Linear and Nonlinear Control of Small-Scale Unmanned Helicopters

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Model-Based Control of Unmanned Rotorcraft provides a comprehensive study of modeling and control of small unmanned rotorcraft (helicopters), and explores the technical challenges involved. The text also serves as a step-by-step reference on the modeling and control of small, unmanned helicopters.

There has been significant interest for designing flight controllers for small-scale unmanned helicopters. Such helicopters preserve all the physical attributes of their full-scale counterparts, being at the same time more agile and dexterous. This book presents a comprehensive and well justified analysis for designing flight controllers for small-scale unmanned helicopters guarantying flight stability and tracking accuracy. The design of the flight controller is a critical and integral part for developing an autonomous helicopter platform. Helicopters are underactuated, highly nonlinear systems with significant dynamic coupling that needs to be considered and accounted for during controller design and implementation. Most reliable mathematical tools for analysis of control systems relate to modern control theory. Modern control techniques are model-based since the controller architecture depends on the dynamic representation of the system to be controlled. Therefore, the flight controller design problem is tightly connected with the helicopter modeling.

This book provides a step-by-step methodology for designing, evaluating and implementing efficient flight controllers for small-scale helicopters. Design issues that are analytically covered include:

• An illustrative presentation of both linear and nonlinear models of ordinary differential equations representing the helicopter dynamics. A detailed presentation of the helicopter equations of motion is given for the derivation of both model types. In addition, an insightful presentation of the main rotor's mechanism, aerodynamics and dynamics is also provided. Both model types are of low complexity, physically meaningful and capable of encapsulating the dynamic behavior of a large class of small-scale helicopters.

• An illustrative and rigorous derivation of mathematical control algorithms based on both the linear and nonlinear representation of the helicopter dynamics. Flight controller designs guarantee that the tracking objectives of the helicopter's inertial position (or velocity) and heading are achieved. Each controller is carefully constructed by considering the small-scale helicopter's physical flight capabilities. Concepts of advanced stability analysis are used to improve the efficiency and reduce the complexity of the flight control system. Controller designs are derived in both continuous time and discrete time covering discretization issues, which emerge from the implementation of the control algorithm using microprocessors.

• Presentation of the most powerful, practical and efficient methods for extracting the helicopter model parameters based on input/output responses, collected by the measurement instruments. This topic is of particular importance for real-life implementation of the control algorithms.

This book is suitable for students and researches interested in the development and the mathematical derivation of flight controllers for small-scale helicopters. Background knowledge in modern control is required.

The comprehensive study of modeling and control of small unmanned rotorcraft (helicopters) addressing all technical challenges faced when dealing with such unstable, nonlinear and underactuated systems;A detailed reference text that if followed step-by-step allows scientists, engineers, researchers and practitioners to model accurately and control (fly) small unmanned helicopters;Reference point-by-point analytical 'tool' that should be next to every small unmanned rotorcraft

Dr. Raptis joined the faculty of Mechanical Engineering at the University of Massachusetts Lowell as an Assistant Professor in Fall 2012. He is the director of the Autonomous Robotic Systems Laboratory (ARSL). Dr. Raptis received his Dipl-Ing. in Electrical and Computer Engineering from the Aristotle University of Thessaloniki, Greece and his Master of Science in Electrical and Computer Engineering from The Ohio State University in 2003 and 2006, respectively. In 2010 he received his Ph.D. degree in the department of Electrical Engineering at the University of South Florida. In the same year he joined the Intelligent Control Systems Laboratory (ICSL) and the School of Electrical and Computer Engineering at the Georgia Institute of Technology as a Postdoctoral Research Fellow. From October 2011 to August 2012 he had a joint appointment with ICSL and the Aerospace Systems Design Laboratory (ASDL) in the department of Aerospace Engineering at the Georgia Institute of Technology.

