Model Order Reduction Based on Agglomerative Hierarchical Clustering.

Area of Science:

• Engineering
• Control Systems
• Computational Mathematics

Background:

• High-order dynamical systems pose challenges in analysis and control.
• Existing model order reduction techniques often lack efficiency or robustness.
• Accurate reduced-order models are crucial for simulation and real-time applications.

Purpose of the Study:

• To introduce and evaluate an improved clustering-based method for dynamical system model order reduction.
• To enhance the accuracy and robustness of reduced-order models.
• To compare the proposed method against existing techniques using various system orders and types.

Main Methods:

• Development of Agglomerative Hierarchical Clustering based on Performance Evaluation (HC-PE).
• Clustering system poles in a hierarchical dendrogram to determine reduced-order denominator.
• Utilizing Mean-Squared Error (MSE) for pole placement refinement.
• Calculating reduced model numerator coefficients via Padé Approximation (PA) or Genetic Algorithm (GA).

Main Results:

• HC-PE demonstrated superior performance with minimum MSEs across single-input single-output (SISO) and multi-input multi-output (MIMO) systems.
• The method successfully reduced models up to 48th order.
• Robustness was confirmed through disturbance and parameter variation tests on a triple-link inverted pendulum model.

Conclusions:

• HC-PE offers an effective and robust approach for model order reduction.
• Both PA and GA are viable options for numerator calculation, with PA showing a slight performance edge.
• The proposed HC-PE method provides an attractive alternative to current model order reduction techniques.