Impact of Modeling Simplifications on the Dynamics and Control of the Furuta Pendulum
DOI:
https://doi.org/10.59796/jcst.V16N3.2026.197Keywords:
furuta pendulum, rotary inverted pendulum, bond graph, multibond graph, energy shaping, linear-quadratic regulator (LQR)Abstract
This study analyzes the impact of modeling simplifications on the dynamics and control performance of the Furuta pendulum. A complete multibond graph model is developed, incorporating full system dynamics, and providing an energetically consistent and modular framework. The model is validated against a Simulink-Simscape reference, achieving a maximum normalized root mean squared error (NRMSE) of 0.2035 × 10–3. The commonly used simplified model, which neglects secondary inertias, is compared with full-dynamics models under open- and closed-loop conditions. Open-loop results show appreciable discrepancies, with NRMSE values increasing notably for both θ1 and θ2 as the inertias are progressively increased. A nonlinear control scheme based on energy shaping, collocated partial feedback linearization, and linear quadratic regulation (LQR) is designed using the simplified model. In closed loop, the controller achieves swing-up and stabilization in all cases within 10 seconds. For nominal and moderately increased inertias, performance degradation is minimal, with settling times around 7.4 s and control effort between 0.453 and 0.475 N2m2s. However, for large inertias, the settling time increases to 8.91 s, control effort rises to 0.655 N2m2s, and an additional oscillation is required. These results show that simplified models are suitable for control design under typical conditions, while full-dynamics models are essential for validation and robustness assessment.
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