Comparative analysis of LQR and PID control for a reaction-wheel stabilized cube under actuator saturation constraints

Reaction-wheel-stabilized Cubli-type platforms are widely used as ground testbeds for small-spacecraft attitude control, but the coupling between actuator saturation and the achievable domain of attraction has not been mapped in a unified simulation framework. This paper closes that gap using a CAD-driven Simscape Multibody pipeline (SolidWorks → Simscape → Model Linearizer → LQR/PID synthesis → saturated nonlinear validation) and reports three contributions: a head-to-head comparison of LQR and PID on an identical plant with matched saturation limits, a parametric mapping of the LQR domain of attraction against maximum motor torque <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>a</mml:mi> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> </mml:math> and a quantitative torque-margin criterion for the jump-up maneuver. For a 130 mm cube driven by a Nidec 24H BLDC motor ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>a</mml:mi> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> </mml:math> = 0.04 N·m), LQR settles in 0.5 s – six times faster than a Simulink-tuned PID (3 s) – at 30 % lower peak flywheel velocity (85 vs. 120 rad/s). Sweeping <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>τ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>m</mml:mi> <mml:mi>a</mml:mi> <mml:mi>x</mml:mi> </mml:mrow> </mml:msub> </mml:math> from 0.04 to 0.50 N·m expands the domain of attraction from 3° to 45° with diminishing returns above 0.20 N·m, and a 12.5× torque margin over the Nidec 24H is needed for jump-up. The framework yields directly applicable actuator-sizing rules for reaction-wheel ground testbeds and CubeSat-class attitude control.