fluid momentum, such as thrusters, can provide low-velocity control, the use of multiple thrusters increases drag, reducing efficiency particularly when travelling at high speeds. The ability to adopt and maintain any attitude on the surface of a sphere with a zero radius turning circle would allow an underwater robot to approach its missions in a fully 3-D manner, optimizing the use of its thrusters, sensors, and power supply in a way that has not been possible previously. Purpose of this thesis is to approach the subject in a different direction and make advancements, the zero-G concept. This method is mainly uses in satellites to control its motions.

Keywords: Underwater Remotely Operated Vehicle (ROV), Autonomous Underwater Vehicle (AUV), Control Momentum Gyro (CMG) Proportional-Integral-Derivative controller (PID), Linear-Quadratic Regulator (LQR), Center of Mass (CM)

iii

TABLE OF CONTENTS (Cont’d)

CHAPTER TITLE PAGE

TITLE PAGE i ACKNOWLEDGEMENTS ii ABSTRACT iii TABLE OF CONTENTS iv LIST OF FIGURES vi LIST OF TABLES viii

1 INTRODUCTION 1

1.1 Introduction 1 1.2 Problem Statement 2 1.3 Objective 2 1.4 Limitations and Scope 2

2 LITERATURE REVIEW 3

2.1 Introduction 3 2.2 Systems with Reaction Wheels 3 2.3 Balance Control of Bicycle Robot 4 2.4 Underwater Robots 7

3 METHODOLOGY 11

3.1 Mathematical modelling of the system 11 3.2 System overview 13 3.3 Hardware model 15

4 SIMULATION AND RESULTS 23

4.1 PID simulations 23 4.2 State space and LQR calculations 33

5 CONCLUSION AND RECOMMENDATION 40

5.1 Conclusion 40 5.2 Recommendation 40

REFERENCES 41

LIST OF FIGURES (Cont’d)

FIGURE TITLE PAGE

Figure 2.1 A cutaway view of a typical reaction wheel 3 Figure 2.2 Schematic of tumbler-reaction system 4 Figure 2.3 Self-balancing bicycle robot 5 Figure 2.4 The scheme of bicycle robot 5 Figure 2.5 The simulation results of single gyroscopic stabilizer 6 Figure 2.6 The simulation results of double gyroscopic stabilizer 6 Figure 2.7 Single gimbal control momentum gyro 7 Figure 2.8 Pyramid configuration of CMGs 8 Figure 2.9 Control system block diagram 8 Figure 2.10 A photo of the AUV 9 Figure 2.11 Mechanism of actuators 9 Figure 2.12 Mechanism of actuators 10 Figure 3.1 Motor placement of the ROV 11 Figure 3.2 Forces acting on the ROV body 11 Figure 3.3 Translational forces acting on the ROV body 13 Figure 3.4 System overlay 14 Figure 3.5 Solid works design of the ROV 15 Figure 3.6 Actual model of the ROV 15 Figure 3.7 Actual model of the ROV 16 Figure 3.8 Final reaction wheel 16 Figure 3.9 Weight adjusting component 17 Figure 3.10 The broken propeller 17 Figure 3.11 3D printed new propeller 18 Figure 3.12 Electronic components 18 Figure 3.13 Pololu motor 19 Figure 3.14 High current motor driver 19 Figure 3.15 Brushless thrust moto 20 Figure 3.16 High current ESC 20 Figure 3.17 Sensor module 21 Figure 3.18 Barometric pressure sensor 21 Figure 3.19 Surface communication unit 22 Figure 3.20 Surface communication 22 Figure 4.1 Response to impulse disturbance of uncontrolled system in yaw 23 Figure 4.2 Response to impulse disturbance of PID system in yaw 24 Figure 4.3 Yaw disturbance 25 Figure 4.4 Response to impulse disturbance of uncontrolled system in pitch 26 Figure 4.5 Response to impulse disturbance of PID system in pitch 27 Figure 4.6 Experimental response in pitch angle to impulse disturbance 28 Figure 4.7 Experimental response in pitch angle to impulse disturbance 29 Figure 4.8 Response to impulse disturbance of uncontrolled system in roll 30 Figure 4.9 Response to impulse disturbance of PID system in roll 31 Figure 4.10 Experimental response in roll angle to impulse disturbance 32

