MULTIVARIABLE SLIDING MODE CONTROL DESIGN FOR AIRCRAFT ENGINES SIRIRAT SANGWIAN Bachelor of Science in Mechanical Engineering Cleveland State University, Cleveland, Ohio August 2009 submitted in partial fulfillment of requirements for the degree MASTER OF SCIENCE IN MECHANICAL ENGINEERING at the CLEVELAND STATE UNIVERSITY August 2011 This thesis has been approved for the department of MECHANICAL ENGINEERING and the College of Graduate Studies by: Thesis Chairperson, Hanz Richter, Ph.D. Department & Date Jerzy Sawicki, Ph.D. Department & Date Lili Dong, Ph.D. Department & Date ACKNOWLEDGMENTS I would like to thank Dr. Hanz Richter for being my advisor throughout this project. With his expertise and his support, I am able to feed my passion of aviation in the form of education and to obtain my master's degree at the same time. I truly appreciate all of the valuable time that Dr. Richter has spent on this project, without him I would not have been able to make this thesis possible. I would like to express my gratitude to Dr. Jerzy Sawicki and Dr. Lili Dong for serving as my committee members. I also would like to thank my family, especially my mother who always gives me comfort and unconditionally loves me. Her role model has given me the courage to never give up. In addition, I would like to acknowledge Dr. William Atherton who inspired me to obtain my master's degree at Cleveland State University and for his guidance throughout my studies at Cleveland State University. Finally, I wish to dedicate this thesis to the Mechanical Engineering Department at Cleveland State University. Without CSU's financial support, I never would have made it through. MULTIVARIABLE SLIDING MODE CONTROL DESIGN FOR AIRCRAFT ENGINES SIRIRAT SANGWIAN ABSTRACT Many control theories are used in controlling aircraft engines. However, the multi- variable sliding mode control is not yet established in this application even though it has a lot of potential in dealing with complex and nonlinear systems such as aircraft engines. Therefore, a guideline in developing multivariable sliding mode control law for an aircraft engine is presented in this thesis. The problem of chattering in the sliding mode control is suppressed by the use of the boundary layer method. The con- trol logic is tested by implementing NASA's Commercial Modular Aero-Propulsion System Simulation 40k (C-MAPSS40k). Simulation results are analyzed and com- pared to the results obtained from the baseline controller. The robust property of multivariable sliding mode control is also examined by altering the flight condition of the engine. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] iv TABLE OF CONTENTS ABSTRACT iv LIST OF FIGURES viii LIST OF TABLES xi I INTRODUCTION 1 1.1 Motivation . 1 1.2 Aircraft Engine Controller . 2 1.3 Scope of Thesis . 5 II AIRCRAFT ENGINES 7 2.1 Aircraft Engines . 7 2.2 Aircraft Engine Components . 8 2.2.1 Inlet . 8 2.2.2 Compressor . 8 2.2.3 Combustor . 9 2.2.4 Turbine . 9 2.2.5 Nozzle . 10 2.3 Type of Aircraft Engines . 11 2.3.1 Ramjet . 11 2.3.2 Turbojet . 11 2.3.3 Turbofan . 13 2.3.4 Turboprop . 14 2.4 Specific Fuel Consumption . 14 2.5 Aircraft Engine Maintenance . 15 2.6 Engine Station Numbering . 16 v III AIRCRAFT ENGINE CONTROLS AND C-MAPSS40K 18 3.1 Introduction . 18 3.2 Aircraft Engine Characteristics . 20 3.2.1 Stall and Surge . 21 3.3 Thrust Control . 26 3.4 Commercial Modular Aero-Propulsion System Simulation 40k (C- MAPSS40k) . 28 3.4.1 C-MAPSS40k Engine Model . 31 3.4.2 Linearization . 36 IV SLIDING MODE CONTROL 37 4.1 Introduction . 37 4.2 Concept of Sliding Mode Control . 38 4.3 Sliding Mode Control Design . 42 4.3.1 Defining Sliding Surface . 44 4.3.2 Designing the Control Law . 45 4.3.3 Maintaining Trajectories on The Sliding Surfaces . 46 4.4 Chattering Problem . 47 4.5 Remarks . 48 V IMPLEMENTATION OF SLIDING MODE CONTROL 50 5.1 Introduction . 50 5.2 Sliding Mode Control for Aircraft Engine . 51 5.2.1 Plant Model . 51 5.2.2 Reference Model and The Control Law . 55 5.3 Values and Dimensions Assignment of System Parameters . 55 5.4 Control Law Verification . 57 5.5 Sliding Mode Controller in C-MAPSS40k . 66 vi 5.6 Comparison Between the Sliding Mode Controller and the Baseline Controller . 73 5.7 Evaluate the Robustness of Sliding Mode Control . 77 VI CONCLUSIONS AND FUTURE WORK 84 6.1 Conclusions . 84 6.2 Future Work . 