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 τ m a x and a quantitative torque-margin criterion for the jump-up maneuver. For a 130 mm cube driven by a Nidec 24H BLDC motor ( τ m a x = 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 τ m a x 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.

Accurate dynamic modeling is the foundation of every model-based control design for reaction-wheel stabilized systems, yet most published studies reproduce analytical derivations from scratch without reporting the practical decisions and configuration errors that arise when the model is implemented in Simscape Multibody. This paper presents a reproducible methodology for building a high-fidelity model of a Cubli-type self-balancing cube, proceeding from a SolidWorks 2024 CAD assembly to a linearized third-order state-space representation ready for controller synthesis. Three implementation pitfalls that are rarely discussed in the literature are identified: the placement of the CAD origin, which determines whether the imported model behaves as a stable compound pendulum or as the intended inverted pendulum; the default angular units in the PS-Simulink Converter, which silently degrade any control law tuned for radians; and the kinematic realization of the edge contact. The resulting linearized model is validated through eigenvalue analysis, a controllability rank test, and a short LQR stabilization benchmark. The methodology is directly transferable to reaction-wheel-stabilized satellites and other underactuated rigid-body platforms that share the same modeling workflow.