Purdue University Purdue e-Pubs Department of Electrical and Computer Department of Electrical and Computer Engineering Technical Reports Engineering August 1991 Real-Time Helicopter Flight Control: Modelling and Control by Linearization and Neural Networks Tobias J. Pallett Purdue University School of Electrical Engineering Shaheen Ahmad Purdue University School of Electrical Engineering Follow this and additional works at: https://docs.lib.purdue.edu/ecetr Pallett, Tobias J. and Ahmad, Shaheen, "Real-Time Helicopter Flight Control: Modelling and Control by Linearization and Neural Networks" (1991). Department of Electrical and Computer Engineering Technical Reports. Paper 317. https://docs.lib.purdue.edu/ecetr/317 This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional information. Real-Time Helicopter Flight Control: Modelling and Control by Linearization and Neural Networks Tobias J. Pallett Shaheen Ahmad TR-EE 91-35 August 1991 Real-Time Helicopter Flight Control: Modelling and Control by Lineal-ization and Neural Networks Tobias J. Pallett and Shaheen Ahmad Real-Time Robot Control Laboratory, School of Electrical Engineering, Purdue University West Lafayette, IN 47907 USA ABSTRACT In this report we determine the dynamic model of a miniature helicopter in hovering flight. Identification procedures for the nonlinear terms are also described. The model is then used to design several linearized control laws and a neural network controller. The controllers were then flight tested on a miniature helicopter flight control test bed the details of which are also presented in this report. Experimental performance of the linearized and neural network controllers are discussed. It was found from experimentation that the adaptive neural network technique was able to improve helicopter flight performance. ACKNOWLEDGMENTS We would like to thank the following people for their assistance on various portions of this research over the last two years. First, we would like to thank Brad Wolfert for all of his work in helping to setup the flight control test bed. Without his work, this - project would never have got off the ground. We would also like to thank Yung-Tat Lam for many hours of his time helping debug particularly tricky problems in the code. We also thank Dave Azpel and Charles A. Barnet from the Electrical Engineering Instrumentation Shop for making available equipment necessary to carry out our experiments. Finally we would like to thank everyone in the Real-time Robot Control Group at Purdue University for listening to presentations on our results and providing helpful insights: Mohamed Zribi, Mohammad S. Shaikh, Akihiro Ando, Jerry Robichaux, Atef J. Al-Najjar, Zohreh Erfan, Chaun Pai, and Shengwu Luo. TABLE OF CONTENTS Page LIST OF FIGURES .......................... v i LIST OF SYMBOLS .......................... ix CHAPTER I: MOTIVATION. PAST WORK AND THESIS ORGANIZATION ........................ 1 1.0Motivation ......................... 1 1.1 Past Work on Helicopter Flight Control .......... 2 1.2 Organization of Thesis ................... 4 CHAPTER II: HELICOPTER DYNAMICS IN HOVERING FLIGHT ... 5 2.0 Introduction ........................ 5 2.1 Theoretical Model for Hovering Helicopter ....... 6 2.1.1 Momentum Theory ................ 7 2.1.2 Blade Element Theory ..............1 0 2.1.3 Assumptions and Losses .............1 9 2.2 Proposed Model for Miniature Helicopter in Vertical Flight ............................ 3 0 2.2.1 Position Equation ................. 3 1 2.2.1.1 Description ................3 1 2.2.1.2 Proposed Methods of Parameter Determination and Model Verification ..3 3 2.2.2 Combustion Engine and Rotational Velocity Equation .......................3 4 2.2.2.1 Description ................3 4 2.2.2.2 Proposed Methods of Parameter Determination and Model Verification ....3 6 2.2.3 Collective Pitch Equation ............. 3 9 Page 2.2.3.1 Description ................3 9 2.2.3.2 Proposed Methods of Parameter Determination and Model Verification ..4 0 2.3 Conclusions ........................4 1 CHAPTER I11 . EXPERIMENTAL TEST BED ............. 4 3 3.0 Introduction ........................4 3 3.1 The Menu Interface ....................4 5 3.2 The Servo Subsystem ...................4 5 3.3 The Data Collection Subsystem ..............4 8 3.4 The Control Subsystem ..................5 1 3.5 The Helicopter and Flight Stand .............5 2 3.6 Conclusions .........................5 5 CHAPTER IV . CONTROLLER DESIGN ................ 5 6 4.0 Introduction ........................5 6 4.1 Linearized Control .....................5 7 4.1.1 Linear Approximation of Nonlinear System ..5 7 4.1.1.1 Linearization of the Helicopter Dynamics in Hover ..............5 9 4.1.2 Controller Design for Linearized System: Pole Placement ......................6 4 4.1.2.1 Linearized Hover Control of the Helicopter .................6 6 4.1.2.2 Simulations ................ 