ABSTRACT
Proportional-Integral-Derivative (PID) controllers have been widely used in process industry for decades, from small industry to high technology industry, but they still remain poorly tuned by use of conventional tuning methods like the Zeigler-Nichols method. In this work, PID controller’s parameters for deep space antenna positioning system were optimized using Genetic Algorithm (GA). Using genetic algorithm, the tuning of the controller results in the optimum controller being evaluated for the system every time. The system was modelled using Bond-Graph in 20Sim environment and the PID Controller was optimized using GA in Matlab/Simulink environment in order to get the optimum value for its parameters. Simulation result shows that the performance of the optimized PID Controller using Genetic Algorithm (GA) for deep space antenna positioning system at response values of 2.2412sec rise time, 2.9861sec settling time and 0% overshoot and undershoot is better than the conventionally, Zeigler-Nichols method, tuned Controller at response values of 0.8568sec rise time, 9.2289sec settling time, 66.3812% overshoot and 23.1264% undershoot; thereby comparing the work at an amplifier gain value of 100. Results for different amplifier gain values also show that the system response at an amplifier gain of 250 produced the best response in terms of rise time, settling time and overshoot but has a problem of peaking in its transient state characteristics
TABLE OF CONTENTS
Title Page……………………………………………………………………………………ii
Declaration…………………………………………………………………………………iii
Certification…………………………………………………………………………………iv
Dedication…………………………………………………………………………………..v
Acknowledgement………………………………………………………………………….vi
Abstract……………………………………………………………………………………viii
List of Plates…………………………………………………………………………………xi
List of Figures………………………………………………………………………………xi
List of Tables……………………………………………………………………………….xiv
List of Abbreviations……………………………………………………………………..,,xv
Definations………….……………………………………………………………………. xvii
List of Appendixes…………………………………………………………………………xviii
1.0 INTRODUCTION ………………………………………………………………………………………………… 1
1.1 Background ………………………………………………………………………………………………………. 1
1.2 Statement of the Problem ……………………………………………………………………………………. 3
1.3 Aim and Objectives ……………………………………………………………………………………………. 3
1.4 Significance of Research/Justification ………………………………………………………………….. 4
1.5 Scope of Work …………………………………………………………………………………………………… 4
1.6 Present Research ……………………………………………………………………………………………….. 5
2.0 LITERATURE REVIEW ………………………………………………………………………………………. 6
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2.1 Overview of Fundamental Concepts …………………………………………………………………….. 6
2.1.1 Deep space antenna position control system ……………………………………………………. 6
2.1.1.1 Block diagram reduction for the antenna azimuth position control system…..15
2.1.2 PID controller ……………………………………………………………………………………………. 18
2.1.2.1 Proportional control action……………………………………………………19
2.1.2.2 Integral control action…………………………………………………………20
2.1.2.3 Derivative control action………………………………………………………21
2.1.2.4 Design procedures…………………………………………………………….22
2.1.2.5 Tuning PID controllers……………………………………………………….23
2.1.3 Genetic algorithm (GA)……………………………………………………………..26
2.1.4 Bond graph………………………………………………………………………..30
2.1.4.1 Characteristic of bond graph elements …………………………………………………… 31
2.1.4.2 Systematic procedure to derive a bond–graph model…………………………32
2.2 Review of Related Past Works …………………………………………………………………………… 36
3.0 MATERIALS AND METHOD …………………………………………………………………………….. 38
3.1 Introduction……………………………………………………………………………38
3.2 Materials/Equipment……………………………………………………………………38
3.3 Derivation of Bond Graph Models of the System……………………………………..38
3.4 Open-Loop Model of the System ……………………………………………………………………….. 39
3.4.1 The potentiometer…………………………………………………………………39
3.4.2 Mathematical modelling of nonlinear motor system………………………………41
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3.5 Closed-Loop Model of the System……………………………………………………………………… 43
3.6 PID Tuning using GA ………………………………………………………………………………………. 46
3.7 Simulation of the System………………………………………………………………47
4.0 RESULTS AND DISCUSSION ……………………………………………………………………………. 48
4.1 Results ……………………………………………………………………………………………………………. 48
4.2 Discussion of Results…………………………………………………………………..58
4.3 Comparison of Work ………………………………………………………………………………………… 59
5.0 SUMMARY, CONCLUSION AND RECOMMENDATION …………………………………… 61
5.1 Summary..…………………………………………………………………………..61
5.2 Conclusion……………………………………………………………………………61
5.3 Recommendation……………………………………………………………………62
References ……………………………………………………………………………………………………………….. 63
APPENDIX A………………………………………………………………………………..66
APPENDIX B…………………………………………………………………………………67
APPENDIX C………………………………………………………………………………..68
APPENDIX D……………………………………………………………………………….70
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CHAPTER ONE
INTRODUCTION
1.1 Background Antennas are electrical devices which convert electric power into radio waves, and vice versa (Gawronski, 2008). They communicate with spacecraft by sending commands (uplink) and receiving information (downlink) from it (Gawronski, 2008). An antenna tracking (the act or process of following the trail) a satellite must keep the satellite well within its beam-width in order not to lose track (Nise, 2006). Therefore, in order to ensure this due to Earth’s rotation, the antenna as shown in Plate I is continuously positioned with the aid of a controller and a drive mechanism. This implies that suitable and efficient positioning of antenna structure will enhance signal clarity, wider coverage area and satisfactory reception of radiated signal (Agubor et al., 2013). However, for frequencies in the Ka-band, there is need for a very efficient tracking (Gawronski, 2008). This requirement is a driver for the upgrade of control systems of antennas.
