Model reduction for LPV systems based on approximate modal decomposition

TL;DR

This paper introduces a new LPV model reduction method that uses modal decomposition and clustering to simplify large-scale systems without relying on traditional interpolation techniques.

Contribution

It proposes a novel LPV model reduction approach based on modal decomposition and hierarchical clustering, avoiding complex interpolation procedures.

Findings

Effective reduction of large-scale LPV systems demonstrated

Avoids the need for model interpolation, simplifying the process

Numerical case studies validate the approach's applicability

Abstract

The paper presents a novel model order reduction technique for large-scale linear parameter varying (LPV) systems. The approach is based on decoupling the original dynamics into smaller dimensional LPV subsystems that can be independently reduced by parameter varying reduction methods. The decomposition starts with the construction of a modal transformation that separates the modal subsystems. Hierarchical clustering is applied then to collect the dynamically similar modal subsystems into larger groups. The subsystems formed from the groups are then independently reduced. This approach substantially differs from most of the previously proposed LPV model reduction techniques, since it performs manipulations on the LPV model and not on a set of linear time-invariant (LTI) models defined at fixed scheduling parameter values. Therefore the model interpolation, which is the most challenging part of most reduction techniques, is avoided. The applicability of the developed algorithm is thoroughly investigated and demonstrated by numerical case studies.