Ads: Get Admission into 200 Level and Study any Course in any University of Your Choice. Low Fees | No JAMB UTME. Call 09038456231

Development of a Position and Trajectory Tracking Control of Ball and Plate System Using a Double Feedback Loop Structure

ADS! Obtain Up to N300,000 Cash in the 2020 Aspire Contest

Development of a Position and Trajectory Tracking Control of Ball and Plate System Using a Double Feedback Loop Structure.

ABSTRACT

This research work presents the development of a position and trajectory tracking control of ball and plate system. The ball and plate control system was considered as a double feedback loop structure (a loop within a loop), for effective control of the system.

The inner loop was designed using linear algebraic method by solving a set of Diophantine equations. The outer loop was designed using H-infinity sensitivity approach.

A virtual reality model of the ball and plate system using the virtual reality modelling language (VRML) and graphical user interface (GUI) based simulation model of the system were developed in MATLAB 2013a.

The results of the simulation of the system showed that the plate was stabilized at 0.3546 seconds and the ball was able to settle at 1.7087 seconds.

The trajectory tracking error of the system using the H-infinity controller was 0.0095 m. The improvements in terms of trajectory tracking error and settling time of the system when compared with the single loop H-infinity (SLH) controller are 71.8% and 60.5% respectively.

The improvements when compared with the double loop structure using fuzzy sliding mode controller are 52.5% and 51.2% in terms of the trajectory tracking error and settling time respectively.

TABLE OF CONTENTS

TITLE PAGE
DECLARATION i
CERTIFICATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT vi
TABLE OF CONTENTS vii
LIST OF FIGURES xi
LIST OF TABLES xiii
LIST OF APPENDICES xiv
LIST OF ABBREVIATION xv
CHAPTER ONE: INTRODUCTION
1.1 Background 1
1.2 Significance of Research 2
1.3 Problem Statement 3
1.4 Aim and Objectives 4
CHAPTER TWO: LITERATURE REVIEW
2.1 Introduction 5
2.2 Review of Fundamental Concepts 5
2.2.1 Ball and Plate System 5
2.2.1.1 Control system design 11
2.2.2 Nonlinear Systems 12
2.2.3 Controllability and Observability 13
2.2.3.1 Stability 14
2.2.3.2 Trajectory and motion tracking 16
2.2.3.3 Path following 17
2.2.4 Types of Controllers 18
2.2.4.1 H controller 19
2.2.4.2 H Mixed sensitivity problem 22
2.2.5 Linear Algebraic Method 23
2.2.5.1 Transient and steady-state requirements 25
2.2.5.2 Implementation by two-parameter configuration 27
2.2.5.3 Actuator parameters 31
2.2.5.4 Inner loop design 33
2.2.6 Virtual Reality Modelling Language (VRML) as a 3-D Modelling Tool 35
2.2.7 Simulink® 3D Animation 37
2.2.8 Graphical User Interface (GUI) 38
2.3 Review of Similar Works 39
CHAPTER THREE: MATERIALS AND METHODS
3.1 Introduction 55
3.2 Methodology 55
3.2.1 Ball and Plate System Modelling 56
3.2.2 Decomposition of the Ball and Plate System 56
3.2.3 Linearization of the Ball and Plate System 57
3.2.4 Controllability and Observability Test for the Ball and Plate System 58
3.3 Selection of the Actuator Parameters 59
3.3.1 Two-Port Parameter Configuration 63
3.4 Determination of the H Controller 64
3.5 Development of the Virtual Reality (VR) Model of the Ball and Plate System
65
3.6 Development of the Simulation Environment in MATLAB Simulink 66
3.6.1 Development of the Inner Loop Controller 66
3.6.2 Development of the Outer Loop Controller 67
3.6.3 Development of the Ball Dynamics of the Ball and Plate System 68
3.6.4 Development of the Reference Signal for the Trajectory Tracking 70
3.7 Graphical User Interface (GUI) of the Ball and Plate System 70
3.8 Performance Evaluation 71
3.8.1 Trajectory Tracking Error 71
3.8.2 Transient Response 71
3.9 Comparison of Results 71
CHAPTER FOUR: RESULTS AND DISCUSSION
4.1 Introduction 72
4.2 Result of the Controllability and Observability Test on the System 72
4.3 Result of the Actuator Parameter 72
4.4 Result of Two-Port Parameter Configuration 73
4.5 Result of the H Controller 75
4.6 Result of the Virtual Reality (VR) Model 76
4.7 Result of the Trajectory Tracking of the Ball and Plate System 78
4.8 Result of the Graphical User Interface (GUI) for the Circular Trajectory
Tracking 79
4.9 Result of the Circular Trajectory Tracking Using H-infinity Controller
Considering the Ball and Plate System as a Single Loop System 79
4.10 Comparison of the Results 80
4.10.1 Comparison of the controllers based on the Step Response Performance
Index 81
4.10.2 Comparison of the Developed Controller with that of Negash and Singh
(2015) 82
CHAPTER FIVE: CONCLUSION AND RECOMMENDATIONS
5.1 Conclusion 83
5.2 Limitation 83
5.3 Significant Contributions 83
5.4 Recommendations for Further work 84
REFERENCES