Dr. Valavanis received the Diploma in Electrical and Electronic Engineering (5 years of study) in 1981 from the National Technical University of Athens (, Greece, and he completed the Professional Engineer (PE) exams in Electrical and Mechanical Engineering in February 1982.  He received the M.Sc. degree in Electrical Engineering and the PhD degree in Computer and Systems Engineering from Rensselaer Polytechnic Institute (RPI) ( in 1984 and 1986, respectively. From 1987 to 1990 he held the Analog Devices Career Development Chair for Assistant Professors at the Department of Electrical and Computer Engineering, Northeastern University (, Boston, where he was also Director of the Robotics Laboratory.

From 1991 to 1999 he was with The Center for Advanced Computer Studies (CACS), University of Louisiana at Lafayette ( where he served as Associate Professor (1991-1995) and Professor (since 1995) of Computer Engineering, as Associate Director for Research at the A-CIM Center (1993-1999) and as Director of the Robotics and Automation Laboratory. He also held the A-CIM/[TC]2/Regents Professorship in Manufacturing.

From 1999-2003, he was Professor in the Department of Production Engineering and Management, Technical University of Crete (, Greece, where he also served as Director of the Laboratory of Intelligent Systems and Robotics, Director of the Graduate Program and Chair of the University Industrial Advisory Board.

From 2003-August 2008 he was Professor at the Department of Computer Science and Engineering, University of South Florida (, where he also served as Deputy Director at the Center for Robot-Assisted Search and Rescue (CRASAR) until the summer of 2005. In 2006, he created the Unmanned Systems Laboratory in the College of Engineering, in which he served as Director. He was also the Managing Director of the National Institute for Applied Computational Intelligence (NIACI) and a Faculty Associate at the Center for Urban Transportation Research (CUTR).

He joined the University of Denver on September 1, 2008, as Professor and Chair of the Electrical and Computer Engineering Department. Since July 1, 2009, he is also Acting Chair of the Computer Science Department. In 2009, he established the DU Unmanned Systems Laboratory (DU2SL), serving as its Director.

He is also Guest Professor in the Faculty of Electrical Engineering and Computing, Department of Telecommunications, University of Zagreb (, Croatia.

Dr. Valavanis' research interests are focused in the areas of Unmanned Systems, Distributed Intelligence Systems, Robotics and Automation. He has published over 300 book chapters, technical journal/transaction and referred conference papers. He has co-authored the book Intelligent Robotic Systems: Theory, Design and Applications (with Dr. G. N. Saridis), Kluwer Academic Publishers, 1992; he co-edited (with B. Siciliano) the book Control Problems in Robotics and Automation, Lecture Notes in Control and Information Sciences, Vol. 230, Springer-Verlag, 1998. He also co-authored (with J. Balic, N. Tsourveloudis and S. Ioannidis) the book Intelligent Manufacturing Systems: Programming and Control, University of Maribor Publications, 2003. He is also the Editor (and co-author of nine chapters) of the book Advances in Unmanned Aerial Vehicles: State of the art and the road to autonomy, Springer, 2007. He co-edited the book (with P. Oh and L. A. Piegl) Unmanned Aircraft Systems - International Symposium on Unmanned Aerial Vehicles, UAV'08, Springer, 2009; he co-authored the book (with K. Dalamagkidis and L. A. Piegl) On Integrating Unmanned Aircraft Systems in to the National Airspace System: Issues, Challenges, Operational Restrictions, Certification, and Recommendations<, Springer, 2009 the Second Edition of this book will be published in 2011. He also edited the book Intelligent Control Applications to Engineering Systems, Springer, 2009, and the book  Selected Papers from the 2nd International Symposium on Unmanned Aerial Vehicles, (with R. Beard, P. Oh, A. Ollero, L. Piegl, H. D. Shim), Springer, 2010. Most recently, he published the book Linear and Nonlinear Control of Small-Scale Unmanned Helicopters (I. A. Raptis, K. P. Valavanis), Springer 2011. His most recent book project, to be completed in 2012, is the Handbook of Unmanned Aerial Vehicles (UAVs), with emphasis on: UAV History and Fundamentals, UAV Technologies, UAV Integration into the National Airspace, Applications, Who is Who in UAVs, Future Trends (K. P. Valavanis, G. J. Vachtsevanos), to be published by Springer. Further, he is publishing the book K. P. Valavanis (Editor), Unmanned Aerial Vehicles, Selected Papers from the 3rd UAV Symposium held in Dubai, June 2010 (in print, to be published in early 2011). In addition, he is the co-author (with G. Atsalakis and K. Zopounidis) of the book Stock Market Forecasting Techniques (in Greek), published by Klidarithmos (ISBN 978-960-461-121-8) in 2008.

