Automatic generation of LFTs from object-oriented Modelica models

Linear Fractional Transformations (LFT) are a widely used model description formalism in modern control and system identification theory. Deriving such models from physical first principles is a non-trivial and often tedious process, if carried out manually. Tools already exist to transform symbolic transfer functions and symbolic state-space representations into reduced-order LFTs, but these descriptions are still quite far from a natural, physical-based, object oriented description of physical and technological systems. This paper presents a new approach to obtain reduced-order LFT models starting from equation-based, object-oriented descriptions of the plant dynamics, formulated using the Modelica language. This allows to reduce the gap between user-friendly model representations, based on object diagrams with physical connections, block diagrams with signal connection, and generic differential-algebraic models, and the use of advanced LFTbased control techniques. The presented approach can be applied to any process model which is linear in its variables, including models with implicit algebraic equations and higher-index models.