Dynamic Coupling and Active Boundary Control of an ODE-PDE Rigid-Flexible Multibody System
Year: 2026
Type: preprint
Abstract: The deployment of quadrotor UAVs for suspended cargo transport introduces complex dynamic challenges, as the flexible suspension cable acts as a distributed-parameter system exhibiting multi-modal vibrations. Unmitigated, these coupled PDE-ODE dynamics severely degrade flight stability during dynamic trajectories. Traditional control approaches often rely on simplified rigid-pendulum models or require impractical bilateral actuation on both the vehicle and the payload. This paper proposes a novel composite boundary control strategy that achieves simultaneous three-dimensional trajectory tracking and active vibration suppression using exclusively the control action of the aerial platform. The architecture integrates a high-order feedforward trajectory planner, a Proportional-Derivative (PD) tracking loop, and an active Boundary Control (BC) law. A major methodological contribution of this work is the analytical formulation and linearization of the highly coupled non-linear system. By exploiting this validated state-space representation, closed-loop eigenvalues can be computed analytically, enabling the comprehensive evaluation of the multi-dimensional control performance landscape in seconds rather than requiring computationally prohibitive numerical simulations. A dense parametric sweep of the tuning gains ($K_p$, $K_d$, $K_{bc}$) demonstrates that active boundary damping invariably accelerates energy dissipation. The analysis reveals a maximum theoretical performance efficiency improvement of 74.43\% compared to classical passive configurations. Crucially, this global optimum manifests when the baseline system possesses minimal natural damping, demonstrating that the boundary controller effectively rescues the coupled aerial system from persistent oscillatory transients. Ultimately, this work provides a mathematically rigorous and computationally efficient framework for the stabilization of distributed-parameter aerial transportation systems.
Source: Research Square
Institutions: University of Salerno, Universidad Carlos III de Madrid
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165480146