Simulation-Based Analysis of Disturbance-Robust PID Attitude Control for a 3U CubeSat in LEO with an MPC Benchmark

Abstract

This paper presents a simulation-based study of three-axis attitude stabilisation for a 3U CubeSat in a 400 km circular low Earth orbit. A control-oriented attitude dynamics model is derived from Euler's rigid-body rotational equations under smallangle and principal-axis assumptions, yielding analytically decoupled single-axis transfer functions and a six-state continuous-time state-space representation. The dominant environmental disturbance torques- atmospheric drag, solar radiation pressure, and residual magnetic dipole-are quantified using parameters consistent with the NRLMSISE-00 atmospheric model and the IGRF-13 geomagnetic field model, and are shown to be several orders of magnitude below the available reaction-wheel authority. Independent fixed-gain PID controllers are designed for each attitude axis using the Ziegler–Nichols ultimate-gain procedure and implemented in MATLAB/Simulink R2023b, while a constrained per-axis model predictive controller (MPC) is introduced as a benchmark. Simulation results show that the PID controller achieves three-axis nadir pointing with settling times of approximately 80 s, negligible steady-state error under bounded periodic disturbances, and zero sensitivity to a decade-range variation in atmospheric density across the solar cycle. In contrast, the MPC benchmark produces smoother torque profiles, lower peak angular-rate excursions, and superior actuator constraint adherence at the cost of modestly increased settling time on some axes and substantially higher computational complexity. For the considered 3U CubeSat mission scenario, the tuned PID architecture provides the most favourable trade-off between pointing performance, implementation simplicity, and on-board resource requirements.