Experimental study of nonlinear PPF-based active vibration controllers for a carbon fiber beam subject to mass changes Experimental study of nonlinear PPF-based active vibration controllers

• Published in: Nonlinear dynamics Vol. 113; no. 18; pp. 24159 - 24178
• Main Authors: Hameury, Celia, Amabili, Marco
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.09.2025
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Classical Mechanics; Control; Dynamical Systems; Physics; Physics and Astronomy; Statistical Physics and Dynamical Systems; Vibration; Active vibration control; Nonlinear vibrations; PPF; Softening nonlinear system; Nonlinear active vibration control
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-025-11607-0

Many algorithms have been developed for controlling nonlinear vibrations in carbon fiber structures, with varying levels of success. Among these are those derived from positive position feedback (PPF), introducing a nonlinear term designed to counter the nonlinear vibrations, which have performed well. But how would such novel PPF-based algorithms respond to system uncertainty, such as mass changes? This work aims to study the robustness of PPF and PPF-based algorithms in the control of nonlinear vibrations of structures subject to mass changes. For this research, a carbon fiber beam clamped at both ends was considered, with two piezoelectric actuator-sensor pairs used for control. A multi-input multi-output (MIMO) PPF-based nonlinear controller with two PPF filters was used to control the structure, with the PPF filters tuned to the first and second mode of the beam respectively. The mass of the beam was then augmented by lumped masses of 27 g and 57 g, added to the center of the structure. The controller was now used to attenuate the vibrations of the set-up under these new conditions, with no parameter changes made to the control algorithm. The MIMO nonlinear PPF was compared to both SISO and linear counterparts. Both modes 1 and 2 were considered. The MIMO nonlinear PPF was found to be the most effective in reducing the vibrations of the structure, even when its mass was increased. However, the SISO linear PPF also performed remarkably well, and demonstrated unexpected robustness to the mass change, indicating the capabilities of this algorithm under structural changes. This research further demonstrated the overall robustness of PPF and PPF-based algorithms to natural frequency change, and therefore their use in tackling vibration problems on structures even when uncertainty may be present.