He has organized two International Advanced Robotics Programme (IARP) meetings in Lisbon, Portugal, and Lafayette, LA, he has taught Tutorial Workshops at the IEEE CDC, ACC, and ICRA, Conference on Telecommunications (ConTel) and the Mediterranean Conference in Control and Automation. He served as Associate Editor of the IEEE Transactions in Robotics and Automation from 2/1996-2/1999, as the Robotics and Automation Society Discrete Event Dynamic Systems Technical Committee co-Chair for two years, and as an Associate Editor of the IEEE Robotics and Automation Society Magazine from 1994 to 1995. He was Editor-in-chief of the Magazine for ten years (1996-2005). He was also the Book Review Editor of the Journal of Intelligent and Robotic Systems until 2006, and since then, he serves as the Editor-in-Chief of the Journal. He serves on the Editorial Advisory Board of the International Series on Microprocessor Based and Intelligent Systems Engineering Series published by Springer. He also served as a member of the IEEE Robotics and Automation Society Awards Committee for three years, and as co-chair/chair of the Aerial Robotics and Unmanned Aerial Vehicles Technical Committee (2008-2010).  

Dr. Valavanis has been on the organizing committee of many IEEE conferences, serving as General, Program, Registration and Local Arrangements Chair. He was the General Chair (with F. Lewis) of the 11th  Mediterranean Conference on Control and Automation, June 2003, and the Program Chair of the 2004 IEEE ICRA. He was the General Chair (with P. Anstaklis) of the 15th Mediterranean Conference on Control and Automation, June 2007, and the General Chair (with W. Gruver) of the IEEE SMC International Conference on Distributed Human-Machine Systems, March 2008. He is also the General Chair of the 2011 IEEE Multi-Conference on Systems and Control, the Conference Chair of the 16th IASTED International Conference on Control and Applications, June 2011, and the General Chair of the 2011 International Conference on Unmanned Aircraft Systems. In 1998, he was elected as Vice President Administration of the IEEE Mediterranean Control Association (MCA). He was a Distinguished Speaker in the IEEE Robotics and Automation Society (- 2003), a senior member of IEEE and a Fellow of the American Association for the Advancement of Science. He is also a Fulbright Scholar.   