Figure 4.11 Experimental data of depth control by moving forward and changing 33 pitch angle Figure 4.12 Response to impulse disturbance of LQR system for yaw 34 Figure 4.13 Experimental response in yaw angle to impulse disturbance 35 Figure 4.14 Response to impulse disturbance of LQR system for pitch 36 Figure 4.15 Experimental response in pitch angle to impulse disturbance 37 Figure 4.16 Response to impulse disturbance of LQR system for roll 38 Figure 4.17 Experimental response in roll angle to impulse disturbance 39

vii

LIST OF TABLES

TABLES TITLE PAGE

Table 2.1 List of researches on different types underwater vehicles 10 Table 4.1 Values of inertia and coefficient of drag 34

viii

CHAPTER 1

INTRODUCTION

1.1 Introduction

One of the major portions of mechatronics is control algorithms. With the advancement of mechatronics engineering, immense interest is of mobile robots has been reported in last few decades. Many researchers are developing and using control algorithms due to its potential applications which may include intelligent vehicles, recue robots, underwater robots, flying robots and drones, etc. Although a many great numbers of researches being done on flying robots and land vehicles, researches on underwater robots and vehicles is relatively low. Exploring the deep sea is a high risk task. Even if the vessel is designed to endure very high water pressure in greatest depths, malfunctions and emergencies can happen. Therefore having a human crew in the craft is dangerous. Utilizing advanced control algorithms and robotic technology, unmanned vehicles can be given the task.

The system uses gyro-momentum to control the attitude of the vehicle. The gyroscope is an interesting display of motion and dynamics. The movement of a gyroscope’s spin axis causes a torque which results in the precession seen in spinning tops and other gyroscope based applications. With the dynamics of gyroscope motion understood, we can develop such a system.

1.2 Problem Statement

As mentioned in the introduction actuators that deflect fluid momentum is not very efficient in controlling the attitude of an underwater explore robot. Maneuverability and the stability is very important to such a robot. Therefore the purpose of this project is to develop an efficient system to control the attitude of an underwater robot.

1.3 Objective

The main objective of this project is to develop an underwater robot system and design a controller that can control pitch, yaw, roll and the stability of an underwater vehicle without using fluid momentum displacement methods. Only one thrust propellers will be used in the design and it will only control the liner velocity of the vehicle. Depth variations will be made by changing the pitch angle and propel forward or backward.

 Designing the pitch, yaw and roll control mechanism using gyro.

 Develop the stabilization system to minimize the unnecessary oscillation.

1.4 Limitations and Scope

 To change the altitude, the vehicle has to move forward or backward by maintaining a certain pitch angle.

 The rover has a semi-autonomous control method. The attitude parameters are fed by surface mounted controller. Communication will be done through a hard line.

 For this prototype the runtime is limited to about 20 minutes since the rover is powered by batteries. This limitation can be simply avoided by powering the rover through a hard line from the surface.

 For easy maneuverability the system has to be in neutral buoyancy. For that reason the rover weight a little more than 10kg.

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

This chapter contain a literature survey regarding recently conducted researchers on different types of underwater remotely operated vehicles (ROV) which is important and relevant for this research. In addition to that, researches on stabilizing unbalanced systems using reactions wheels and their control algorithms are also reviewed.

2.2 Systems with Reaction Wheels

Reaction wheels are used in a vast range of systems such as satellites, ships. Also researches on self-balancing bicycle robot, inverted pendulum, etc.

In 2015 Mehrjardi, Mohamad Fakhari, Hilmi Sanusi, and Mohd Alauddin Mohd Ali [1] presented a Proposed Satellite Reaction Wheel Model. A typical reaction wheel consists of a high inertia flywheel powered by a brushless DC motor. A cutaway view of a reaction wheel is shown in Fig.2.1. By adjusting the motor electric current the flywheel can speed up or slow down, and, by reaction, an opposite torque is applied to the satellite.

Figure 2.1: A cutaway view of a typical reaction wheel[3]

The proposed reaction wheel model is based on following simple mechanics laws.