85 BIBLIOGRAPHY 87 APPENDIX 90 A MATLAB PROGRAMS 91 vii LIST OF FIGURES 2.1 Schematic Diagram of a Ramjet Engine (from [6]) . 12 2.2 Schematic Diagram of a Turbojet Engine (from [7]) . 12 2.3 Schematic Diagram of a Turbofan Engine (from [8]) . 14 2.4 Schematic Diagram of a Turboprop Engine (from [10]) . 15 3.1 Engine Operating Envelope of Generic Turbojet and Turbofan (from [3]) 21 3.2 A stage of VSV (from [14]) . 24 3.3 A Bleed Valve (from [14]) . 24 3.4 A Bleed Valve (from [14]) . 25 3.5 Surge Margin on a Compressor Map (from [3]) . 26 3.6 Diagram of Thrust Control Using Fan Speed Nf ............ 27 3.7 C-MAPSS40k Graphical User Interface (from [16]) . 29 3.8 Schematic of The Twin Spool, Turbofan Engine (from [18]) . 31 3.9 PAX200 Engine's Operating Envelope (from [16]) . 32 3.10 C-MAPSS40k Complete Block Diagram (from [16]) . 33 3.11 Diagram of the Engine Controller Used in C-MAPSS40k (from [16]) . 33 3.12 Fuel Metering Valve Diagram (from [16]) . 34 3.13 Variable Stator Vane Actuator Diagram (from [14]) . 34 3.14 Variable Bleed Valve Actuator Diagram (from [14]) . 34 5.1 Diagram of a Sliding Mode Controller With an Augmented Plant . 52 5.2 Diagram of The Sliding Mode Control Modelled in Simulink . 59 5.3 Desired and Actual Values of ∆Nf vs. Time . 60 5.4 Desired and Actual Values of ∆Nc vs. Time . 60 5.5 Desired and Actual Values of ∆SMHP C vs. Time . 61 5.6 Reference State and Actual State of ∆Nf vs. Time . 61 viii 5.7 Reference State and Actual State of ∆Nc vs. Time . 62 5.8 Reference State and Actual State of ∆Wf vs. Time . 62 5.9 Reference State and Actual State of VSV Command vs. Time . 63 5.10 Reference State and Actual State of VBV Command vs. Time . 63 5.11 Fuel Flow Rate Command vs. Time . 64 5.12 VSV Command vs. Time . 64 5.13 VBV Command vs. Time . 65 5.14 Sliding Variables vs. Time) . 65 5.15 Diagram of the Sliding Mode Controller Implemented in the C-MAPSS40k 67 5.16 Diagram of the Sliding Mode Control Logic Inside the SMC Block . 68 5.17 Fan Speed Nf vs. Time . 69 5.18 Core Speed Nc vs. Time . 69 5.19 Stall Margin of High Pressure Compressor (SMHPC) vs. Time . 70 5.20 Control Input of Fuel Flow Rate vs. Time . 70 5.21 Control Input of Variable Stator Vanes vs. Time . 71 5.22 Control Input of Variable Bleed Valve vs. Time . 71 5.23 Sliding Variables vs. Time . 72 5.24 Fan Speed Nf vs. Time . 74 5.25 Core Speed Nc vs. Time . 74 5.26 Stall Margin of High Pressure Compressor (SMHPC) vs. Time . 75 5.27 Control Input of Fuel Flow Rate vs. Time . 75 5.28 Control Input of Variable Stator Vanes vs. Time . 76 5.29 Control Input of Variable Bleed Valve vs. Time . 76 5.30 Fan Speed Nf vs. Time . 79 5.31 Core Speed Nc vs. Time . 79 5.32 Stall Margin of High Pressure Compressor (SMHPC) vs. Time . 79 5.33 Control Input of Fuel Flow Rate vs. Time . 80 ix 5.34 Control Input of Variable Stator Vanes vs. Time . 80 5.35 Control Input of Variable Bleed Valve vs. Time . 80 5.36 Sliding Variables vs. Time . 81 5.37 Fan Speed Nf vs. Time . 81 5.38 Core Speed Nc vs. Time . 81 5.39 Stall Margin of High Pressure Compressor (SMHPC) vs. Time . 82 5.40 Control Input of Fuel Flow Rate vs. Time . 82 5.41 Control Input of Variable Stator Vanes vs. Time . 82 5.42 Control Input of Variable Bleed Valve vs. Time . 83 5.43 Sliding Variables vs. Time . 83 x LIST OF TABLES 2.1 Fundamental Station Numbers [12] . 17 3.1 Operation Conditions of C-MAPSS40k (from [16]) . 30 3.2 Simulation Inputs of C-MAPSS40k (from [16]) . 30 3.3 Simulation Inputs of C-MAPSS40k (from [16]) . 35 5.1 Dimension of Matrix Parameters . 56 5.2 Values of Linearized State Space Matrices and Transformation Matrices 57 5.3 Defined Desired, Initial and Delta Values of Nf , Nc, and SMHPC . 58 5.4 Settling Time of System Parameters . 73 5.5 Percent Error of Nf , Nc, and SMHPC . 83 xi CHAPTER I INTRODUCTION Aircraft engines are complex dynamic systems with uncertain parameter varia- tions, therefore multivariable sliding mode control is an excellent candidate to utilize as a control law for these systems. This thesis establishes practical procedures for designing multivariable sliding mode control and applies them to a turbofan engine, which is widely used in commercial aircrafts due to its efficiency and quieter opera- tion. In addition, by utilizing the multivariable sliding mode control in creating the control law for an aircraft engine, the horizon of the control theory for aircraft en- gines is expanded.