INTRODUCTION

1.1 Background

Balancing systems are one of the most popular and challenging test platforms for control engineers. Such systems are like the traditional cart-pole system (inverted pendulum), the ball and beam system, double and multiple inverted pendulums (Mohajerin et al., 2010).

The ball and plate system is a generalization of the famous ball and beam benchmark system.

The latter is a two degree of freedom (DOF) system consisting of a ball that can roll on a rigid beam, while the former is a four DOF system consisting of a ball that can roll freely on a rigid plate (Moarref et al., 2008).

However, it is more complicated than the ball and beam system due to its coupling of multi-variables. This under-actuated system has only two actuators and is stabilized by just two control inputs (Ghiasi & Jafari, 2012).

Since the movement of the ball over the plate can reach high speeds, the design of a suitable controller for this system is a major challenge; therefore, these systems are not commonly used in laboratories (Galvan-Colmenares et al., 2014).

The system consists of a plate pivoted at its centre such that the slope of the plate can be manipulated in two perpendicular directions (Dong et al., 2011). A servo system consists of motor controller card and two servo motors to tilt the plate.

Intelligent vision system is used for measurement of a ball position from a CCD camera. The problem of the motion control of this system is to control the position of a ball on a plate for both static positions and desired paths.

The slope of the plate can be manipulated in two perpendicular directions, so that the tilting of the plate will make the ball move on the plate (Dong et al., 2011).

REFERENCES

Andinet, N. H. (2011). Design of Fuzzy Sliding Mode Controller for the Ball and Plate System. (Masters of Science Thesis), Addis Ababa Institute of Technology, Addis Ababa., Published. Awtar, S., Bernard, C., Boklund, N., Master, A., Ueda, D., & Craig, K. (2002). Mechatronic design of a ball-on-plate balancing system. Mechatronics, 12(2), 217-228.

Bai, M., Lu, H., Su, J., & Tian, Y. (2006). Motion control of ball and plate system using supervisory fuzzy controller. Paper presented at the The Sixth World Congress on Intelligent Control and Automation, WCICA 2006.

Borah, M., Majhi, L., Roy, P., & Roy, B. (2014). Design of a Fractional Order PD Controller Tuned by Firefly Algorithm for Stability Control of the Nonlinear Ball and Plate System. Paper presented at the IEEE International Conference on Advanced Communication Control and Computing Technologies, Ramanathapuram, India.

Burns, R. S. (2001). Advanced Control Engineering (Vol. 3). Linacre House, Jordn Hill, Oxford OX2 8DP 225 Wildwood Avenue, Woborn, MA 01801-2041: Butterworth-Heinemann. Chen, C.-T. (1995). Analog and Digital Control System Design: Transfer-function, State-space, and Algebraic Methods. New York, USA: Oxford University Press, Inc.

Cheng, C.-C., & Chou, C.-C. (2016). Fuzzy-Based Visual Servo with Path Planning for a Ball-Plate System. International Symposium on Intelligent Computing Systems (ISICS), 97-107. doi: 10.1007/978-3-319-30447-2_8

Enter your email address:

Delivered by TMLT NIGERIA

Join Over 3,500 000+ Readers Online Now!


=> FOLLOW US ON INSTAGRAM | FACEBOOK & TWITTER FOR LATEST UPDATES

ADS: KNOCK-OFF DIABETES IN JUST 60 DAYS! - ORDER YOURS HERE

COPYRIGHT WARNING! Contents on this website may not be republished, reproduced, redistributed either in whole or in part without due permission or acknowledgement. All contents are protected by DMCA.
The content on this site is posted with good intentions. If you own this content & believe your copyright was violated or infringed, make sure you contact us at [[email protected]] to file a complaint and actions will be taken immediately.

Tags: , ,

Comments are closed.