τm=I휔̇ +τc휔+sin(휔)

Where, b , is the coefficient of viscous friction, τ c is the Coulomb friction torque, d is the starting torque, and ωs is known as Stribeck speed. The friction in a reaction wheel can be broken down into viscous friction and coulomb friction. The viscous friction τv , varies with temperature and speed, and the coulomb friction is a constant. Bearing lubricant causes viscous friction in the reaction wheel. The viscosity of bearing lubricant depends on temperature. Generally viscous friction has a direct relation with speed of wheel and inverse relation with temperature. The coulomb friction τc , is caused by rolling friction within the reaction wheel

bearing. This drag torque is defined as the smallest amount of torque which if applied continuously will keep the flywheel rotating.

τn= τm- τd τz= -τn= -dH⁄푑푡

Where, τ n is the net torque, τ m is the motor torque, τ d is the friction torque, τ z is the reaction torque applied to the satellite.

Reaction wheels are used in active disturbance rejection systems. Niu, Sanku, Jie Li, and Chengwei Yang. 2015[2]. Such system is a self-stabilized platform and its mechanical structure and premium stability properties can be used for active wind disturbance reject of Micro Air Vehicles (MAVs) in Atmospheric Boundary Layer (ABL) area. The system developed by Niu, Sanku, Jie Li, and Chengwei Yang. 2015[2] is a tumbler-reaction wheel system. The advantage of tumbler-reaction wheel structure is that the reaction torque induced by reaction wheel could attenuate disturbance torque to keep body stable.

Figure 2.2: Schematic of tumbler-reaction system[2]

This system consists of three parts which are reaction wheel, tumbler and servo actuator. The reaction wheel and the tumbler are connected by DC motor servo actuator. There is a half circle shape frame at the bottom of the tumbler and a girder is fixed at the frame. A counterweight can be positioned on different position of the girder for change of canter of gravity and improvement of dynamic performance. The reaction wheels are driven by DC motor servo actuators individually.

According to the figure 2.2 the center of gravity position of the tumbler is presented as,

xo1= -l3α + l1sin α yo1= l1cos α

2.3 Balance Control of Bicycle Robot

There are several researches on balancing control of bicycle robot by usig a flywheel.Thanh,Bui Trung, and Manukid Parnichkun 2008 [3] invented and developed autonomous bicycle robot by using the principal of gyroscopic effect, and the system consists of gyroscopic stabilizer.

The algorithm designed to control balancing of the bicycle robot was by using H2/H∞ control. There were three control loops for controlling the autonomous system; gyroscopic effect for balancing, steering control for controlling the direction and rear wheel control for controlling the velocity. These controls were assembled on embedded PC/PC-104.

Figure 2.3: Self-balancing bicycle robot[3]

With the help of gyroscopic stabilizers, Beznos, A. V 1998[4] developed a bicycle robot. The system was employed with two gyroscopic spinning in opposite directios as shown in the figure 2.4. In this system two programmable controller were used which is was on Intel 80C196KC chip with a clock speed of 20MHz, and communicate between the controller via CAN bus. The experiment was carried out on balancing and tracking of bicycle robot by mimetic field, and capable of testing the tracking along the path of robot at speed of 1m/s.

Figure 2.4: The scheme of bicycle robot[4]

Spry, Stephen C., and Anouck R. Girard 2008[5] in their paper explained about the configurations, dynamic and control of gyroscopic stabilization of unstable vehicles. Dynamic equation for a gyroscopic stabilizer was derived by using Lagrange’s method and the results

was implemented by simulation. Configurations consist of single and double gyroscope cases, then compare the simulation results between two cases as shown in figure 2.5 ad figure 2.6.

Figure 2.5: The simulation results of single gyroscopic stabilizer[5]

Figure 2.6: The simulation results of double gyroscopic stabilizer [5]

Another interesting application of using flywheel is to balance a unicycle robot. The experiment was performed by Dao, Minh-Quan, and Kang-Zhi Liu 2005 [6]. The principal of gyroscope was used for balancing the unicycle. The system consisted of two gyroscopes which rotated at the same speed but in the opposite directions for balancing of lateral stabilization.

Even though these researches are not directly link to this thesis, the control algorithms and mathematical models can be related since the main actuator is very similar.

