Control Algorithms for a Two Tank Liquid Level System: An Experimental Study Soumya Ranjan Mahapatro Department of Electrical Engineering National Institute of Technology, Rourkela Rourkela-769008, Odisha, India Control Algorithms for a Two Tank Liquid Level System: An Experimental Study A thesis submitted in partial fulfilment of the requirements for the award of the award of degree Master of Technology by Research in Electrical Engineering by Soumya Ranjan Mahapatro Roll No: 611EE104 Under the Guidance of Prof.Bidyadhar Subudhi Department of Electrical Engineering National Institute of Technology, Rourkela Rourkela-769008, Odisha, India 2012-2014 Department of Electrical Engineering National Institute of Technology, Rourkela CERTIFICATE This is to certify that the thesis titled “Control Algorithms for a Two Tank Liquid Level System: An Experimental Study”, by Mr. Soumya Ranjan Mahapatro submitted to the National Institute of Technology Rourkela for the award of Master of Technology by Research in Electrical Engineering is a record of bona fide research work carried out by him in the Department of Electrical Engineering, under my supervision. We believe that this thesis fulfills part of the requirements for the award of the degree of Master of Technology by Research. The results embodied in this thesis have not been submitted for the award of any degree elsewhere.
Place: Rourkela Prof.Bidyadhar Subudhi Date: Dedicated To My Loving Parents …Soumya Ranjan Mahapatro Acknowledgement First and foremost, I am deeply grateful to my supervisor Prof.Bidyadhar Subudhi and Prof.Subhojit Ghosh for their impetus, excellence guidance. In the beginning, Dr S Ghosh introduced me to this coupled tank liquid level control problem and had to leave NIT Rourkela in a year. Actually his Vision and support gave a fundamental base to this thesis. Then I came to under the guidance of Prof Bidyadhar Subudhi.
Really, I am indebted to my supervisor Prof. Bidyadhar Subudhi for his stimulant guidance and also for his gracious encouragement throughout the work. I would like to express my gratitude to the members of Masters Scrutiny Committee, Prof.Pati, and Prof.Behera for their advice. I am also very much obliged to Prof.
Anup Ku Panda Head of the Department of Electrical Engineering, N.T Rourkela for providing all the possible facilities towards this research work. Also thank to other faculty members in the department. I am also thankful to laboratory staff of Control and Research lab and office staff of our department for their excellent service and help. I am very much grateful to my senior research scholars Dushmanta Kumar Das, Basanta Sahu, Sathyam Bonala, Raja Rout, Subhasish Mahapatra, Pradosh Sahu, Muralidhar Killi and my research colleagues Amrit Anand Mahapatra, Chavi Surendu Sharma and all research members of Control and Robotics Lab of NIT Rourkela for their cooperation, help.
I would also like to acknowledge the Ministry of Human Resource and Development, India (MHRD) for the grant of scholarship for the last two years to pursue the research. I also express my deep gratitude to my parents Soudamini Mahapatro and Padma Charan Mahapatro, my brother, my brother-in-law and sister for their love, support and encouragement. Soumya Ranjan Mahapatro Abstract The liquid level control in the coupled tank system (CTS) is a classical benchmark control problem. The dynamics of CTS resembles with that of many real systems such as distillation column, boiler process, oil refineries in petrochemical industries and many more.
It is a most challenging benchmark control problem owing to its non-linear and non-minimum phase characteristics. Furthermore, its physical constraints are also pose complexity in its control design. The thesis provides the description of a CTS along with its hardware setup used for carrying out research work. Usually, system identification is a procedure to obtain the mathematical model of a physical system from the experimental input-output data of the system.
The entire process of identifying a system from input and output data broadly consists of six steps. It begins with an experimental design followed by data collection and data preprocessing, next a suitable model structure is selected, then the parameters of the model are estimated and finally the model is validated using the experimental data. The present work is aimed at utilizing the existing as well as developing new tools of system identification for obtaining a suitable model for the studied coupled tank apparatus. Based on the identified model, control algorithms are developed in order to maintain constant liquid levels in the presence of disturbances which is arising due to sudden opening of the valve in the tanks.
