Linear fractional representations (LFRs) 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 and error-prone process, if carried out manually. Tools already exist to transform symbolic transfer functions and symbolic state-space representations into reduced-order LFRs, but these descriptions are still quite far from a natural, physical-based, object-oriented description of physical and technological systems and are moreover hard to integrate with model identification tools. In this chapter a new approach to LFR modelling and identification starting from equation-based, object-oriented descriptions of the plant dynamics (formulated using the Modelica language) and input-output data is presented. This approach allows to reduce the gap between user-friendly model representations, based on object diagrams with physical connections, block diagrams with signal connections, and generic differential-algebraic models, and the use of advanced LFR-based identification and control techniques.

Chapter Contents:

• Abstract
• 4.1 Introduction
• 4.2 Applicable models and LFRs
• 4.2.1 Applicable plant models
• 4.2.2 Linear fractional representations
• 4.3 Transformation of non-linear DAE models into LFR
• 4.3.1 Definitions and assumptions
• 4.3.2 Re-ordering of the system equations
• 4.3.3 Elimination of known parameters
• 4.3.4 Solving the system equations
• 4.3.5 Formulation of the system equations as a cascaded connection of LFRs
• 4.3.6 Construction of the LFR of the DAE
• 4.3.7 Implementation of the algorithm
• 4.3.8 Simulation of the LFR
• 4.4 Application example: identification of LFR models
• 4.5 Conclusions
• References

Inspec keywords: object-oriented programming; differential algebraic equations; control engineering computing; parameter estimation; formal languages; nonlinear control systems; formal specification

Other keywords: LFR; Modelica language; model description formalism; linear fractional representation; object-oriented description; nonlinear plant dynamics; integrated modelling; object diagram; parameter estimation; differential-algebraic model

Subjects: Formal languages and computational linguistics; Object-oriented programming; Control engineering computing; Formal methods; Algebra; Nonlinear control systems; Simulation, modelling and identification