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An adaptive attitude tracking control approach for an unmanned helicopter with parametric uncertainties and measurement noises

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Abstract

The attitude control system design for an unmanned helicopter is always a challenging task because the vehicle dynamics are highly nonlinear and fully coupled and subject to parametric uncertainties. This paper presents an adaptive attitude tracking controller with dual model structure, which achieves significant tracking performance and has good capability to overcome the adverse effect of measurement noises on the convergence of adjustable parameters. Moreover, a modified controller with variable gain elements is designed to further reduce the adverse effect of measurement noises on the adjustable system output in the later stage of the adaptive learning process. A series of hardware-in-loop simulations have verified the proposed adaptive control schemes. The suggested design methodologies featured in this paper are effective control tools that can help bridge the gaps between adaptive control theory and the need of realistic applications such as high-performance unmanned helicopters.

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Abbreviations

A :

system matrix

A q̇ p A q̇ r :

system matrices of adjustable system and reference model about the trim state, respectively

B :

operating frequency range, Hz

B :

control-input matrix

B q̇ p B q̇ r :

control-input matrices of adjustable system and reference model about the trim state, respectively

C m :

sensitivity coefficient

D :

variance

e, e f :

tracking error θ m -θ and its filtered version, deg

e f 0 :

noise-free part of e f

e r :

tracking error θ r -θ, deg

e q̇ f :

state error vector with filters

E :

expectation

E :

unknown equivalent trim disturbance vector

G d :

transfer function of linear compensator

G e :

transfer function of error compensator

G f :

transfer function of filter

G m :

transfer function of tracking model

G p :

transfer function of adjustable system

G r :

transfer function of reference model

M q̇• :

aerodynamic parameter

M q̇* :

aerodynamic parameter vector

k c , k q , k θ :

adjustable parameters

k ci , k qi , k ui , k θi :

learning coefficients of adjustable parameters

k a c , k a q , k a θ :

modified versions of adjustable parameters

k e c , k e q , k e θ :

modified versions of adjustable parameters

k e :

variable gain element

\(\widehat k\) θi :

modified version of learning coefficient k θ

K ci , K qi , K θi :

positive integral kernels

K cp , K qp , K θp :

nonnegative functions

K * :

adjustable parameter vector

p, q, r :

roll, pitch and yaw rates linearized about the trim state, deg/s

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{p} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{q} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{r} \) :

roll, pitch and yaw rates, deg/s

u, v, w :

forward, lateral and vertical velocities linearized about the trim state, m/s

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{u} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{v} ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{w} \) :

forward, lateral and vertical velocities, m/s

u q̇ :

input vector

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{U} ,U\), U :

system input and its linearized version about the trim state

U e , U 0 :

trim input and nominal trim input

x q̇ p ,x q̇ r :

state vectors of reference model and adjustable system, respectively

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{X} ,X\), X :

state vector and its linearized version about the trim state

X e , X 0 :

trim state and nominal trim state

δ e , δ a , δ r , δ c :

pitch cyclic, roll cyclic, tail rotor collective and main rotor collective linearized about the trim state, deg

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\delta } _e ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\delta } _a ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\delta } _r ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\delta } _c \) :

pitch cyclic, roll cyclic, tail rotor collective and main rotor collective, respectively, deg

δ ea , δ ef :

adjustable system input signal and its filtered version

δ ec :

manipulated input signal

δ ee , δ em :

outputs of G e in response to θ, θ m , respectively

\({\overline \delta _*}\) :

equivalent disturbance

\({\widetilde \delta _*}\) :

equivalent external disturbance

\({\widehat \delta _*}\) :

compensation signal for compensating for \({\widetilde \delta _*}\)

δ * :

coupled disturbance vector

δ *f :

filtered version of δ *

∆ θf , ∆ qf :

optional positive threshold values

ε f :

output of G d in response to θ rf - θ f

ε f0 :

noise-free part of ε f

ε u , ε x :

estimate errors of U e , X e , respectively

η :

unknown equivalent trim disturbance

λ c , λ e , λ q , λ q :

optional positive constants

θ, ϕ, ψ :

pitch, roll and yaw angles linearized about the trim state, deg

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\theta } ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\varphi } ,\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{\psi } \) :

pitch, roll and yaw angles, deg

θ 0, \({\dot \theta _0}\) :

noise-free parts of θ, \({\dot \theta _0}\), respectively

θ f :

filtered version of θ

θ f0, \({\dot \theta _{f0}}\) :

noise-free parts of θ f , \({\dot \theta _f}\), respectively

θ m :

tracking model output

θ rf :

output of reference model with filter

Θ:

aerodynamic parameter set

τ :

time window width

τ qe , τ θe :

differential and proportional coefficients of G e

ω m :

natural frequency, rad/s

\({\xi _{{\varepsilon _f}}}\) :

mixed noise in ε f

ξ θ , ξ q :

measurement noises in θ, \(\dot \theta \), respectively

\({\xi _{{\theta _f}}}\), ξ qf :

filtered versions of ξ θ , ξ q

ζ m :

damping ratio

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Authors and Affiliations

  1. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao St., Nanjing, 210016, China

    Shouzhao Sheng & Chenwu Sun

Authors
  1. Shouzhao Sheng
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  2. Chenwu Sun
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Corresponding author

Correspondence to Shouzhao Sheng.

Additional information

Recommended by Associate Editor Wen-Hua Chen under the direction of Editor Duk-Sun Shim. This work was sponsored by National Natural Science Foundation of China under Grant No. 61374188, Aeronautical Science Foundation of China under Grant No. 2013ZC52033, Natural Science Foundation of Jiangsu Province, China under Grant No. BK20141412, Applied Basic Research Programs of Natural Science Foundation of Jiangsu Province, China under Grant No. BY2015003-10.

Shouzhao Sheng received his PhD degree in Control Theory and Control Engineering from Nanjing University of Aeronautics and Astronautics in 2005. His research interests include flight control, adaptive control and system identification.

Chenwu Sun received his Bachelor degree in Control Engineering from Heilongjiang University in 2013. He is currently a PhD candidate in the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics. His research interests include flight control and adaptive control.

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Sheng, S., Sun, C. An adaptive attitude tracking control approach for an unmanned helicopter with parametric uncertainties and measurement noises. Int. J. Control Autom. Syst. 14, 217–228 (2016). https://doi.org/10.1007/s12555-014-0244-8

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  • DOI: https://doi.org/10.1007/s12555-014-0244-8

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