This research proposes a simplified approach to the modelling of quadruple tank
system via the use of bond graph technique. The novelty of this approach is that
quadruple tank system equations are easier to obtain. In addition, the process of
obtaining the system equations is less prone to error because of the use of the
pictorial advantage of bond graph. This is an advantage for complex systems
such as Multi Input Multi Output (MIMO) systems. The 20-SIM software (bond
graph technique software) was used in this work. In order to address the inherent
multivariable constraint issues of the quadruple tank system such as looping and
coupling effects, while minimizing the cost of control, the quadruple tank system
was partitioned into Single Input Single Output (SISO) systems. This established
the basis for the implementation of the Decentralized Model Predictive Control
(DMPC) for the quadruple tank system. Due to the numerical ill-conditioning of
the system state equations, a Quadratic Programming (QP) based scheme with
inequality constraints was adopted. This was implemented in the Control toolbox
of MATLAB. The classical predictive control scheme, achieved control horizon
of a numerical value of one, and prediction horizon has values between 1 and
fifty with an average settling time of 0.8439 seconds. However, the QPDMPC
schemes’ control horizon (M 10) and prediction horizon (M )
accommodating increasing values (infinite horizon) with time while the settling
time of 0.04 seconds was attained. Validation of the controllers was carried out
relative to classical PID controller.
TABLE OF CONTENTS
LIST OF FIGURES xi
LIST OF ABBREVIATIONS xiii
CHAPTER ONE: INTRODUCTION
1.1 BACKGROUND 1
1.2 MOTIVATION 2
1.3 AIM AND OBJECTIVES 4
1.4 PROBLEM STATEMENT 4
1.5 METHODOLOGY 5
1.6 SIGNIFICANT CONTRIBUTIONS 5
1.7 THESIS OUTLINE 6
CHAPTER TWO: LITERATURE REVIEW
2.1 INTRODUCTION 7
2.2 OVERVIEW OF FUNDAMENTAL CONCEPTS 7
2.2.1 Dynamic Modelling 7
2.2.2 Multi-Process Systems 8
2.2.3 Quadruple Tank System 9
2.2.4 Fluid Dynamics Theory 10
2.2.5 Controllers 12
2.2.6 Decentralized Control 13
2.2.7 System Decoupling 14
2.2.8 Right Half Plane Zeros 15
2.2.9 The Bond Graph Approach 16
2.2.10 20-sim Simulation Software 23
2.2.11 Decentralized Model Predictive Control 24
2.2.12 Parameter Estimation Application 32
2.2.13 Proportional Integral and Differential (PID) Control 33
2.3 REVIEW OF SIMILAR WORKS 34
CHAPTER THREE: QUADRUPLE TANK PROPOSED SOLUTION
3.1 INTRODUCTION 39
3.2 BOND GRAPH IMPLEMENTATION 39
3.2.1 Variables 44
3.2.3 Behavioural Equations 47
3.2.4 Nonlinear System Dynamics 47
3.2.5 System Equations 48
3.3 LINEARISATION OF SYSTEM DESCRIPTIVE EQUATIONS 49
3.3.2 Input – Output Pairing 57
3.3.3 Decoupling Derived Linear Time Invariant Model 58
CHAPTER FOUR: RESULTS AND DISCUSSIONS
4.1 INTRODUCTION 62
4.2 OPEN-LOOP RESPONSE OF MIMO QUADRUPLE TANK SYSTEM 62
4.3 CONTROLLERS AND APPLICATION 64
4.3.1 Decentralized Model Predictive Control Application on Quadruple Tank System 65
4.3.2 Results for DMPC 65
4.3.3 Results Proportional Integral Differential Controller Application 76
CHAPTER FIVE: SUMMARY AND CONCLUSION
5.1 INTRODUCTION 83
5.2 SUMMARY 83
5.3 CONCLUSION 83
5.4 LIMITATIONS 84
5.5 RECOMMENDATIONS FOR FURTHER WORK 84
APPENDIX A 96
APPENDIX B 104
The production of qualitative, desired finished products in the process industries involves a multi processes which includes transformation of raw materials from their chemical or physical form to usable forms. The activity involves energy streams interacting with raw materials to transform the raw materials to the desired finished products(Wolfgang, 2010). Many of the multi processes are predominantly carried out in biological processing units, biochemical, bio-fuels enterprises, cement industries, chemical producing plants, electrochemical industries, glass, ceramics process industries, power generation industries, water industries and tank system storage departments. Constraints like loop interaction, phase shift, instability, plant mismatch, minimum and non-minimum phase behaviours, etc. are often encountered in the industrial processes. Some of these have been studied with the use of the benchmark tank systems. Continuous stirred tanks, two tanks, three interconnected tanks and quadruple tanks have over the years been used to study the behaviour of these industrial multi process characteristics. The quadruple tank system is used as a benchmark for applications in process control, mainly because of its strong nonlinear behaviour. It is a control of multiple inputs and multiple outputs (MIMO), in which inputs pump voltages from two inputs and outputs are liquid levels of lower tanks. This system presents not only a nonlinear feature, but also an interaction between inputs and outputs linked to the system flow directionality.
Several control techniques to improve the controllability, observability and robust performance of these industrial processes are found in literature. Among the popular ones are Proportional Integral Differential (PID) control, Linear Quadratic Gaussian (LQG), Sliding Mode Control and H-Infinity control. However, Model Predictive Control (MPC) has become a popular advanced control technology implemented in large scale industrial process plants due to its ability to handle input and state constraints(Necoara & Clipici, 2013). Model Predictive Control is also found to be suited for real time and on-line implementation(Alipouri & Poshtan, 2013; Mahapatro et al., 2014).
