Gain-Scheduled H∞ Attitude Control of a 6U CubeSat Under Inertia Uncertainty and Actuator Constraints
- 1Department of Mechanical Engineering, Faculty of Engineering, Hakkari University, Hakkari 30000, Turkey
Abstract
Accurate attitude control of small spacecraft becomes challenging when inertia variations, imperfect state estimates, environmental disturbances, and limited actuator authority simultaneously affect the closed-loop response. This study presents an estimation-aware robust attitude-control framework for a three-axis rigid 6U CubeSat equipped with three orthogonally mounted reaction wheels. The nonlinear simulation model incorporates coupled spacecraft–wheel dynamics, payload-dependent inertia variations, sensor noise, gyroscope bias, environmental disturbance torques, and reaction-wheel torque, speed, and momentum constraints. A multiplicative extended Kalman filter (MEKF) estimates the quaternion attitude and gyroscope bias from gyroscope, magnetometer, and Sun-sensor measurements. Using the estimated attitude and angular rate, a gain-scheduled (H∞) estimated-state-feedback controller is synthesized over a four-vertex inertia polytope. Discrete-time linear matrix inequality conditions are imposed on all 16 plant–controller vertex combinations to establish quadratic stability and a prescribed disturbance-attenuation bound for the embedded polytopic error model. An MEKF-based linear-quadratic regulator and a fixed-gain (H∞) controller are employed as benchmarks. Performance is assessed through four deterministic scenarios and 200 paired Monte Carlo simulations. Under combined inertia uncertainty, sensor degradation, external disturbances, and actuator constraints, the proposed controller reduces the root-mean-square attitude error to 1.350°, compared with 2.001° for fixed-gain (H∞) and 2.988° for MEKF–LQR. It also decreases the tracking-error settling time to 31.68 s and limits maximum wheel-momentum utilization to 57.9%. The proposed method achieves a 99.0% Monte Carlo success rate, compared with 94.0% and 82.5% for the respective benchmarks. These results indicate that physically informed gain scheduling improves the preservation of tracking performance and actuator authority across payload-dependent operating conditions.
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BibTeX
@article{durmusoglu2026gainscheduled,
title = {{Gain-Scheduled H∞ Attitude Control of a 6U CubeSat Under Inertia Uncertainty and Actuator Constraints}},
author = {Aslı Durmuşoğlu},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14193639},
url = {https://www.mdpi.com/2227-7390/14/19/3639},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Gain-Scheduled H∞ Attitude Control of a 6U CubeSat Under Inertia Uncertainty and Actuator Constraints
AU - Aslı Durmuşoğlu
PY - 2026
DA - 2026/10/08
JO - Mathematics
DO - 10.3390/math14193639
UR - https://www.mdpi.com/2227-7390/14/19/3639
AB - Accurate attitude control of small spacecraft becomes challenging when inertia variations, imperfect state estimates, environmental disturbances, and limited actuator authority simultaneously affect the closed-loop response. This study presents an estimation-aware robust attitude-control framework for a three-axis rigid 6U CubeSat equipped with three orthogonally mounted reaction wheels. The nonlinear simulation model incorporates coupled spacecraft–wheel dynamics, payload-dependent inertia variations, sensor noise, gyroscope bias, environmental disturbance torques, and reaction-wheel torque, speed, and momentum constraints. A multiplicative extended Kalman filter (MEKF) estimates the quaternion attitude and gyroscope bias from gyroscope, magnetometer, and Sun-sensor measurements. Using the estimated attitude and angular rate, a gain-scheduled (H∞) estimated-state-feedback controller is synthesized over a four-vertex inertia polytope. Discrete-time linear matrix inequality conditions are imposed on all 16 plant–controller vertex combinations to establish quadratic stability and a prescribed disturbance-attenuation bound for the embedded polytopic error model. An MEKF-based linear-quadratic regulator and a fixed-gain (H∞) controller are employed as benchmarks. Performance is assessed through four deterministic scenarios and 200 paired Monte Carlo simulations. Under combined inertia uncertainty, sensor degradation, external disturbances, and actuator constraints, the proposed controller reduces the root-mean-square attitude error to 1.350°, compared with 2.001° for fixed-gain (H∞) and 2.988° for MEKF–LQR. It also decreases the tracking-error settling time to 31.68 s and limits maximum wheel-momentum utilization to 57.9%. The proposed method achieves a 99.0% Monte Carlo success rate, compared with 94.0% and 82.5% for the respective benchmarks. These results indicate that physically informed gain scheduling improves the preservation of tracking performance and actuator authority across payload-dependent operating conditions.
SN - 2227-7390
ER -