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article · Applied Mechanics

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

2026Open accessHelwan University

In plain language

High-speed rotating machinery often faces persistent challenges from nonlinear vibrations. A control strategy combining hydrodynamic journal bearings with active magnetic bearings uses a state-dependent parameter proportional-integral-plus (SDP-PIP) controller formulated within a non-minimal state-space framework. The underlying system is modelled with four degrees of freedom, accounting for short-bearing approximations of hydrodynamic forces alongside nonlinear electromagnetic forces. Tested across rotational speeds spanning 130 to 500 radians per second through numerical simulations, the strategy undergoes sensitivity analyses under parameter variations and benchmarking against conventional proportional-integral-derivative (PID) control. The SDP-PIP controller suppresses nonlinear vibrations, effectively stabilising oil-whirl and oil-whip instabilities across the tested operating speeds. Compared to PID control, the approach delivers superior vibration attenuation and preserves stable journal motion with reduced oscillation amplitudes, particularly when operating near unstable regimes.

Key takeaways

  • A state-dependent parameter proportional-integral-plus controller suppresses nonlinear vibrations in hybrid rotor-bearing systems combining journal and active magnetic bearings.
  • Numerical simulations across rotational speeds from 130 to 500 radians per second demonstrate effective stabilisation of oil-whirl and oil-whip instabilities.
  • The controller achieves lower oscillation amplitudes and superior vibration attenuation compared to conventional proportional-integral-derivative control.
  • Stable journal motion is maintained even when operating near unstable regimes and under parameter variations.

Why it matters

Excessive vibrations in high-speed rotating machinery can cause severe mechanical failure through fluid-induced phenomena such as oil-whirl and oil-whip. Demonstrating that magnetic bearings can actively stabilise journal motion near unstable operating thresholds provides an engineering route to safer, smoother-running rotating equipment, reducing the risk of sudden operational disruptions in high-speed industrial machinery.

Commercialisation angle

The method targets high-speed rotating machinery equipped with hybrid hydrodynamic and active magnetic bearings, relevant to turbomachinery manufacturers and industrial equipment designers. As the findings are derived exclusively from four-degree-of-freedom numerical simulations spanning 130 to 500 radians per second, the technology represents early-stage research that requires physical prototyping and experimental testing before commercial deployment.

AI-generated from the published abstract. Always read the original work before citing.

Abstract

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.

Research topics

  • Tribology and Lubrication Engineering
  • Magnetic Bearings and Levitation Dynamics
  • Gear and Bearing Dynamics Analysis

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DOI: 10.3390/applmech7030068

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