A serious challenge in the steps for the design and analysis of a mechatronics system is to generate a computer model for control analysis, diagnosis design, sensor selection/positioning, and actuator sizing(Samantaray & Bouamama, 2008). Indeed, mechatronics problems are interdisciplinary engineering systems problems, involving engineering knowledge(mechanical, electrical, pneumatic, thermal.) and various technological components such as sensors, controllers, actuators, and transducers that need to be properly designed and integrated(Paynter, 1970; Wolfgang, 2010). Hence, bond graph, which is a graphical modelling technique, is easily most suitable for unifying the various aspects of mechatronic systems (Paynter, 1970; Wang, 2009). The significance of bond graphing over system equation derivation techniques like variational method, network graphic technique is the ease with which the approach enables hierarchy and well-structured modelling based on a unified language(Paynter, 1970) . The modelling, analysis and control of a multi process system which
involves MIMO state variables(Wang, 2009), Tank system requires the use of a robust modelling technique that guarantee accurate modelling of the nonlinear physical phenomenon of the system, as well as an adaptive control mechanism. Efficient control mechanism for quadruple tank system requires an adaptive controller. Model predictive control scheme is well adapted for such problems some of which are in the forms of loop interactions, non-minimum phase zero, minimum phase zero, non-linearity etc.
The overall advantages of an adaptive control scheme to nonlinear control systems are as stated in (Wang, 2009); (i) The technique must use simple concepts. (ii) The controller tuning must be physically realisable and yet robust. (iii) The technique should be usable in either supervisory or primary control modes.
(iv) Automatic constraint setup and handling should be feasible for real time applications(Rosinova & KozĂˇkovĂˇ, 2012) .
The quadruple tank is a benchmark multiprocess setup (besides single tank, two tank, and three tank), which has been found in literatures to exhibit most of the challenges inherent in industrial process production lines(Garg & Tangirala, 2014). Productivity and safety therefore relies on effective handling of the challenges; uncertainty as regards to model mis-match due to errors in modelling, loop interaction, disturbance, noise and instability. Bond graph has been selected for the purpose of modelling the system. This is because the technique is based on the energy characteristics of each constituent component that contribute to the entire system built (Wellstead, 2000). Adding to this is the need to control the system behaviours based on the model. The adaptive controllers such as those
based on Model Predictive Control techniques have been used for this purpose. The advantage includes the fact that it is effected based on the very system behavioural equations; hence it tracks the system trajectory naturally.
1.3 AIM AND OBJECTIVES
The aim of this research is the modelling of a multi-process system (quadruple tank system), using bond graph technique and its control based on Decentralised Model Predictive Control approach. The following are the objectives of this work:
1. Development of quadruple tank system model using Bond Graph Method.
2. Extraction/Validation of the system parameter equations from the decoupled causal model using 20-sim
3. Determination of the linear model of the discrete state space format using MATLAB/Simulink control tool box software
4. Design a Decentralised Model Predictive Control based on Robust Quadratic Programming approach.
1.4 PROBLEM STATEMENT
A physical system can be described by the use of mathematical description of its dynamic behaviour. Hence, a suitable unifying concept which captures most physical variables and dynamics is energy. Accuracy in the modelling of a nonlinear multi process system that is characterised by multi-stage energy transformation without over-simplification is the most important challenge faced by researchers and hence impacts the system performance subsequently. Perhaps, thinking of a physical system as operating upon a pair of variables whose product
is proportional to power makes modelling as close to reality as possible. Bond graph method which incorporates these advantages is used for modelling of the quadruple plant in this work. Furthermore, the control of the multi-process system requires a robust controller algorithm with efficient predictive characteristics and high accuracy.
This section captures the methodological approach adopted in this research.
1. Identify the various elements and energy exchange, ports and storage of the quadruple tank.
2. Map out the bonds and apply causality on them.
3. Validation of the nonlinear model using 20-sim.
4. Model the plant in Simulink
5. Write a code to extract the discrete state space model.
6. Test for controllability and observability of the system.
7. Design a suitable decoupling scheme for the plant.
8. Decouple the system into two Single Input Single Output (SISO) systems.
9. Use Relative Gain Array, to choose the input/output pair with less interaction.
10. Design the DMPC controller for specific systems obtained in (9) and incorporate it in the controlled system derived from (1-9) above.
11. Result analysis and validation using Classical controller PID.
1.6 SIGNIFICANT CONTRIBUTIONS
The following are the significant contributions of this research:
1) Development of a Bond Graph model of the quadruple tank system, which has overcome the mathematical complexities of conventional method and which has been validated using 20-sim Simulator.
2) Design of a robust Quadratic Programming Decentralized Model Predictive Controller (QPDMPC) which stabilized and efficiently tracked the system even in the presence of numerical-ill conditions.
1.7 THESIS OUTLINE
The general idea for this work is shown in Chapter One. In Chapter Two, the bases and foundation for achieving the aims and objectives of this work was established through the review of fundamentals and related works pertaining to modelling and control of systems, in particular to multi-process systems. The control theory and principles of operation are also reviewed. Furthermore, Chapter Three presents the modelling of the quadruple tank MIMO system via bond graph technique with derivation of system equations. The use of 20-sim to validate the modelled system was also carried out herein. The system decoupler and decoupling design implementation was shown and the SISO systems obtained. While chapter four, discusses the results obtained during simulations and their effects were discussed. Finally, in Chapter Five, the conclusion based on the entire work is presented.
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