6 9 4.1.2.3 Flight Tests ................ 7 5 4.1.3 Optimal Control Design (Algebriac Riccati Equation) ...................... 81 4.1.3.1 Optimal Hover Control of the Helicopter ................... 8 5 4.1.3.2 Simulations ................8 7 4.1.3.3 Flight Tests ................ 9 2 4.1.4 Conclusions: Linearized Control ......... 9 3 4.2 Neural Network Control of the Helicopter in Vertical Flight ............................ 9 4 4.2.1 Two-layer Neural Network Construction . 9 4 4.2.2 Two-layer Neural Network Adaptive Algorithm ...................... 9 7 Page 4.2.3 Off-line Training of Inverse Dynamics . 100 4.2.4 MasterISlave On-line Neural Network Control . 104 4.2.5 Simulations ....................10 5 4.2.6 FIight Tests ....................110 4.2.7 Neural Network Control Discussions ..1 1 7 4.2.7 Conclusions: Neural Network Control . 1 19 4.3 Conclusions ........................1 1 9 CHAPTER V . SUMMARY. CONCLUSIONS AND RECOMMENDATIONS .....................12 1 5.0SummaI-y .........................121 5.1 Conclusions ........................1 2 1 5.2 Recommendations ....................12 2 BIBLIOGRAPHY ...........................12 5 APPENDICES Appendix A: Detailed Description of Menu Options . 129 Appendix B: Listing of the Real-time Control Code . 13 2 Appendix C: Characteristic Equation for State Feedback Control Matrix; Determinant(hI5 -(A+BK)) . 15 7 LIST OF FIGURES Figure Page 2.1 Simplistic Free Body Diagram of Hovering Helicopter . 5 2.2 Induced Velocities in the Vicinity of the Hovering Rotor (Prouty [2]) ................... 7 2.3 Geometry of Blade Element (Prouty [2]) ......... 1 0 2.4 Orientation of Blade Element (Prouty [2]) ...12 2.5 Theoretical & Realistic Lift Distributions (Prouty [2]) . 2 0 2.6 Tapered Rotor Blades (Prouty [2]) ............2 4 2.7 Wake Rotation (Prouty [2]) ................ 2 4 2.8 (a) Tip Vortex Locations with and (b) without Wake Contraction (Prouty [2]) ................ 2 6 2.9 Tip Vortex Interference (Prouty [2]) ..........2 6 2.10 Ground Effect: Thrust Increase at Constant Power (Johnson [I]) ...................... 2 9 2.1 1 Effective Drag Area of Rotor Blades ........... 3 5 3.1 Test Bed System Organization .............. 4 3 3.2 Test Bed Hardware Block Diagram ............ 44 3.3 Servo Subsystem Block Diagram ............. 4 6 3.4 Servo Module ....................... 4 7 Figure Page Data Collection Subsystem Block Diagram ........ 4 8 Data Collection Software Tree .............. 50 Control Software Tree .................. 5 2 Miniature Helicopter and Flight Stand ......... 5 3 Linearized State Feedback Control Block Diagram ... 66 Position Step Response Using Linearized Pole Placement Controller ....................... 70 Collective Pitch Servo Input During Simulated Hover Control ......................... 7 1 Collective Pitch During Simulated Hover Control . 7 2 Rotational Velocity During Simulated Hover Control . 7 3 Throttle Servo Input During Simulated Hover Control . 7 4 Position Step Response During Hover Control ...... 7 7 Collective Pitch During Hover Control .......... 7 8 Rotational Speed During Hover Control ......... 7 9 Throttle Servo Input During Hover Control ....... 8 0 Position Step Response Simulation Using Optimal State Feedback Controller .................. 8 8 Collective Pitch Servo Input During Simulated Optimal Hover Control ..................... 8 9 Collective Pitch During Simulated Optimal Hover Control ......................... 9 0 Figure Page 4.14 Rotational Velocity During Simulated Optimal Hover Control ......................... 9 1 4.15 Throttle Servo Input During Simulated Hover Control . 92 4.16 A Two-layer Neural Network with Hard Nonlinearities . 9 5 4.1 7 Off-line Training Block Diagram (Widrow, Winter [15]) .100 4.18 Training Perceptron Weights to Equilibrium Inputs ..........................10 2 4.19 Further Training to Varying Input ........1 0 3 Master/Slave Control Block Diagram (2ak [29]) .....105 Master/Slave Neural Network Control Simulations . 106 Master/Slave Robustness Simulations (0.1%) . .I08 Master/Slave Robustness Simulations (0.2%) . .109 Two-layer Neural Network Implemented for Flight Tests. ......................... .I11 Position Step Response Using Neural Network Control .1 12 Collective Pitch Servo Input During Neural Network Hover Control ......................1 1 3 Collective Pitch During Neural Network Hover Control . 1 14 Throttle Servo Input During Neural Network Hover Control ..........................I1 5 Rotational Velocity During Neural Network Hover Control ..........................I16