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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.



Chapter 1. Introduction

This Chapter presents the rationale for the book, defines the problem to be solved along with the challenges that need to be overcome, and concludes with a summary of the linear and nonlinear controller methodologies that will be detailed in subsequent Chapters.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 2. Review of Linear and Nonlinear Controller Designs

This Chapter reviews several flight controller designs for unmanned rotorcraft. Flight control systems have been proposed and tested on a wide range of rotorcraft types and configurations. This review includes controller designs for several rotorcraft types such as full-scale, small-scale and experimental platforms (gimbaled on a vertical stand). Existing flight control systems use tools from all fields of control theory by incorporating into the controller design classical, modern and intelligent control techniques.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 3. Helicopter Basic Equations of Motion

The objective of this Chapter is to provide the basic equations of motion of the helicopter, when the helicopter is treated as a rigid body. The equations of motion are derived by implementing Newton’s second law that deals with vector summations of all forces and moments as applied to the helicopter relative to an inertial reference frame. However, for practical reasons, analysis may be significantly simplified if motion is described relative to a reference frame rigidly attached to the helicopter. When this is the case, the equations of motion are derived relative to this non-inertial, body-fixed frame. The end result of this Chapter is the complete state space representation of the helicopter equations of motion in the configuration space.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 4. Simplified Rotor Dynamics

The helicopter’s main source of propulsion is provided by the main and tail rotor. The aerodynamic forces and moments are nonlinear functions of motion characteristics and controls. Due to the complexity and the uncertainty associated with the aerodynamic phenomena, a detailed model of the forces and moments produced by the main rotor would be of high order and completely impractical for any controller design. In this Chapter, the modeling approach presented in (Koo and Sastry in Proceedings of the 37th IEEE Conference on Decision and Control, vol. 4, 1998, pp. 3635–3640; Lee et al. in Proceedings of Society of Instrument and Control Engineers, 1993, pp. 1385–1390; Mettler in Identification Modeling and Characteristics of Miniature Rotorcraft, Kluwer Academic Publishers, Norwell, 2003; Mettler et al. in Presented at the American Helicopter Society 55th Forum, May 1999 ) is followed to arrive at a simplified derivation of the main rotor dynamics and the produced thrust force vector that are considered sufficient for controller design purposes.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 5. Frequency Domain System Identification

Any helicopter flight controller design requires knowledge of a mathematical model that accurately describes the dynamic behavior of the helicopter. This mathematical model is represented by a set of ordinary differential equations. Establishing such a model for helicopters is a challenging task. This Chapter provides a thorough description of a frequency domain identification procedure for the extraction of linear models that correspond to certain operating conditions of the helicopter. The discussed methodology was initially presented in (Tischler and Remple in Aircraft and Rotorcraft System Identification, AIAA Education Series, AIAA, Washington, 2006) and it has been successfully applied for a small-scale helicopter in the work reported in (Mettler in Identification Modeling and Characteristics of Miniature Rotorcraft, Kluwer Academic Publishers, Norwell, 2003). The frequency domain identification procedure is evaluated for an experimental small-scale Radio Controlled (RC) Raptor 90 SE helicopter using the X-plane flight simulator. The Raptor 90 SE helicopter has also been used for the evaluation and comparison of the several controller designs and identification methods that are presented in this book.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 6. Linear Tracking Controller Design for Small-Scale Unmanned Helicopters

The previous Chapter presented an analytical methodology for the extraction of a linear dynamic model for a small-scale helicopter based on (Mettler in Identification Modeling and Characteristics of Miniature Rotorcraft, Kluwer Academic Publishers, Norwell, 2003; Tischler and Remple in Aircraft and Rotorcraft System Identification, AIAA Education Series, AIAA, Washington, 2006) . Modern control techniques are model based, in the sense that the controller architecture depends on the dynamic description of the system. Therefore, the knowledge of the helicopter linear dynamic model is very valuable for designing (autonomous) flight controllers. This Chapter presents a systematic procedure for the design of a flight controller based on the linear dynamic representation of the helicopter. The controller objective is for the helicopter to track predefined reference trajectories of the inertial position and the yaw angle.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 7. Nonlinear Tracking Controller Design for Unmanned Helicopters

The previous Chapter presented a tracking controller of the position and heading of a helicopter based on the linearized helicopter dynamics. The adopted parametric linear model, on which the flight controller is based on, represented the quasi steady state behavior of the helicopter dynamics at hover.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 8. Time Domain Parameter Estimation and Applied Discrete Nonlinear Control for Small-Scale Unmanned Helicopters

This Chapter deals with the dual problem of parameter estimation and nonlinear discrete control of helicopters. The objective is to develop a practical identification and control solution for direct application to an autonomous helicopter flight system. Although most controller designs are in continuous time, this Chapter considers the discrete time dynamics of the helicopter. The shift of the helicopter control problem to discrete time is twofold: Control algorithms are executed by microprocessors. The discretization effect of the helicopter dynamics should be incorporated into the controller design. In addition, time domain parametric identification is much simpler and computationally more efficient when the system equations are discretized.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 9. Time Domain System Identification for Small-Scale Unmanned Helicopters Using Fuzzy Models

The system identification method presented in this Chapter is based on a Takagi–Sugeno fuzzy system that represents the translational and rotational velocity dynamics of the helicopter. For the parameter estimation of the Takagi–Sugeno fuzzy system a classical RLS algorithm is used, which allows the identification to take place on-line since parameter updates are produced whenever a new measurement becomes available. The validity of this approach is also tested using the X-Plane simulator.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 10. Comparison Studies

This Chapter provides an extensive evaluation and comparison of the controller designs that have been presented in this book. The comparative study is completed by executing several nonaggressive and aggressive flight maneuvers that test the derived controllers in terms of stability and tracking accuracy. The test maneuvers are produced by inertial position (or velocity) and yaw reference trajectories. The reference trajectories are specially designed in order to examine the performance of the controllers in multiple operating conditions that cover a wide portion of the flight envelope. Some of the reference trajectories are particularly aggressive investigating the physical limitations of the helicopter. The controllers were tested for the Raptor 90 SE RC helicopter, which operates in the X-Plane flight simulator environment.
Ioannis A. Raptis, Kimon P. Valavanis

Chapter 11. Epilogue

It is true that helicopters are highly nonlinear underactuated systems with significant dynamic coupling. In general, they are considered to be much more unstable than fixed-wing aircraft. Their nature imposes significant challenges to the controller design.
Ioannis A. Raptis, Kimon P. Valavanis


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