2.4 Underwater Robots

Submarine maneuver is a 6-DOF space motion. The motion of submarine can be simplified as the horizontal and vertical plane movement campaign when neglecting the rolling movement and the influence of coupling between the two planes. To control horizontal motion the submarine has a usual rudder as surface ships do. However in vertical motion, a submerged submarine needs a control surface to maintain the desired depth and pitch angle. The submerged submarine can gain a tactical advantage which is a lot depending on whether its vertical plane control is good enough. He, Jingjing,2015 [7] conducted a study on the submarine vertical motion. In this paper, an active output feedback fault-tolerant control design for submarine vertical movement was proposed. The observer was given an unknown disturbance input, and then an observer was designed to diagnose all the actuator faults by decupling external disturbance from actuator faults. Then a fault parameter tracking law was designed to estimate the fault parameters of bow and stern planes. An adaptive H∞ dynamic output feedback fault-tolerant control scheme was proposed using the estimated fault parameters of the bow and stern planes.

This project simulated results for vertical movement control with using conventional actuator method but with a complex control theory. My thesis is approaching the problem in a completely different direction. However the mathematics models of above mentioned project is relevant to my thesis.

However this thesis is focusing on an underwater robot that uses no outer surface actuators to control the attitude. Thornton, Blair 2007 [8] developed an autonomous underwater vehicle using gyro momentum to control the attitude.

Figure 2.7: Single gimbal control momentum gyro(CMG)[8] 7

A single gimbal CMG is a torque generator that consists of a flywheel mounted orthogonally on an actuated gimbal, as illustrated in Figure 2.8. A CMG system is composed of a number of identical CMG units arranged in a defined configuration. For each unit, the flywheel spins with an angular momentum vector along its axis of rotation. For single gimbal units, the state of the system is defined by the angle about the gimbal axis, which is orthogonal to the momentum axis. Rotations of the gimbal generate a gyroscopic torque that acts about the mutually orthogonal axis and has a magnitude equal to the vector rate of change of the angular momentum stored. The unit vectors form a rotating coordinate system that tracks the nutation and precession of each CMG to follow its orientation.

Figure 2.8: Pyramid configuration of CMGs [8]

This project used a pyramid configuration of CMG system that consists of four units arranged symmetrically about its center. The gimbal axis of each unit lies normal to the surface of a pyramid with a skew angle of β. The symmetrical nature is convenient for attitude control as it allows independent actuation about all three rotational axes. However, with only four units, the system was minimally redundant and this has posed significant challenges for singularity avoidance.

Figure 2.9: Control system block diagram [8]

In this research paper they have used Lyapunov’s direct method to assess stability as robot control law. It is a very advanced and complex method. However this thesis tends to address the stability problem in a simple method.

Kawaguchi Katsuyoshi 1993 [9] developed a shuttle type autonomous underwater vehicle (AUV). The AUV consists of cylindrical body and a pair of wings which provided lift force. Also a system displaces the location of the center of gravity longitudinally and laterally by moving a weight. The AUV did not have a propeller thruster but moved aside by gliding. When the vehicle came to the destination depth, it drops a decent weight and becomes positive buoyant for ascent. The wings then provide the down force necessary to stay level for the gliding motion. The AUV controls its trajectory changing pitch angle and roll angle by displacing the center of gravity. Two actuators in a hull move a weight longitudinally and laterally.

Figure 2.10: A photo of the AUV [9]

Figure 2.11: Mechanism of actuators [9]

The Sea Otter 2 mini ROV [10] is a product for military use. It is designed to identify, locate and dispose of n9aval mines. The design consists of multiple thrusters for control depth, pitch, yaw, roll and liner velocity.

Figure 2.12: Mechanism of actuators [10]

Table 2.1: List of researches on different types underwater vehicles

Ref Topic Method

[8] Zero-G Class Underwater Robots Pyramid configuration of CMG system and thrust propeller

[9] Development and Sea Trials of a Shuttle Type AUV No propeller used. “ALBAC” Wings to create lift force. Changing the position of CG for pitch and roll.

Using a weight for descend.

[10] The Sea Otter 2 mini ROV Multiple thrusters

CHAPTER 3

METHODOLOGY

3.1 Mathematical modelling of the system

The system is made up of 4 sub-systems. Three of the sub-systems consist of inertial wheel which control the rotational movement of yaw, pitch and roll direction and the other for control the translational movement. However for rotation movement, all yaw, pitch and roll directional sub-systems are similar.

