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Nonlinear disturbance observer-based robust control of attitude tracking of rigid spacecraft

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Abstract

Robust control of attitude tracking system between two rigid spacecraft is addressed using nonlinear disturbance observer-based control technique. A relative attitude dynamics model is derived for spacecraft tracking maneuver, where parameter uncertainty and environmental disturbances are considered as disturbance torques. A composite control technique is proposed for robust attitude tracking of a rigid spacecraft about a spacecraft under multiple disturbances by combining a nonlinear disturbance observer with an asymptotic tracking control. The proposed nonlinear disturbance observer is used to enhance the disturbance attenuation ability and robustness performance against uncertain inertia parameter and disturbances by estimating and compensating for the disturbances through feedforward. Stability and tracking performance of the nonlinear disturbance observer are analyzed. Furthermore, the stability of the composed control approach consisting of the asymptotic tracking control and nonlinear disturbance observer is established through Lyapunov method. Simulation results show that the composite control technique can significantly enhance disturbance attenuation ability, robust dynamics performance and the desired relative attitude tracking accuracy of a rigid spacecraft under external disturbances and uncertain inertia matrix.

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Abbreviations

\({\varvec{q}_c}\) :

Quaternion of the chief spacecraft

\({\varvec{q}_d}\) :

Quaternion of the deputy spacecraft

\({\varvec{\omega }_c}\) :

Angular velocity of the chief spacecraft

\({\varvec{\omega }_d}\) :

Angular velocity of the deputy spacecraft

\({\varvec{q}_d}\) :

Quaternion of the deputy spacecraft

\({\varvec{q}}\) :

Relative quaternion between the chief and deputy spacecraft body frames

\({\varvec{\omega }}\) :

Angular velocity of the deputy relative to the chief

\(\varvec{d}\) :

Lumped disturbance

\({\hat{{\varvec{d}}}}\) :

Lumped disturbance estimate

\(\varvec{d}_e\) :

Estimate error of the lumped disturbance

\(\varvec{\ell }\) :

Sliding surface

\(\varvec{z}\) :

Internal state of the nonlinear observer

\(\varvec{p}(\varvec{\omega })\) :

Vector-valued function to be designed in the nonlinear observer

\(\varvec{u}_c\) :

Asymptotic tracking control

\(\varvec{u}\) :

Composite control

\(\{\varvec{B}_c\}\) :

Vector expressed in the body frame of the chief spacecraft

\(\{\varvec{B}_d\}\) :

Vector expressed in the body frame of the deputy spacecraft

c :

Notation for the body frame of the chief spacecraft

d :

Notation for the body frame of the deputy spacecraft

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Authors and Affiliations

  1. Department of Earth and Space Science and Engineering, Lassonde School of Engineering, York University, Toronto, ON, M3J 1P3, Canada

    Daero Lee

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Lee, D. Nonlinear disturbance observer-based robust control of attitude tracking of rigid spacecraft. Nonlinear Dyn 88, 1317–1328 (2017). https://doi.org/10.1007/s11071-016-3312-1

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  • DOI: https://doi.org/10.1007/s11071-016-3312-1

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