Modeling and identification of Linear Parameter-Varying systems

Student thesis: Doctoral Thesis


A lot of research exists on the modeling, identification and control of Linear Time-Invariant (LTI) systems. The “Linear” part pertains to the input-output behavior. If applying a force F causes a displacement x, doubling the force will result in twice the movement 2F→2x. Moreover, a “Time-invariant” system will show the same dynamic behavior, independent of the time of the experiment.
An ever-increasing demand on industrial processes results in plants that do not meet the assumptions of linearity or time-invariance. In this thesis, we study the set of Linear Parameter-Varying (LPV) systems, where the plant can change as a function of an external “scheduling” variable. Examples include varying the length of a violin string while it is played, or the impedance of a resistor that varies with the temperature.
A more industrial application is a tower crane, that needs to move a (big) mass, in three dimensions. The dynamic behavior of this crane depends, among other things, on the length of the cable, which varies when the mass is transported vertically. Specifically, we aim to identify an LPV model that is suitable for control, from experimental data.
By tackling the identification problem in the frequency domain, both discrete- and continuous-time models can be handled in a very similar way. In both cases, throughout the thesis, we will promote the use of periodic signals where possible, because they share a natural affinity with the frequency domain.
The main contributions are consistent identification methods for LPV Input-Output (IO) and State Space (SS) models. The first is very useful for physical insight into the parameter-varying dynamics, while the latter is commonly used in control synthesis.
Date of Award7 Mar 2016
Original languageEnglish
Awarding Institution
  • Electricity
SupervisorRik Pintelon (Promotor), John Lataire (Co-promotor), Jan Swevers (Jury), Roland Tóth (Jury), Marion Gilson-Bagrel (Jury), Patrick Guillaume (Jury), Johan Deconinck (Jury) & Francesco Ferranti (Jury)


  • modeling
  • Identification
  • Parameter-varying systems

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