3.1.1 System Model for yaw, pitch and roll direction

The orientation of three DC motors which control yaw, pitch and roll are show in the bellow diagram.

Figure 3.1: Motor placement of the ROV

Figure 3.2: Forces acting on the ROV body 11

Since the center of buoyancy and the center of mass is nearly overlap, the upright force and the weight cancel each other out. In this system torque produced by the motor τm acts on the reaction wheel. The torque on the rover τ is the reaction torque of the reaction wheel acts in the opposite direction. And the drag force would be F. For drag calculation the shape of the rover is considered as spherical.

τm - Fd = τ (Equation 3.2)

τm = kt i = kt V/R = kv V (Equation 3.2)

Drag force given by yaw and pitch

2 Fd = 0.5 A Cd ρ Ẋ (Equation 3.3)

Considering Ẋ2 ≈ 2Ẋ for lower speed and Ẋ= r 휃̇

From (Equation 3.3)

Fd = 0.5 A Cd ρ (2 r 휃̇) = A r Cd ρ 휃̇ (Equation 3.4)

Ayaw,pitch = 0.075 m2

Ryaw,pitch = 0.15m

Cd yaw,pitch = 0.42

Considering C=A r Cd ρ (Equation 3.5)

Fd = C 휃̇ (Equation 3.6)

For roll, drag force is given by

Fd = 8 η r3휃̇= C 휃̇ (Equation 3.7)

kv V - C 휃̇ = I휃̈ (Equation 3.8) The torque constant with respect to the motor voltage kv = 0.05Nm/V . The drag coefficient for yaw and pitch C = 4725. And the drag coefficient for roll direction C = 1.15*10-5. Moment 2 2 of inertia for yaw, pitch and roll follows Iyaw = 23.73kgm , Ipitch = 23.93kgm and Iroll = 3.27kgm2 .

3.1.2 System Model for X direction

The translational force is given by a single propeller at the back of the rover.

Figure 3.3: Translational forces acting on the ROV body

F - Fd = mẌ (Equation 3.9)

τm = kt i = kt V/R = kv V (Equation 3.10)

For low speeds assume Ẋ2 ≈ 2Ẋ

From (Equation 3.3) , (Equation 3.9) and (Equation 3.10)

kv V – 2C Ẋ = mẌ (Equation 3.11) C = 15.75 m = 10kg

3.2 System overview

ROV has two main sub-systems. The user can give the yaw, pitch, roll and speed parameters from a control module on the ground. To execute the user given data, ROV has another microcontroller with the control algorithm for precise maneuvering.

Figure 3.4: System overlay

Inside the ROV there are three DC motors which have similar specifications to control yaw, pitch and roll angels. Each motor has been connected to the Arduino through three single channel motor drivers. Each driver can support up to 35A of current. The digital IMU and the magnetometer is in the same modular unit. Therefore it is convenient to get both data at once. Outside the ROV a brushless motor has been used for the thruster. The motor is connect the Arduino through a high current ESC.

3.3 Hardware model

3.3.1 Mechanical design

A simple mechanical design is shown below that is created with solid works.

Figure 3.5: Solid works design of the ROV

Figure 3.6: Actual model of the ROV

Figure 3.7: Actual model of the ROV

Underwater housing is made in acrylic. The housing consists of two parts so it can be open effortlessly. Reaction wheels are made in steel.

Figure 3.8: Final reaction wheel

Center of mass and center of buoyancy overlapping is very crucial for the dynamic of the ROV. Therefor for changing the center of mass a weight system has been implemented to the rover.

Figure 3.9: Weight adjusting component

The ring shaped component can be slid up and down along the groove and tighten in any positon. Using this method the center of mass can be easily change all x, y and z direction of the ROV. Four steel rods of 2kg have been used to change the center of mass. This component has been design in solid works and fabricated by 3D printing.

3.3.2 Underwater propeller

Previously an aftermarket propeller has been used. The motor was sufficient for the thrust needed, however the propeller was destroyed under process of testing.

Figure 3.10: The broken propeller 17

After that a more tested and durable open source propeller was used. Slight adjustment have been made in the original design and used 3D printing to fabricate the propeller.

