Design of Control Laws and State Observers for Fixed-Wing UAVs

Simulation and Experimental Approaches

1st Edition - September 29, 2022
Authors: Arturo Tadeo Espinoza-Fraire, Alejandro Enrique Dzul López, Ricardo Pavel Parada Morado, José Armando Sáenz Esqueda
Language: English
Paperback ISBN:
9 7 8 - 0 - 3 2 3 - 9 5 4 0 5 - 1
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 9 5 4 0 4 - 4

Design of Control Laws and State Observers for Fixed-Wing UAVs: Simulation and Experimental Approaches provides readers with modeling techniques, simulations, and results from r… Read more

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Design of Control Laws and State Observers for Fixed-Wing UAVs: Simulation and Experimental Approaches provides readers with modeling techniques, simulations, and results from real-time experiments using linear and nonlinear controllers and state observers. The book starts with an overview of the history of UAVs and the equations of motion applied to them. Following chapters analyze linear and nonlinear controllers, state observers, and the book concludes with a chapter discussing testbed development and experimental results, equipping readers with the knowledge they need to conduct their own stable UAV flights whether in simulation or real-time.

1 Introduction

1.1 Classification of UAVs

1.2 Nonmilitary applications of fixed-wing UAVs

1.3 Control systems in fixed-wing UAVs

1.4 State observer systems in fixed-wing UAVs

2 Aerodynamic principles

2.1 The importance of aerodynamic principles

2.1.1 The atmosphere

2.1.2 Atmospheric pressure

2.1.3 Standard atmosphere

2.1.4 Air temperature

2.1.5 Air density

2.1.6 Airplane wing

2.1.7 Bernoulli theorem

2.1.8 The center of pressure

2.2 Forces acting in flight

2.2.1 Flight opposition (resistance)

2.2.2 Thrust

2.2.3 Lift

2.3 Axes of an airplane

2.3.1 Aircraft control surfaces

2.3.2 The structure of an airplane

2.4 Concluding remarks

3 Equations of motion of a fixed-wing UAV

3.1 Control surfaces of a fixed-wing MAV

3.2 Frame coordinates in fixed-wing UAVs

3.3 Governing physics of a fixed-wing UAV

3.4 Motion of a rigid body

3.5 Kinematic model

3.6 Uncoupled model of the fixed-wing UAV

3.6.1 Longitudinal dynamics

3.6.2 Directional and lateral dynamics

3.6.3 Change of variables

3.7 Concluding remarks

4 Linear controllers

4.1 PD and PID controllers

4.2 LQR controller

4.3 LQR controller with the discrete-time Kalman filter

4.4 Concluding remarks

5 Nonlinear controllers

5.1 Nested saturation controller

5.2 Backstepping controller

5.3 Sliding mode controller

5.4 Nested saturation with sliding mode

5.5 Nested saturation with 2-SM

5.6 Nested saturation with HOSM

5.7 Backstepping with SM

5.8 Backstepping with 2-SM

5.9 Backstepping with HOSM

5.10 MIT rule based on the gradient method with sliding mode theory

5.11 Concluding remarks

6 State observers

6.1 Applications and concepts of state observers in control theory

6.2 Complementary filters

6.3 Sliding mode observers

6.3.1 Sliding surface

6.3.2 Shear effect and sliding patch

6.3.3 System damping

6.4 Nonlinear extended state observer

6.5 Backstepping observer

6.6 Simulation results of the control laws with observers

6.6.1 PD control law with observers

6.6.2 Backstepping control law with observers

6.6.3 Roll motion simulations with PD control law with observers

6.6.4 Yaw motion simulations with PD control law with observers

6.6.5 Altitude motion simulations with PD control law with observers

6.6.6 Roll motion simulations with backstepping control law with observers

6.6.7 Yaw motion simulations with backstepping control law with observers

6.6.8 Altitude movement simulations with backstepping control law with observers

6.7 Concluding remarks

7 Testbed and experimental results

7.1 Experimental testbed

7.2 Motors or actuators in a testbed

7.3 Inertial measurement unit (IMU)

7.4 Telemetry

7.5 Optocoupler

7.6 Microcontroller and altimeter

7.7 Microprocessor Rabbit 6000

7.8 Li-po battery

7.9 Experimental results for linear and nonlinear controllers

7.9.1 PD controller

7.9.2 PID controller

7.9.3 LQR controller

7.9.4 LQR controller with discrete-time Kalman filter

7.9.5 Backstepping controller

7.10 Experimental results for linear and nonlinear observers

7.10.1 Luenberger observer applied to a fixed-wing UAV with PD control law

7.10.2 SMO applied to a fixed-wing UAV with PD control law

7.10.3 NESO applied to a fixed-wing UAV with PD control law

7.10.4 SMO applied to a fixed-wing UAV with backstepping control law

7.10.5 NESO applied to a fixed-wing UAV with backstepping control law

7.11 Concluding remarks

A Mathematical review

A.1 Vectors
A.2 Linear transformations
A.3 Euclidean norm
A.4 Matrices
A.5 Spectral norm
A.6 P-norms
A.7 Dyadic product, cross product, and antisymmetric matrix
A.8 Topological concepts
A.8.1 Sets
A.8.2 Metric spaces
A.8.3 Linear independence
A.8.4 Sequence convergence
A.9 Functions
A.9.1 Continuous functions
A.9.2 Differentiable functions
A.9.3 Mean value theorem
A.9.4 Implicit function theorem
A.9.5 Gronwall–Bellman inequality
A.10 Contraction mapping

