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Backstepping approach for design of PID controller with guaranteed performance for micro-air UAV

  • Yusuf KartalEmail author
  • Patrik Kolaric
  • Victor Lopez
  • Atilla Dogan
  • Frank Lewis
Article
  • 21 Downloads

Abstract

Flight controllers for micro-air UAVs are generally designed using proportional-integral-derivative (PID) methods, where the tuning of gains is difficult and time-consuming, and performance is not guaranteed. In this paper, we develop a rigorous method based on the sliding mode analysis and nonlinear backstepping to design a PID controller with guaranteed performance. This technique provides the structure and gains for the PID controller, such that a robust and fast response of the UAV (unmanned aerial vehicle) for trajectory tracking is achieved. First, the second-order sliding variable errors are used in a rigorous nonlinear backstepping design to obtain guaranteed performance for the nonlinear UAV dynamics. Then, using a small angle approximation and rigorous geometric manipulations, this nonlinear design is converted into a PID controller whose structure is naturally determined through the backstepping procedure. PID gains that guarantee robust UAV performance are finally computed from the sliding mode gains and from stabilizing gains for tracking error dynamics. We prove that the desired Euler angles of the inner attitude controller loop are related to the dynamics of the outer backstepping tracker loop by inverse kinematics, which provides a seamless connection with existing built-in UAV attitude controllers. We implement the proposed method on actual UAV, and experimental flight tests prove the validity of these algorithms. It is seen that our PID design procedure yields tighter UAV performance than an existing popular PID control technique.

Keywords

Quadrotor nonlinear controller trajectory tracking backstepping controller inverse kinematics 

Nomenclature

ξ

position vector in Earth frame

U

velocity vector in Body frame

ξd

desired position vector in Earth frame

xd

desired position in x-axis in Earth frame

yd

desired position in y-axis in Earth frame

zd

desired position in z-axis in Earth frame

x

current position in x-axis in Earth frame

y

current position in y-axis in Earth frame

z

current position in z-axis in Earth frame

xB

desired position in x-axis in Body frame

yB

desired position in y-axis in Body frame

zB

desired position in z-axis in Body frame

R

rotation matrix from Earth to Body frame

F

force vector in the Earth frame

Fd

desired force vector in Earth frame

Fg

gravitational force vector in Earth frame

g

gravitational acceleration

μ

thrust produced in Body frame z-axis

μd

desired total thrust in Body frame z-axis

wB

angular velocity matrix in Body frame

u

forward velocity in Body frame

v

sideward velocity in Body frame

w

vertical velocity in Body frame

p

roll rate

q

pitch rate

r

yaw rate

e

error term

ϕ

roll angle

θ

pitch angle

ψ

yaw angle

ϕd

desired roll angle

θd

desired pitch angle

ψd

desired yaw angle

IB

inertia matrix

m

mass of the quadrotor

l

lever length

t

thrust factor

τB

torque vector

Ω

angular velocity of rotor

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Notes

Acknowledgments

The author Mr. Kartal thanks Turkish Aerospace for the scholarship granted.

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Copyright information

© South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  • Yusuf Kartal
    • 1
    Email author
  • Patrik Kolaric
    • 1
  • Victor Lopez
    • 1
  • Atilla Dogan
    • 2
  • Frank Lewis
    • 1
  1. 1.University of Texas at Arlington Research InstituteForth WorthUSA
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of Texas at ArlingtonTexasUSA

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