A lot of research works have been directed in the past several years to develop the control strategies for a CTS. But, few works have been reported for validating the developed control strategies through the experimental setup. Thus, there lies a good opportunity to develop some advanced controllers and to implement them in real-time on the experimental set-up of a CTS in the laboratory. The objectives of the present work is to maintain the water level at the desired set point value and also simultaneously ensure robust performances when there is a load disturbance.
Initially, for regulating desired liquid level in both the tanks, a LMI based PI controller has been designed and implemented in real-time on a CTS. Usually, in this approach PI controller design problem is formulated as a state feedback controller design problem, which is further solved by exploiting a convex optimization approach. But, it yields slower response. Hence, an adaptive fuzzy PI (AFPI) controller has been developed to obtain better liquid level performance compared to LMI based PI controller.
This developed AFPI controller consists of two parallel connected PI controllers such as a primary and a secondary PI controller.In primary part, parameters of the PI controllers are fixed which is tuned by Ziegler-Nichols method and in secondary part, parameters are altered implicitly by means a suitable choice of fuzzy rules in real-time.This developed AFPI controller provides precise liquid level owing to large range of operating conditions because the fuzzy logic controller ( FLC) covers a wide range of operating conditions which is the main advantage of this controller. After implementing the developed AFPI in real-time, it has been observed from the experimental response that it gives good tracking response but it yields overshoot which is undesirable. Hence, in order to obtain good tracking as well as robust performance, a sliding mode controller has been designed. But from experimental as well as simulation results it is observed that, it suffers from chattering problem which possess a serious concern such as chance of damaging of the actuator of the setup.
Therefore, in order to reduce the chattering problem, an adaptive fuzzy sliding mode controller (AFSMC) is developed and also it is implemented in real-time. From both the experimental results, i. both under load disturbance and without disturbance it is observed that the proposed AFSMC control gives robust control performance in order to maintain constant desired liquid level in both the tanks as compared to other presented controller. Contents Abstract v Contents vii List of Figures ix List of Tables xi List of Abbreviations xii Chapter-1 Introduction 1.1 Description of the Coupled Tank System 1 1.2 Description of the Coupled Tank Experimental Setup 4 1.1 Real Time Workshop 4 1.3 Literature Survey on Control Strategies Applied To Coupled Tank System (CTS) 6 1.6 Thesis Organization 10 Chapter-2 Dynamics Modeling of a Coupled Tank System 2.1 Coupled Two Tank Dynamics 11 2.2 System Identification to Obtain Dynamic Model of 14 Coupled Tank System 2.3 Results obtained from System Identification 18 2.4 Chapter Summary 20 Chapter-3 A LMI Based PI Controller Design for the Coupled Tank System 3.2 Linear Matrix Inequality (LMI): A Brief Introduction 22 3.3 A LQR-LMI framework Based Formulation for PI Controller Design 23 3.4 Results and Discussions 26 3.5 Chapter Summary 31 Chapter-4 An Adaptive Fuzzy PI Controller Design for the Coupled Tank System 4.1 Design of an Adaptive Fuzzy PI Controller 32 4.2 Design of Fuzzy Logic Control (FLC) 34 4.3 Results and Discussions 38 4.4 Chapter Summary 41 Chapter-5 Design and Real Time Implementation of a Sliding Mode Controller for the Coupled Tank System 5.2 Development of Sliding Mode Control Law 43 5.1 Control Law for Tank-1 43 