### Abstract

Two fractional proportional-integral-derivative controllers are proposed for rigid spacecraft rotational dynamics. In the first strategy, the controller is developed on the tangent bundle of SO(3), which is the Lie group of rigid-body rotational motion, using states consisting of a rotation matrix and an angular velocity vector in the fractional-order derivative and integral feedback terms. In the second strategy, the exponential coordinates are used to design the controller. The fractional derivative and integral feedback terms have adjustable orders that can be used to tune the closed-loop response. The performances of the controllers are studied numerically for different values of the derivative and integral fractional orders in terms of control effort, steady-state response characteristics, and robustness to unmodeled disturbances; and the results are compared with those of an integer-order controller. It is shown that the inclusion of fractional orders in the controllers allows for a desired shape and spectrum of the controlled response to be obtained by tuning the fractional derivative and integral orders. For instance, the settling time and control effort may be simultaneously reduced, in contrast to the case of integer feedback control in which a tradeoff exists between these competing design specifications. The proposed fractional feedback attitude control strategies thus allow for a greater degree of flexibility over their integer-order analogs.

Original language | English (US) |
---|---|

Pages (from-to) | 2185-2198 |

Number of pages | 14 |

Journal | Journal of Guidance, Control, and Dynamics |

Volume | 41 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 2018 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Aerospace Engineering
- Space and Planetary Science
- Electrical and Electronic Engineering
- Applied Mathematics

### Cite this

*Journal of Guidance, Control, and Dynamics*,

*41*(10), 2185-2198. https://doi.org/10.2514/1.G002956

**Spacecraft attitude fractional feedback control using rotation matrices and exponential coordinates.** / Nazari, Morad; Butcher, Eric A.; Sanyal, Amit.

Research output: Contribution to journal › Article

*Journal of Guidance, Control, and Dynamics*, vol. 41, no. 10, pp. 2185-2198. https://doi.org/10.2514/1.G002956

}

TY - JOUR

T1 - Spacecraft attitude fractional feedback control using rotation matrices and exponential coordinates

AU - Nazari, Morad

AU - Butcher, Eric A.

AU - Sanyal, Amit

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Two fractional proportional-integral-derivative controllers are proposed for rigid spacecraft rotational dynamics. In the first strategy, the controller is developed on the tangent bundle of SO(3), which is the Lie group of rigid-body rotational motion, using states consisting of a rotation matrix and an angular velocity vector in the fractional-order derivative and integral feedback terms. In the second strategy, the exponential coordinates are used to design the controller. The fractional derivative and integral feedback terms have adjustable orders that can be used to tune the closed-loop response. The performances of the controllers are studied numerically for different values of the derivative and integral fractional orders in terms of control effort, steady-state response characteristics, and robustness to unmodeled disturbances; and the results are compared with those of an integer-order controller. It is shown that the inclusion of fractional orders in the controllers allows for a desired shape and spectrum of the controlled response to be obtained by tuning the fractional derivative and integral orders. For instance, the settling time and control effort may be simultaneously reduced, in contrast to the case of integer feedback control in which a tradeoff exists between these competing design specifications. The proposed fractional feedback attitude control strategies thus allow for a greater degree of flexibility over their integer-order analogs.

AB - Two fractional proportional-integral-derivative controllers are proposed for rigid spacecraft rotational dynamics. In the first strategy, the controller is developed on the tangent bundle of SO(3), which is the Lie group of rigid-body rotational motion, using states consisting of a rotation matrix and an angular velocity vector in the fractional-order derivative and integral feedback terms. In the second strategy, the exponential coordinates are used to design the controller. The fractional derivative and integral feedback terms have adjustable orders that can be used to tune the closed-loop response. The performances of the controllers are studied numerically for different values of the derivative and integral fractional orders in terms of control effort, steady-state response characteristics, and robustness to unmodeled disturbances; and the results are compared with those of an integer-order controller. It is shown that the inclusion of fractional orders in the controllers allows for a desired shape and spectrum of the controlled response to be obtained by tuning the fractional derivative and integral orders. For instance, the settling time and control effort may be simultaneously reduced, in contrast to the case of integer feedback control in which a tradeoff exists between these competing design specifications. The proposed fractional feedback attitude control strategies thus allow for a greater degree of flexibility over their integer-order analogs.

UR - http://www.scopus.com/inward/record.url?scp=85053674663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053674663&partnerID=8YFLogxK

U2 - 10.2514/1.G002956

DO - 10.2514/1.G002956

M3 - Article

AN - SCOPUS:85053674663

VL - 41

SP - 2185

EP - 2198

JO - Journal of Guidance, Control, and Dynamics

JF - Journal of Guidance, Control, and Dynamics

SN - 0731-5090

IS - 10

ER -