Stabilizing Saturation-Based Vibration Control of Self-Excited Structures via Feedback First-Order Filter Integration: Analytical and Numerical Investigations with Time-Delay Effects

Purpose: This study proposes a novel hybrid control strategy, termed the Integral Resonant Nonlinear Saturation Controller (IRNSC), to actively suppress self-excited vibrations in nonlinear structures. The IRNSC is designed to overcome the instability limitations of the classical Nonlinear Saturation Controller (NSC) and the monotonic increase in vibration amplitude observed with the Integral Resonant Controller (IRC) when excitation amplitude increases. Method: The IRNSC combines the saturation effect of a second-order nonlinear filter with the damping capability of a first-order IRC. The controller is applied to a self-excited system describing the transverse vibration of a cantilever beam with a tip mass, subject to harmonic base excitation and constant airflow. The system is modeled as a two-degree-of-freedom structure coupled with a first-order differential equation that includes the closed-loop time delay. The method of multiple scales is employed to derive the amplitude-phase modulation equations, and the system dynamics are analyzed through different response curves, stability charts, time histories, and Poincaré maps. Results: The main finding reveals that two critical limitations, namely, the emergence of a narrow instability region near the structure’s natural frequency when using the NSC, and the monotonically increasing oscillation amplitude with base excitation under the IRC, are both effectively addressed by the IRNSC. By leveraging the NSC’s nonlinear saturation and the IRC’s damping behavior, the IRNSC operates as an intelligent hybrid controller, actively mitigating resonant vibrations within a tunable frequency band and transitioning seamlessly to passive damping outside this range. Conclusion: The IRNSC demonstrates self-adaptive hybrid behavior, ensuring stable, amplitude-limited vibrations across a wide excitation range. Analytical predictions and numerical simulations show strong agreement, confirming the robustness of the proposed approach and highlighting its practical potential for controlling self-excited vibrations in real-world applications.