Abstract
Fractional Order PID (FOPID) controllers are developed for regulating product’s purity in distillation columns. It is widely known that poorly tuned PID controllers lead to bad quality of products and accompanied reduction in profit margin in the process industry. In distillation columns, tight composition control of products with 98% purity level is not achievable with simple pressure controllers only due to sensitivity to disturbances. Therefore, Fractional Order PID FOPID controllers are proposed to solve these multivariable impurity problems. Fractional Order PID FOPID controllers have extra tuning parameters that can counteract effects of time delays in distillation columns if properly tuned. This property is exploited as a tool for improved performance. Original contributions of this thesis include the development of three new design methods for multivariable FOPID controllers and results are analysed using inverse maximum singular value of relevant sensitivity functions to assess robust stability. Several conventional PID controller design methods are also reviewed for the purpose of comparison.
Thereafter, a decentralised Fractional Order PID FOPID control system is developed for multivariable systems based on plant’s critical frequency point and results show improved performance over conventional PID controllers. The proposed critical frequency point method provides very easy-to-use tuning rules similar to Cohen-Coontuning rule for integer-order Fractional Order PID controllers. In addition, a new decentralised multivariable Fractional Order PID FOPID controller is also proposed based on Internal Model Control(IMC) method but settings are tuned using Biggest Log-magnitude Technique (BLT). This IMC-Fractional Order PID control design scheme overcomes the need for critical frequency point experiments. Another contribution of this thesis is the development of a novel discrete Fractional Order Predictive PI (FOPPI) control design scheme suitable for linear multivariable systems. Comparative study of these methods is presented.Simulation results prove that both top and bottoms products’ purity of 98% are achievable with improved disturbance rejection when using the proposed Fractional Order PID FOPPI controller. In comparison, simpler Fractional Order PID FOPID control design schemes developed in continuous time are found to meet design objectives but at the expense of having a more conservative control action.
INTRODUCTION
In order to achieve excellent trajectory tracking performances, an improved genetic algorithm (IGA) is presented to search for the optimal proportional-integral-derivative Fractional Order (PID) controller parameters for the robotic excavator. Firstly, the mathematical model of kinematic and electro-hydraulic proportional control system of the excavator are analyzed based on the mechanism modeling method. On this basis, the actual model of the electro-hydraulic proportional system are established by the identification experiment. Furthermore, the population, the fitness function, the crossover probability and mutation probability of the SGA are improved: the initial PID parameters are calculated by the Ziegler-Nichols (Z-N) tuning method and the initial population is generated near it; the fitness function is transformed to maintain the diversity of the population; the probability of crossover and mutation are adjusted automatically to avoid premature convergence.
Moreover, a simulation study is carried out to evaluate the time response performance of the proposed controller, i.e., IGA based Fractional Order PID against the SGA and Z-N based Fractional Order PID controllers with a step signal. It was shown from the simulation study that the proposed controller provides the least rise time and settling time of 1.23 s and 1.81 s, respectively against the other tested controllers. Finally, two types of trajectories are designed to validate the performances of the control algorithms, and experiments are performed on the excavator trajectory control experimental platform. It was demonstrated from the experimental work that the proposed IGA based Fractional OrderPID controller improves the trajectory accuracy of the horizontal line and slope line trajectories by 23.98% and 23.64%, respectively in comparison to the SGA tuned Fractional Order PID controller. The results further indicate that the proposed IGA tuning based PID controller is effective for improving the tracking accuracy, which may be employed in the trajectory control of an actual excavator.
A fuzzy Fractional Order PID control algorithm is studied based on improved particle swarm optimization (PSO) to perform Brushless DC (BLDC) motor control which has high accuracy, good anti-jamming capability and steady state accuracy compared with traditional Fractional Order PID control. The mathematical and simulation model is established for BLDC motor by simulink software, and the speed loop of the fuzzy Fractional Order PID controller is designed. The simulation results show that the fuzzy PID control algorithm based on PSO has higher stability, high control precision and faster dynamic response speed.
Recent years many flight control systems and industries are employing Fractional Order PID controllers to improve the dynamic behavior of the characteristics. In this paper, Fractional Order PID controller is developed to improve the stability and performance of general aviation aircraft system. Designing the optimum Fractional Order PID controller parameters for a pitch control aircraft is important in expanding the flight safety envelope. Mathematical model is developed to describe the longitudinal pitch control of an aircraft. The Fractional Order PID controller is designed based on the dynamic modeling of an aircraft system. Different tuning methods namely Zeigler-Nichols method (ZN), Modified Zeigler-Nichols method, Tyreus-Luyben tuning, Astrom-Hagglund tuning methods are employed. The time domain specifications of different tuning methods are compared to obtain the optimum parameters value. The results prove that PID controller tuned by Zeigler-Nichols for aircraft pitch control dynamics is better in stability and performance in all conditions. Future research work of obtaining optimum PID controller parameters using artificial intelligence techniques should be carried out.
TABLE OF CONTENTS
Title page
Certification
Dedication
Acknowledgement
Table of Contents
Abstract
CHAPTER ONE: INTRODUCTION
- Background to the study
- Statement of the Problem
- Research questions
- The Objectives of the Study
- Significance of the Study
- Scope of the Study
- Operational Definition of Terms
CHAPTER TWO: LITERATURE REVIEW AND THEORETICAL FRAMEWORK
2.1 Review of Related Literature
2.2 Empirical Studies
2.3 Theoretical Framework
2.4 Review of Relevant concept of Fractional Order PID controller
2.5 Summary of the literature
CHAPTER THREE: METHODOLOGY
3.1 Research Design
3.2 Population of the Study
3.3 Sample Size and Sampling Techniques
3.5 Validation of the Research Instrument
3.6 Reliability of the Research Instrument
3.7 Research Procedure
3.8 Methods of Data Analysis
CHAPTER FOUR: RESULT AND DISCUSSION OF FINDINGS
4.1 Data presentation and analysis
4.2 Testing of hypothesis
4.3 Discussion of finding
CHAPTER FIVE: SUMMARY CONCLUSION AND RECOMMENDATION
5.1 Introduction
5.2 Summary of Study
5.3 Summary of Major Findings
5.4 Recommendations
5.5 Limitation of the Study
5.6 Suggestions for Future Research
References
Appendix
List of the Tables
4.1 Analysis of Research Questionnaire Administered
4.1 Distribution of Respondents by Sex
4.2 Age Distribution
4.3 Marital Status Distribution
4.4 Educational Qualification Distribution
4.5 Years of Service Distribution
4.6 Research Question One
4.7 Research Question Two
4.8 Research Question three
4.9 Research Hypothesis One
4.10 Research Hypothesis Two
4.11 Research Hypothesis Three
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