B Kinematics and dynamics background

B.1 Kinematics
B.2 Dynamics

C Stability in the Lyapunov sense

C.1 Direct Lyapunov method

D Fundamentals of linear and nonlinear controllers

D.1 Fundamentals of linear controllers
D.1.1 PID and PD controller theory
D.1.2 Linear quadratic regulator (LQR)
D.2 Fundamentals of nonlinear controllers
D.2.1 Nested saturations
D.2.2 Integrator backstepping
D.2.3 Sliding mode control
D.2.4 Model reference adaptive control (MRAC)

E Discrete-time Kalman filter

F
Linear and nonlinear controllers: programs for the embedded system

F.1 PD controller in altitude
F.2 Backstepping controller in altitude

G Linear and nonlinear state observers: programs for the embedded system

G.1 Luenberger observer with PD controller in yaw
G.2 SMO observer with PD controller in altitude

H MATLAB® program to graph

I Altimeter program

Arturo Tadeo Espinoza-Fraire

Arturo Tadeo Espinoza-Fraire has been a professor and researcher in the Faculty of Engineering, Science, and Architecture, University Juárez of the Durango State, Gómez Palacio, Durango, Mexico since 2016. He obtained his BSc degree in Electronic Engineering from the Superior Technological Institute of Lerdo, Cd. Lerdo Durango Mexico, in 2007, and the MSc and the Ph.D. in Electrical Engineering from the Technological Institute of La Laguna, Torreon Coahuila Mexico, in 2011 and 2015, respectively. His research interests are linear and nonlinear control theory, navigation, and control of UAVs and embedded systems. Prof. Espinoza-Fraire has been a member of the Technical International Commit of the International Conference of Unmanned Aerial Systems since 2014 as well as the Research National System with the distinction of level-I in Mexico. He is also an honorific level of the National System of Research in Durango Stater, Mexico.

Affiliations and expertise

Research Professor, Faculty of Engineering, Science, and Architecture, University Juárez of the Durango State, Gómez Palacio, Durango, Mexico.

Alejandro Enrique Dzul López

Alejandro Enrique Dzul López has been a research professor in the Electrical and Electronic Engineering Department, Technological Institute of La Laguna, Torreón, Coahuila, Mexico since 2003. He earned a B.S. in Electronic Engineering and an M.S. in Electrical Engineering from the Instituto Tecnológico de La Laguna in Torreón, México, in 1993 and 1997, respectively, and a Ph.D. in Automatic Control from the Université de Technologie de Compiègne in Compiègne, France, in 2002. His current research interests include nonlinear dynamics and control and real-time control with applications to unmanned aerial systems.

Affiliations and expertise

Research Professor, Electrical and Electronic Engineering Department, Technological Institute of La Laguna, Torreón, Coahuila, Mexico.

Ricardo Pavel Parada Morado

Ricardo Pavel Parada Morado has been a professor in the Academy of Engineering in Manufacturing Technologies, Polytechnic University of Gómez Palacio, Gómez Palacio, Durango, Mexico since 2016. He obtained his B.S. in Electronic Engineering and M.S. in Electrical Engineering from Instituto Tecnológico de La Laguna, Torreón, México, in 2004 and 2007, respectively. His current research interests include state observers, nonlinear dynamics and control, and real-time control with applications to unmanned aerial systems.

Affiliations and expertise

Professor, Academy of Engineering in Manufacturing Technologies, Polytechnic University of Gómez Palacio, Gómez Palacio, Durango, Mexico.

José Armando Sáenz Esqueda

José Armando Sáenz Esqueda is currently a professor and a researcher in the Faculty of Engineering, Science, and Architecture, University Juárez of the Durango State, Gómez Palacio, Durango, Mexico. He graduated from Laguna Institute of Technology in Torreon, Coahuila, Mexico, with a B.E. in Mechatronic Engineering in 2011, an M.Sc. in 2013, and a Ph.D. in 2018. His research interests are kinematic and dynamic modeling, robot control, visual serving, and nonlinear systems control.

Affiliations and expertise

Professor and Researcher, Faculty of Engineering, Science, and Architecture, University Juárez of the Durango State, Gómez Palacio, Durango, Mexico.