This work implements three model order reduction techniques – Static (or Guyan), System Equivalent Reduction Expansion Process (SEREP), and modified SEREP – to reduce the number of degrees of freedom (DOFs) of a rotor system modelled using finite elements method (FEM). The study evaluates the performance of Active Magnetic Bearings (AMBs) \( {\mathcal{H}}_{\infty } \) controllers designed with these reduced models by comparing the system’s dynamic behaviour with that of the full-order model. For low-speed applications, single-input-single-output (SISO) controllers such as PID are commonly used. However, in high-speed rotating machinery, multi-input-multi-output (MIMO) strategies like \( {\mathcal{H}}_{\infty } \) and μ-synthesis are preferred due to their robustness and precision. The \( {\mathcal{H}}_{\infty } \) method requires controllers of the same order as the mechanical model, which becomes computationally infeasible for systems with many degrees of freedom. To address this, model reduction techniques are employed on mechanical system in order to allow the design of reduced-order controllers of AMB that are more practical for implementation. Ensuring the reduced model accurately captures the system dynamics is essential for maintaining control performance. The study uses unbalance responses and mode shapes obtained by reduced and complete models to assess the effectiveness of the \( {\mathcal{H}}_{\infty } \) -based AMB control in minimizing vibrations across the entire operating frequency range.

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Evaluation of Model Reduction for Rotor-Active Magnetic Bearing System Control

  • Sidney Araujo Mendonça,
  • Diogo Stuani Alves,
  • Katia Lucchesi Cavalca Dedini

摘要

This work implements three model order reduction techniques – Static (or Guyan), System Equivalent Reduction Expansion Process (SEREP), and modified SEREP – to reduce the number of degrees of freedom (DOFs) of a rotor system modelled using finite elements method (FEM). The study evaluates the performance of Active Magnetic Bearings (AMBs) \( {\mathcal{H}}_{\infty } \) controllers designed with these reduced models by comparing the system’s dynamic behaviour with that of the full-order model. For low-speed applications, single-input-single-output (SISO) controllers such as PID are commonly used. However, in high-speed rotating machinery, multi-input-multi-output (MIMO) strategies like \( {\mathcal{H}}_{\infty } \) and μ-synthesis are preferred due to their robustness and precision. The \( {\mathcal{H}}_{\infty } \) method requires controllers of the same order as the mechanical model, which becomes computationally infeasible for systems with many degrees of freedom. To address this, model reduction techniques are employed on mechanical system in order to allow the design of reduced-order controllers of AMB that are more practical for implementation. Ensuring the reduced model accurately captures the system dynamics is essential for maintaining control performance. The study uses unbalance responses and mode shapes obtained by reduced and complete models to assess the effectiveness of the \( {\mathcal{H}}_{\infty } \) -based AMB control in minimizing vibrations across the entire operating frequency range.