Robust attitude tracking control for a rigid spacecraft under input delays and actuator errors

ABSTRACT

Attitude control of a rigid spacecraft under input delays, disturbances, parameter uncertainties, actuator errors, and constraints is a challenging problem. In this paper, these problems are considered simultaneously, and a robust control approach to attitude tracking of a rigid spacecraft is exploited. The design methodology is based on three steps: (1) compensating input delays by using the backstepping technique, (2) design of a disturbance observer for the delayed system by using the super-twisting algorithm to estimate unknown internal and external disturbances, then adding a feedforward compensation law based on the estimated signal to the backstepping controller to attenuate the effects of disturbances, (3) employing a robust least-square scheme to map the specified control command on the redundant actuators in the presence of actuator error, including actuator magnitude deviation and misalignment, with regard to actuator amplitude and rate constraints. The effectiveness of the proposed algorithm is shown by various numerical simulations.

KEYWORDS:

• Spacecraft attitude tracking
• super-twisting algorithm
• unknown input delay
• actuator error

Acknowledgments

The authors would like to thank the Associate Editor for giving us the opportunity to improve this paper to its present quality, and the constructive comments made by the anonymous referees.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. See (Johansen & Fossen, 2013) for a survey of recent studies on control allocation methods.

2. In the zero-disturbance case, a relative ideal situation is simulated, i.e. actuator error is neglected and T _td = 0. The results of this scenario are not included because of space reason.

3. At this point, the reasons for introducing conditions (11(11) $$\begin{array}{c}\hfill \varrho >3.5\bar{P}-\frac{1}{2.1\bar{\tau }}\end{array}$$(11) )-(13(13) $$\begin{array}{ccc}\hfill \frac{{\bar{P}}^2}{{\underset{\_}{P}}^{}}& <& \frac{1}{1.5\sqrt{5.01}\bar{\tau }}\hfill \end{array}$$(13) ) become clear. The condition (11(11) $$\begin{array}{c}\hfill \varrho >3.5\bar{P}-\frac{1}{2.1\bar{\tau }}\end{array}$$(11) ) is used in obtaining (A23(A23) $$\begin{array}{cc}\hfill {\dot{v}}_2\le & {\gamma }_3(-\bar{\tau }{\parallel \alpha \parallel }^2-0.4{\bar{\tau }}^2{\gamma }_6^2{\int }_{t-\bar{\tau }}^t{\parallel \alpha \parallel }^2\mathrm{d}\eta \\ & +4.01{\bar{\tau }}^2\frac{{\gamma }_1^2}{\underset{\_}{P}}{\int }_{t-\bar{\tau }}^t{\sigma }_e^{T}P{\sigma }_e\mathrm{d}\eta +802\bar{\tau }{\parallel \mathcal{Q}\parallel }^2).\end{array}$$(A23) ); also, the condition (11(11) $$\begin{array}{c}\hfill \varrho >3.5\bar{P}-\frac{1}{2.1\bar{\tau }}\end{array}$$(11) ) conjugate with (12(12) $$\begin{array}{ccc}\hfill \bar{P}& <& \frac{20}{147\bar{\tau }}\hfill \end{array}$$(12) ) ensures that ϱ is a negative constant; finally, (13(13) $$\begin{array}{ccc}\hfill \frac{{\bar{P}}^2}{{\underset{\_}{P}}^{}}& <& \frac{1}{1.5\sqrt{5.01}\bar{\tau }}\hfill \end{array}$$(13) ) requires that Λ becomes a positive definite matrix or the quadratic form ℵ becomes negative definite.