Plate I: A deep space antenna (Source: Gawronski, 2008)
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The antenna dish rotates with respect to the horizontal axis while the whole structure rotates on a circular track with respect to the vertical axis. The position of antenna is controlled by using gears and feedback potentiometer. Antenna positioning is also controlled by using some controllers (Chishti et al., 2014). A controller aims at minimizing the error between a measured process variable of the controlled system and a reference, by calculating the error and generating a correction signal to the system from the error (Pillai et al., 2013). For getting better response for antenna positioning system, several controllers like Proportional-Integral-Derivative (PID) Controller, Linear Quadratic Regulatory (LQR) Controller, Fuzzy Logic Controller (FLC) etc have been proposed and used.
The Proportional-Integral-Derivative (PID) Controller is widely used in most industrial processes due to their simplicity of operation, ease of design, inexpensive maintenance, low cost, and effectiveness for most linear systems but they still remain poorly tuned. Conventional technique like Zeigler-Nichols method does not give an optimized value for PID controller’s parameters (Pillai et al., 2013).
In this work, the PID controller parameters for antenna positioning system were optimized using Genetic Algorithm (GA). GA is a stochastic global search method that replicates the process of evolution (Pillai et al., 2013). The advantage of GA over other popular and efficient optimization algorithm such as Artificial Neural Networks and Fuzzy Logic is its high convergence speed of execution (Zhang et al., 2009).
The overall system was modelled using bond graphs. Bond graphs are a domain-independent graphical technique that exploits the fundamental laws of energy to model a system very close to reality i.e. nonlinear system (Broenink, 1999). They have certain advantages over network models. In particular, bond graph elements exist which allow multiport elements to be modelled explicitly, whereas network models, even of simple two-port elements, are awkward to draw and manipulate (Wellstead, 1979). From a practical viewpoint the relatively compact nature of bond graphs commends the technique as the basis for computer-aided modelling. This, coupled
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with the development of low-cost, high-speed interactive computer systems, distinguishes the bond graph approach as potentially the most useful of the systematic modelling techniques (Wellstead, 1979)
1.2 Statement of the Problem
The conventional optimization method of Proportional-Integral-Derivative (PID) Controller parameters cannot meet the requirements of control performance in positioning deep space antennas control system. The problems usually encountered in deep space antenna research are:
1. Due to earth’s rotation, there is non-continuous tracking of signal by the deep space antenna. As a result of this, the deep space antennas are continuously positioned with the aid of a drive mechanism and a controller (Gawronski, 2008).
2. Proportional-Integral-Derivative (PID) controllers have been widely used in process industry for decades, from small industry to high technology industry, but they still remain poorly tuned by use of conventional tuning methods like the Zeigler-Nichols method (Pillai et al., 2013).
3. The popular and efficient optimization algorithm such as Artificial Neural Networks and Fuzzy Logic have some disadvantages, such as premature convergence and low convergence speed of execution (Zhang et al., 2009). This implies that GA has a higher speed of execution as compared to them.
1.3 Aim and Objectives
The aim of this research is to optimize the Proportional-Integral-Derivative (PID) Controller parameters for optimum performance and positioning of deep space antenna control system.
The specific objectives are:
1. To develop a nonlinear mathematical model of deep space antenna system using Bond-Graph in 20Sim environment.
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2. To develop a Genetic Algorithm (GA) to tune the Proportional-Integral-Derivative controller in order to achieve specifications and stability parameters in Matlab.
3. To analyse the system and simulate it using Matlab.
4. To validate the work by comparing it with previous and latest work done in this research field.
1.4 Significance of Research/Justification
There are many areas in Nigeria and globally where antennas and its optimization prove to be very useful. Some of these are:
1. The application of antennas and satellite with its optimum performance and upgrade prove to be very useful as part of the space policy and activities of the Federal Republic of Nigeria, implemented through National Space Research and Development Agency (NASRDA) with a mission to pursue the research and development of space science and technology which ensures that Nigeria vigorously pursues the attainment of space capabilities as an essential tool for its socio-economic development and the enhancement of the quality of life of its people.
2. There is much need for constant and efficient communication using optimized antennas since the deployment of communication infrastructure in Nigeria in recent times have been massive. This is as a result of the ever increasing demand of wireless mobile services.
3. There is also more demand for the use of antennas and it’s upgrade for efficient broadcasting of information due to noticeable increase in the establishment of radio and television stations since this sector was deregulated.
1.5 Scope of Work
The scope of this research is limited to:
1. Open-loop model design of the system.
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2. Closed-loop model design of the system with a PID Controller.
3. Using Genetic Algorithm built into Matlab to determine the optimized parameters of the PID controller.
4. Using Matlab/Simulink to simulate the deep space antenna control system.
1.6 Present Research
This present research efforts focuses on optimizing the parameters of the PID controller and the performance is evaluated using some of the following criteria:
1. Settling time of a small step response.
2. Overshoot of a small step response.
3. Overshoot of a large step response.
4. Steady-state error.
5. Amplitude and settling time of a disturbance step.
6. Magnitude of the disturbance transfer function.
7. Phase and gain stability margins.
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