Maximum forward thrust = 35 N Maximum reverse thrust = 30 N Operating voltage = 6 - 12V Maximum current = 27 A Maximum power = 280W

Figure 3.11: 3D printed new propeller

3.3.3 Electronics design

In the ROV microcontroller has two main objectives. Gather sensor values and process them. And according to the command given by the surface control unit and gathered sensor data, actuating each motor.

Figure 3.12: Electronics components

Three pololu metel gear motors have been used for yaw, pitch and roll control. These motors are equipped with encoder consists of 1200 count for revolution.

Figure 3.13: Pololu motor

Nominal voltage = 12V

Rotational speed = 500RPM

Maximum torque = 0.6Nm

Stall current = 5A

High current motor divers have been used for above mentioned motors. The driver is capable of maximum current of 35A and continuous current of 14A. Maximum PWM frequency of 20kHz.

Figure 3.14: High current motor driver

A brushless motor is used for the thrust motor. Which has a high rpm and high thrust than brushed DC motor.

Operating voltage = 6 - 12V Maximum current = 27 A Maximum power = 280W

Figure 3.15: Brushless thrust moto

An electronic speed control (esc) unit has been used to drive the thrust motor. The thrust motor been a brushless motor, to change the rotational direction of the motor polarity of 2 phases has be changed. This ESC has a built in switch to do such task. The speed and the direction is controlled by the value of PWM signal given to the driver. Maximum current is 35A and continuous current is 30A.

Figure 3.16: High current ESC

The GY-87 breakout board is used to get the roll, pitch and yaw values of the ROV. This board is based on InvenSense MPU-6050 sensor. It contains a MEMS accelerometer and a MEMS gyro. Also a magnetometer which is helpful to control yaw and a barrow meter. The data is transmitted to the Arduino board through I2C communication.

Figure 3.17: Sensor module

Barometric pressure sensor has been used for measure the water pressure and that data is used to calculate the depth of the ROV.

Figure 3.18: Barometric pressure sensor

3.3.4 Surface control unit

An Arduino uno board has been used in the surface control unit. To input yaw, pitch and roll headings three rotary potentiometers have been used. To control the translational speed and the direction, a linear potentiometer has been used. This unit also has one of Arduino Ethernet shield to connect with the ROV.

Also the power button of ROV is hard wired to this surface control unit.

Figure 3.19: Surface communication unit

Figure 3.20: Surface communication

CHAPTER 4

SIMULATION AND RESULTS

4.1 PID simulations

For the yaw, pitch and roll control the mathematical equations very similar. Only some of the values of few constant changes.

From (Equation 3.8)

휃 퐾푣 = (Equation 4.1) 푉 퐼푆2+퐶푆

kv = 0.05Nm/V

Yaw angel response to an impulse disturbance of uncontrolled system

Cyaw= 4.725

2 Iyaw = 23.73kgm

Figure 4.1: Response to impulse disturbance of uncontrolled system in yaw

PID simulation for impulse disturbance in yaw

Kp = 7.5

Kd = 4

Ki = 0

Figure 4.2: Response to impulse disturbance of PID system in yaw

The graph bellow shows the experimental response of yaw when an impulse disturbance is applied underwater.

Kp = 2.8

Kd = 0.2

Ki = 0

Figure 4.3: Yaw disturbance

Because of the high viscosity of the water the damping happens naturally. Since the system is and neutral stability.

Pitch angle response to an impulse disturbance of uncontrolled system

Cpitch= 4.725

2 Ipitch = 23.93kgm

Figure 4.4: Response to impulse disturbance of uncontrolled system in pitch

PID simulation for impulse disturbance in pitch

Kp = 7.5

Kd = 4

Ki = 0

Figure 4.5: Response to impulse disturbance of PID system in pitch

The graphs bellow shows the experimental response of pitch when an impulse disturbance is applied underwater. The disturbance is given downward.

