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  • Model-Based Control Techniques

    for Centrifugal Compressors

    Toufik Bentaleb Ph.D Thesis in Information Engineering and Science

    University of Siena

  • UNIVERSITA DEGLI STUDI DI SIENA

    DIPARTIMENTO DI INGEGNERIA DELLINFORMAZIONE

    Model-Based Control Techniques

    for Centrifugal Compressors

    Tesi di Dottorato di

    Toufik Bentaleb

    Advisor: Prof. Andrea Garulli

    Siena, February 2015

    DOTTORATO DI RICERCA IN INGEGNERIA DELLINFORMAZIONE

    CICLO XXVII

  • Model-Based Control Techniques for Centrifugal Compressors

    Toufik Bentaleb,

    Ph.D. Thesis, University of Siena,

    February, 2015.

    This research was financially supported by GE Oil & Gas Nuovo Pignone Florence.

  • ACKNOWLEDGMENTS

    First of all, I would like to thank all those who have shared something with me during these

    years. It is thanks to each one of you that I have managed to grow as much as I have

    done. Among all of you, I am very grateful to Professor Andrea Garulli, who has been the

    best guide I could have ever had. He has taught me so many things, both consciously and

    unconsciously, that I will be in debt with him for a very long time. Without him I would not

    have ever imagined that studying optimal control systems can also be funny.

    I enjoyed the time in Siena with Alessandro, Mirko and Donato who formed with me a

    group of people that I will hardly forget. Moreover, I want to thank people from GE Nuovo

    Pignone of Florence, L. Giovanardi, A. Cacitti, S. De Franciscis, D. Galeotti, and M. Pasquotti.

    I would like to express my gratitude to my family, especially my parents, for their love and

    support. Finally, I would like to thanks my wife, Mira, who made everything possible. She

    sacrificed a lot to keep me on track in finishing this study taking all the duties in the family,

    caring about our two babies unsparing her efforts. Her true love has helped me through all

    the hard periods.

    Siena

    February 27, 2015

    xi

  • Contents

    Preface ix

    Acknowledgements x

    Glossary xii

    1 Introduction 1

    1.1 Turbomachines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.1.1 Centrifugal Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . 2

    1.1.2 Gas Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

    1.2 Compressor Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    1.3 Compressor Surge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    1.4 The Goal of this Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    1.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    2 Control Techniques 11

    2.1 Proportional Integral Control with Anti-Windup . . . . . . . . . . . . . . . . . 11

    2.2 Linear Quadratic Regulator Optimal Control . . . . . . . . . . . . . . . . . . . 12

    2.3 Model Predictive Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

    3 Modeling of Gas Compression Plant 19

    3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

    3.2 Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    3.2.1 Upstream Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

    3.2.2 Downstream Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    3.3 Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    3.4 Orifice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    3.5 Cooler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    3.6 Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    3.6.1 Anti-Surge Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    v

  • 3.6.2 Upstream and Downstream Valves . . . . . . . . . . . . . . . . . . . . 30

    3.7 Centrifugal Gas Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    3.7.1 Compressor Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    3.7.2 Difference between the accuracy of the interpolation methods . . . . . 40

    3.7.3 Performance evaluation of the centrifugal compressor . . . . . . . . . 41

    3.8 Gas Turbine Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

    3.9 Linearization of the Gas Compression System . . . . . . . . . . . . . . . . . . 45

    4 Control Techniques for Pressure Regulation 49

    4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

    4.2 The Discharge Pressure Regulation Problem . . . . . . . . . . . . . . . . . . . 49

    4.2.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

    4.2.2 Implementation of Anti-Windup Proportional-Integral (PI) Control . . 51

    4.2.3 Implementation of LQI . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

    4.2.4 Implementation of MPC . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    4.3 Comparison of Multivariable Control Schemes . . . . . . . . . . . . . . . . . . 54

    5 Surge Prevention 61

    5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

    5.2 Centrifugal Compressor Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

    5.2.1 Compressor Map in (Hp vs Qv) Coordinates . . . . . . . . . . . . . . . 63

    5.2.2 Compressor Map in Invariant Coordinates . . . . . . . . . . . . . . . . 64

    5.3 Distance to Surge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

    5.3.1 Distance to surge in the (Rc 1 vs q2s psd) coordinates . . . . . . . . 66

    5.3.2 Distance to surge in the (hr vs q2s) coordinates . . . . . . . . . . . . . . 67

    5.4 MPC Controller Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

    5.5 Results Analysis and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 73

    5.5.1 Case study I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    5.5.2 Case study II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    5.5.3 Case study III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    5.6 Comparison of Different MPC-Based Control Schemes . . . . . . . . . . . . . . 78

    5.7 Noise Rejection and Chattering Avoidance . . . . . . . . . . . . . . . . . . . . 85

    6 Fuel Consumption Optimization 87

    6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

    6.2 Fuel Map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

    6.3 Fuel Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

    6.4 Open-Loop Fuel Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

    6.4.1 Fuel Minimization by Acting on Inlet Guide Vane at Steady State . . . 90

    6.4.2 Fuel Minimization by Acting on Rotational Speed at Steady State . . . 91

    6.5 Closed-Loop Fuel Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 93

    6.5.1 Closed-Loop Fuel Optimization Local Search . . . . . . . . . . . . . . . 93

    6.5.1.1 Case Study I . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

    6.5.1.2 Case Study II . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

  • 6.5.2 Closed-Loop Fuel Optimization Global Search . . . . . . . . . . . . . . 102

    6.5.2.1 MPC Controller . . . . . . . . . . . . . . . . . . . . . . . . . . 102

    6.5.2.2 Case Study I . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

    6.5.2.3 Case Study II . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

    7 Conclusions and Future Research 109

    A Finite-State Machine 111

    A.1 Finite-State Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

    Bibliography 115

  • PREFACE

    This dissertation is submitted for the degree of Doctor of Philosophy at the University of

    Siena (Universit degli Studi di Siena). The research described herein was conducted under

    the supervision of Professor Andrea Garulli in the Department of Dipartimento di Ingegneria

    dellInformazione e Scienze Matematiche (DIISM), Universita degli Studi di Siena, during

    the period January 2012 through February 2015. It has been financed by GE Oil & Gas

    Nuovo Pignone Florence.

    During my studies I have visited GE Oil & Gas - Nuovo Pignone many times for guidance

    and feedback. I am grateful to my advisors S. De Franciscis and Dr A. Cacitti at GE Oil &

    Gas, who have followed up my work monthly through meetings. De Francisciss expertise

    has been very helpful for my understanding of natural gas compression systems.

    Part of this work has been presented in the following publications:

    T. Bentaleb, A. Cacitti, S. De Franciscis, A. Garulli, Multivariable Control for Regulating High

    Pressure Centrifugal Compressor with Variable Speed and IGV, 2014 IEEE International Con-

    ference on Control Applications (CCA) Part of 2014 IEEE Multi-conference on Systems and

    Control (MSC), October 8-10, 2014, pages 486-491, Antibes, France.

    T. Bentaleb, A. Cacitti, S. De Franciscis, A. Garulli, Model Predictive Control for Pressure

    Regulation and Surge Prevention in Centrifugal Compressors, submitted to the European

    Control Conference ECC15, July 15-17, 2015, Linz, Austria.

    Toufik Bentaleb

    February, 2015

    ix

  • Glossary