1 Introduction.- 1.1 Background Information.- 1.2 The Mathematical Problem ..- 1.3 Controller Designs.- 1.3.1 Linear Controller Design.- 1.3.2 Nonlinear Controller Design.- 1.4 Outline of the Book.- 2 Review of Linear and Nonlinear Controller Designs.- 2.1 Linear Controller Designs.- 2.2 Nonlinear Controller Design.- 2.3 Remarks.- 3 Helicopter Basic Equations of Motion.- 3.1 Helicopter Equations of Motion.- 3.2 Position and Orientation of the Helicopter.- 3.2.1 Helicopter Position Dynamics.- 3.2.2 Helicopter Orientation Dynamics.- 3.3 Complete Helicopter Dynamics.- 3.4 Remarks.- 4 Simplified Rotor Dynamics.- 4.1 Introduction.- 4.2 Blade Motion.- 4.3 Swashplate Mechanism.- 4.4 Fundamental Rotor Aerodynamics.- 4.5 Flapping Equations of Motion.- 4.6 Rotor Tip-Path-Plane Equation.- 4.7 First Order Tip-Path-Plane Equations.- 4.8 Main Rotor Forces and Moments.- 4.9 Remarks.- 5 Frequency Domain System Identification.- 5.1 Mathematical Modeling.- 5.1.1 First Principles Modeling.- 5.1.2 System Identification Modeling.- 5.2 Frequency Domain System Identification.- 5.3 Advantages of the Frequency Domain Identification.- 5.4 Helicopter Identification Challenges.- 5.5 Frequency Response and the Coherence Function.- 5.6 The CIFER c Package.- 5.7 Time History Data and Excitation Inputs.- 5.8 Linearization of the Equations of Motion.- 5.9 Stability and Control Derivatives.- 5.10 Model Identification.- 5.10.1 Experimental Platform.- 5.10.2 Parametrized State Space Model.- 5.10.3 Identification Setup.- 5.10.4 Time Domain Validation.- 5.11 Remarks.- 6 Linear Tracking Controller Design for Small-Scale Unmanned Helicopters.- 6.1 Helicopter Linear Model.- 6.2 Linear Controller Design Outline.- 6.3 Decomposing the System.- 6.4 Velocity and Heading Tracking Controller Design.- 6.4.1 Lateral-Longitudinal Dynamics.- 6.4.2 Yaw-Heave Dynamics.- 6.4.3 Stability of the Complete System Error Dynamics.- 6.5 Position and Heading Tracking.- 6.6 PID Controller Design.- 6.7 Experimental Results.- 6.8 Remarks.- 7 Nonlinear Tracking Controller Design for Unmanned Helicopters.- 7.1 Introduction.- 7.2 Helicopter Nonlinear Model.- 7.2.1 Rigid Body Dynamics.- 7.2.2 ExternalWrench Model.- 7.2.3 Complete Rigid Body Dynamics.- 7.3 Translational Error Dynamics.- 7.4 Attitude Error Dynamics.- 7.4.1 Yaw Error Dynamics.- 7.4.2 Orientation Error Dynamics.- 7.4.3 Angular Velocity Error Dynamics.- 7.5 Stability of the Attitude Error Dynamics.- 7.6 Stability of the Translational Error Dynamics.- 7.7 Numeric Simulation Results.- 7.8 Remarks.- 8 Time Domain Parameter Estimation and Applied Discrete Nonlinear Control for Small-Scale Unmanned Helicopters.- 8.1 Introduction.- 8.2 Discrete System Dynamics.- 8.3 Discrete Backstepping Algorithm.- 8.3.1 Angular Velocity Dynamics.- 8.3.2 Translational Dynamics.- 8.3.3 Yaw Dynamics.- 8.4 Parameter Estimation Using Recursive Least Squares.- 8.5 Parametric Model.- 8.6 Experimental Results.- 8.6.1 Time History Data and Excitation Inputs.- 8.6.2 Validation.- 8.6.3 Control Design.- 8.7 Remarks.- 9 Time Domain System Identification for Small-Scale Unmanned Helicopters Using Fuzzy Models.- 9.1 Introduction.- 9.2 Takagi-Sugeno Fuzzy Models.- 9.3 Proposed Takagi-Sugeno System for Helicopters.- 9.4 Experimental Results.- 9.4.1 Tunning of the Membership Function Parameters.- 9.4.2 Validation.- 10 Comparison Studies.- 10.1 Summary of the Controller Designs.- 10.2 Experimental Results.- 10.3 First Maneuver: Forward Flight.- 10.4 Second Maneuver: Aggressive Forward Flight.- 10.5 Third Maneuver: 8 Shaped Trajectory.- 10.6 Fourth Maneuver: Pirouette Trajectory.- 10.7 Remarks.- 11 Epilogue.- 11.1 Introduction.- 11.2 Advantages and Novelties of the Designs.- 11.3 Testing and Implementation.- 11.4 Remarks.- A Fundamentals of Backstepping Control.- A.1 Integrator Backstepping.- A.2 Example of a Recursive Backstepping Design.- References.

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Linear and Nonlinear Control of Small-Scale Unmanned Helicopters
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Springer Netherlands
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H235mm x B155mm x T12mm
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