Comparative Study of Simplified Models of the Planar Inverted Pendulum: Dynamics and Control

Alvarez P. · Modelling and Simulation in Engineering (2026) · DOI: 10.1155/mse/9353684

Resumen

The inverted pendulum is one of the most studied systems in automatic control, serving as a testbed for new control strategies. One of its variants is the planar inverted pendulum, which consists of a pendulum articulated to a mobile base that moves in a horizontal plane. Although this system has been widely studied, the models employed are simplified and a formulation that captures its full dynamics is still lacking. Moreover, the impact of these simplifications has not yet been assessed. In this research, using the bond graph methodology, a complete and energetically coherent dynamic model of the planar inverted pendulum is developed. No previous work provides a dynamic model with this level of detail. This model was validated by comparing it with a Simulink reference model. Eight simplified models were built and compared using open-loop and closed-loop simulations with a hybrid nonlinear control strategy. The results show that most simplified models exhibit closed-loop responses that closely match those of the full dynamics model, whereas under open-loop conditions significant discrepancies arise in some cases. The study also demonstrates that controllers designed using simplified models can achieve performance comparable to that obtained with a controller designed from the full dynamics model. These findings provide strong support for the widespread use of simplified models for controller design, analysis, and simulation of the planar inverted pendulum and similar systems. Copyright

Instituciones: Universidad Nacional de Trujillo