Depth Control of Variable Buoyancy Systems: A Low Energy Approach Using a VSC with a Variable-Amplitude Law

Underwater exploration relies heavily on autonomous underwater vehicles and sensor platforms for sustained monitoring of marine environments, yet their operational duration is limited by energy constraints. To enhance energy efficiency, various control strategies have been proposed, including robust, optimal, and disturbance-aware approaches. Recent work introduced a variable structure controller (VSC) with a constant-amplitude control action for depth control of a platform equipped with a variable buoyancy module, achieving an average 22% reduction in energy use in comparison with conventional PID-based controllers. In a separate paper, the conditions for its closed-loop stability were proven. This study extends these works by proposing a controller with a variable-amplitude control action designed to minimize energy consumption. A formal proof of stability is provided to guarantee safe operation even under conservative assumptions. The controller is applied to a previously developed depth-regulated sensor platform using a validated physical model. Additionally, this study analyzes how the controller parameters and mission requirements affect stability regions, offering practical guidelines for parameter tuning. A method to estimate oscillation amplitude during hovering tasks is also introduced. Simulation trials validate the proposed approach, showing energy savings of up to 16% when compared to the controller using a constant-amplitude control action.