Kp = 2.8

Kd = 0.2

Ki = 0

Figure 4.6: Experimental response in pitch angle to impulse disturbance

The disterbance given upward for the following resut,

Figure 4.7: Experimental response in pitch angle to impulse disturbance

Roll angel response to an impulse disturbance of uncontrolled system

-5 Cpitch= 1.15x10

2 Ipitch = 0.029kgm

Figure 4.8: Response to impulse disturbance of uncontrolled system in roll

PID simulation for impulse disturbance in roll

Kp = 7.5

Kd = 4

Ki = 0

Figure 4.9: Response to impulse disturbance of PID system in roll

The graph bellow shows the experimental response of roll when an impulse disturbance is applied underwater. The disturbance is given downward

Kp = 1.7, Kd = 0.2, Ki = 0

Figure 4.10: Experimental response in roll angle to impulse disturbance

One of the main limitation is the depth control. Depth is changed using both pitch angel and thrust. Therefore to control the depth the ROV always has to move. The following graphs shows the result of depth control for a given depth profile.

Figure 4.11: Experimental data of depth control by moving forward and changing pitch angle

4.2 State space and LQR calculations

From (Equation 3.8)

휃 = X1 (Equation 4.2)

휃̇ = X2 (Equation 4.3)

V = U (Equation 4.4)

kv U – C X2 = I Ẋ 2 (Equation 4.5)

Ẋ 2 = kv U/I – C X2/I (Equation 4.6)

Ẋ 2 = 0 X1 – C X2/I + kv U/I (Equation 4.7)

̇ 0 1 X1 0 X1 = [ ] [ ] + [ ] [U] (Equation 4.8) X2̇ 0 – C /I X2 kv /I 0 1 A = [ ] (Equation 4.9) 0 – C /I

0 B = [ ] (Equation 4.10) kv /I 33

C = [1 0] (Equation 4.11)

D = [0] (Equation 4.12)

Table 4.1: Values of inertia and coefficient of drag

Yaw Pitch Roll

C 4.725 4.725 1.15x10-5

I(kgm2) 23.70 23.93 3.27

Results of LQR simulation shown below. Graphs shows the response to an impulse disturbance in yaw, pitch and roll directions.

Yaw angle control

600 0 푄 = [ ] 0 1 R =1

K1 = 0.41

K2 =1.44

Figure 4.12: Response to impulse disturbance of LQR system for yaw 34

The graph bellow shows the experimental response of LQR controller of yaw when an impulse disturbance is applied underwater. The experimental gains are much different than the simulation values.

K1 = 1.17

K2 =1.09

Figure 4.13: Experimental response in yaw angle to impulse disturbance

Pitch angle control

600 0 푄 = [ ] 0 1 R =1

K1 = 0.416

K2 =1.45

Figure 4.14: Response to impulse disturbance of LQR system for pitch

The graph bellow shows the experimental response of LQR controller of pitch when an impulse disturbance is applied underwater. The disturbance is given downward. The experimental gains are much different than the simulation values.

K1 = 1.20

K2 =1.09

Figure 4.15: Experimental response in pitch angle to impulse disturbance

For roll control

10 0 푄 = [ ] 0 1 R =1

K1 = 0.05

K2 = 3.42

Figure 4.16: Response to impulse disturbance of LQR system for roll

The graph bellow shows the experimental response of LQR controller of roll when an impulse disturbance is applied underwater. The experimental gains are much different than the simulation values.

K1 = 0.53

K2 =1.09

Figure 4.17: Experimental response in roll angle to impulse disturbance

CHAPTER 5

CONCLUSION AND RECOMMENDATION

5.1 Conclusion

Mathematical model has been derived for PID and LQR implementation. The testing with the PID was successful. For underwater robot, it is crucial to have a center of mass close to buoyancy point. Therefore system becomes a neutral balance system.

5.2 Recommendation

The project was a success. Although it is certainly beneficial to have more torque at the attitude control motors. During testing the most elaborate problems was the heat management inside the ROV. Since it is seal tight the heat from three motors and two batteries stated to have an effect on the sensors. Run time could be increase by supplying power form outside instead of batteries.

REFERENCES

[1] Mehrjardi, Mohamad Fakhari, Hilmi Sanusi, and Mohd Alauddin Mohd Ali. "Developing a proposed satellitereaction wheel model with current mode control." 2015 International Conference on Space Science and Communication (IconSpace). IEEE, 2015.

[2] Niu, Sanku, Jie Li, and Chengwei Yang. "Linear active disturbancerejection control for a tumbler-reaction wheel system." 2015 7th International Conference on Modelling, Identification and Control (ICMIC). IEEE, 2015.

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