5.2 Control Law for Tank-2 46 5.3 Results and Discussions 48 5.4 Chapter Summary 52 Chapter-6 Development of an Adaptive Fuzzy Sliding Mode Controller Design for the Coupled Tank System 6.2 Development of an Adaptive Fuzzy Sliding Mode Controller 54 6.1 Development of Control Law for Tank-1 55 6.2 Development of Control Law for Tank-2 57 6.3 Design of Fuzzy Logic Control 59 6.4 Results and Discussions 62 6.5 Chapter Summary 66 Chapter-7 Conclusions and Suggestions for Future Work 7.2 Contributions of the Thesis 69 7.3 Suggestions for the Future Work 69 References 71 List of Figures Sl Description Page No No 1.1 Coupled Tank Liquid level System Examples 2 1.2 Representation of a Typical Liquid level System 2 1.3 Schematic Diagram of a Coupled Tank Mechanical Unit 3 1.4 Schematic Representation of Experimental Set-up Showing Each Hardware 4 1.5 Schematic of the Real-Time Workshop code generation process 5 2.1 Representation of Coupled Two Tanks Model 11 2.2 A Basic Representation of Black Box Model Identification 14 2.3 Representation of the General Model Structure 15 2.4 Block Diagram of OE Model 15 2.5 Block Diagram of ARX Model 16 2.6 Block Diagram of ARMAX model 17 2.7 Experimental Input Data 18 2.8 Experimental Output versus the Simulated Output of the Identified Model for 18 Tank 1 2.9 Experimental Output versus the Simulated Output of the Identified Model for 19 Tank 2 2.1 Response of Mean Square error plot (MSE) 19 2.1 Model Validation Response by Using Auto-correlation Analysis 19 3.1 Generalized structure of the PI like state feedback controller 24 3.2 Block Diagram of the proposed LMI based PI Controller 26 3.3 Simulation Response of LMI based PI control for control in Tank 1 27 3.4 Simulation Response of LMI based PI control for control in Tank 2 27 3.5 Simulation Response of Ziegler Nichols tuned PI control for level control in 28 Tank 1 3.6 Simulation Response of Ziegler Nichols tuned PI control for level control in 28 Tank 2 3.7 Experimental Response of LMI based PI control for control in Tank 1 28 3.8 Experimental Response of LMI based PI control for control in Tank 2 29 3.9 Experimental Response of Ziegler Nichols based PI control for level control in 29 Tank 1 3.10 Experimental Response of Ziegler Nichols based PI control for level control in 29 Tank 1 4.1 Schematic Structure of Adaptive Fuzzy PI Controller 33 4.2 Schematic representation of a Fuzzy Logic Control system 35 4.3 Fuzzy membership function for input variable 36 4.4 Fuzzy membership function for output input variable 36 4.5 Simulation Response of Adaptive Fuzzy PI (AFPI) for level control in Tank1 39 4.6 Simulation Response of Adaptive Fuzzy PI (AFPI) for level control in Tank 2 39 4.7 Experimental Response of Adaptive Fuzzy PI (AFPI) for level control in Tank 39 1 4.8 Experimental Response of Adaptive Fuzzy PI (AFPI) for level control in Tank 40 2 5.1 Graphical Representation of the Sliding Surface 43 5.2 Schematic structure of Sliding Mode Controller for level control in coupled tank 44 system 5.3 Simulation Response of Sliding Mode Control while level control in Tank 1 49 5.4 Simulation Response of Sliding Mode Control while level control in Tank 2 49 5.5 Response of sliding surface while level control in tank 1 49 5.6 Response of sliding surface while level control in tank 2 50 5.7 Experimental Response of Sliding Mode Control while level control in Tank1 50 5.8 Experimental Response of Sliding Mode Control while level control in Tank 2 50 5.9 Experimental Response of Sliding Mode Control under disturbance rejection 51 mode while level control in Tank 1 5.10 Experimental Response of Sliding Mode Control under disturbance rejection 51 mode while level control in Tank 2 6.1 Schematic Control Structure of the Adaptive Fuzzy Sliding Mode Controller 54 6.2 Block diagram of Adaptive Fuzzy Sliding Mode Control 59 6.