This chapter introduces a time-domain model reductionModel reduction approach designed to simplify high-order dynamic systems while preserving their essential behavior for control applications. When system complexity poses challenges for controller design or real-time implementation, model reductionModel reduction becomes a practical and powerful strategy. Unlike conventional modal analysisModal analysis methods, the technique presented here builds on the aggregation methodAggregation method pioneered by Malinvaud and extended by Aoki, enhanced with system identification and modal analysisModal analysis concepts. The method operates within the state-space framework, using a weighting matrixWeighting matrix to transform original high-order modelsHigh-order model into reduced representations. The reduced models are identified using recursive least-squares (RLS)Recursive Least-Squares (RLS) estimation, ensuring optimal time-domain accuracy while minimizing loss of dynamic fidelity. The selection of dominant modesDominant mode—based on eigenvalue analysis—plays a critical role in constructing meaningful and physically relevant reduced systems. An illustrative example involving a 26th-order rotor-bearing system demonstrates the effectiveness of the method. Reduced models of orders 14, 8, and 6 retain key dynamic features and closely match both the time-domain and frequency-domain behavior of the original system. This technique offers a practical, iterative, and flexible path for engineers to develop computationally efficient, control-ready models, bridging theory and industrial application for large-scaleMultibody Mass–Stiffness–Damping system multibody mass–stiffness–damping systemsMass–stiffness–damping system (MKC systemsMKC system).

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Model Reduction

  • Hai-An Zhu

摘要

This chapter introduces a time-domain model reductionModel reduction approach designed to simplify high-order dynamic systems while preserving their essential behavior for control applications. When system complexity poses challenges for controller design or real-time implementation, model reductionModel reduction becomes a practical and powerful strategy. Unlike conventional modal analysisModal analysis methods, the technique presented here builds on the aggregation methodAggregation method pioneered by Malinvaud and extended by Aoki, enhanced with system identification and modal analysisModal analysis concepts. The method operates within the state-space framework, using a weighting matrixWeighting matrix to transform original high-order modelsHigh-order model into reduced representations. The reduced models are identified using recursive least-squares (RLS)Recursive Least-Squares (RLS) estimation, ensuring optimal time-domain accuracy while minimizing loss of dynamic fidelity. The selection of dominant modesDominant mode—based on eigenvalue analysis—plays a critical role in constructing meaningful and physically relevant reduced systems. An illustrative example involving a 26th-order rotor-bearing system demonstrates the effectiveness of the method. Reduced models of orders 14, 8, and 6 retain key dynamic features and closely match both the time-domain and frequency-domain behavior of the original system. This technique offers a practical, iterative, and flexible path for engineers to develop computationally efficient, control-ready models, bridging theory and industrial application for large-scaleMultibody Mass–Stiffness–Damping system multibody mass–stiffness–damping systemsMass–stiffness–damping system (MKC systemsMKC system).