Nonlinear Vibration Control of a Hybrid Rotor–Bearing System Using a State-Dependent Parameter PIP Controller

This paper presents a novel control strategy for hybrid rotor–bearing systems integrating hydrodynamic journal bearings with active magnetic bearings (AMBs) to address the persistent challenge of nonlinear vibrations in high-speed rotating machinery. The study introduces the application of a state-dependent parameter proportional-integral-plus (SDP-PIP) controller designed within a non-minimal state-space framework, offering a significant advancement over conventional control approaches. A four-degree-of-freedom model incorporating short-bearing approximation for hydrodynamic forces and nonlinear electromagnetic force characterization is developed to capture the complex system dynamics. The controller performance is evaluated through numerical simulations over a range of rotational speeds from 130 to 500 rad/s, together with sensitivity analyses under parameter variations and comparisons with a conventional PID controller. The results show that the proposed controller effectively suppresses nonlinear vibrations and stabilizes oil-whirl and oil-whip instabilities over the investigated operating conditions. In comparison with the PID controller, the SDP-PIP controller provides improved vibration attenuation and maintains stable journal motion with lower oscillation amplitudes, particularly near unstable operating regimes. These findings demonstrate the potential of the SDP-PIP control strategy for enhancing the dynamic performance and operational stability of hybrid journal bearing systems.