Measurement and modelling of weakly nonlinear, slowly time-varying dynamical systems

  • Pintelon, Rik, (Administrative Promotor)

Project Details


Classical system identification and control design techniques assume that the system is linear and time invariant (LTI). Although these methods have been applied for many years with great success to a lot of practical problems (see [1, 2]), most real life systems are only approximately linear and time invariant. Think for example of structures subject to increasing damage, pit corrosion of metals, biological systems, or processes with a varying set point (e.g. flight flutter analysis) or varying system parameters (e.g. telescopic robot arm or semi-active spring-damper system). The following fundamental questions immediately arise: "What is the influence of nonlinear distortions and time-variations on the classical LTI system identification and the controller design methods?", "What is the lower bound on the accuracy of the classical LTI framework applied to nonlinear time-varying systems?", "Is it possible to make a first order correction of the time-variation giving a quasi instantaneous frequency response function (FRF)?", and "Is there a need for new (nonlinear and time-varying) system identification and controller design methods?". To answer these important questions we should be able to quantify in some way the deviation of the true system w.r.t. the ideal LTI behavior. This information should be available before estimating the parametric plant model or designing the controller. Note that classical recursive identification methods [3] offer no solution here. Moreover these methods do not allow to detect the level nor the presence of the nonlinear distortions. To start with, weakly nonlinear (the linear behaviour is dominant), slowly time-varying systems (the time-variation is an order of magnitude slower than the dominating time constant of the system) are studied.

Using well chosen periodic excitation signals, the procedure developed in [4] allows to quantify simultaneously the level of the disturbing noise (measurement and process noise) and the level of the nonlinear distortions on FRF measurements for time-invariant nonlinear systems. In this project we will first of all generalise the approach to nonlinear, slowly time-varying systems. The goal is to quantify beside the noise and nonlinear distortions also the time-variation on the FRF measurements. Once this information available, we can in a second step either make a first order correction of the time variation giving a quasi instantaneous LTI description, or identify a parametric model of the time variation. In the latter case the choice of the parametric model is strongly simplified by the non-parametric representation of the time-variation on the FRF. Exactly the same options exist for the nonlinear distortions: either we try to minimise their influence on the measurements, or we model them and use the non-parametric representation to choose the parametric model. Finally these models are used for physical interpretation (e.g. flight flutter analysis, modelling of the middle ear), diagnosis (e.g. damage detection), simulation, and control. To verify the general applicability of the proposed measurement procedure we will test it on a wide range of practical problems.

The different steps to be elaborated in this project are (the contributing partners are mentioned between parentheses)
1. Development of a general measurement procedure for weakly nonlinear, slowly time-varying dynamical systems, giving an FRF + levels disturbing noise, nonlinear distortions, and time-variation. The procedure will be validated on simulations and real life experiments on a semi-active spring-damper system whose parameters can be varied in a controlled way. The experimental set up is located at the mechanical department of the KUL (partners: VUB-ELEC, VUB-WERK, KUL-PMA, UA-BIMEF).
2. Application to the following problems
2.a. Flight flutter analysis with a continuous flight envelope (VUB-ELEC, VUB-WERK, KUL-PMA),
2.b. Damage detection in mechanical structures (VUB-WERK, VUB-ELEC),
2.c. Modelling of the middle ear (UA-BIMEF, VUB-ELEC, VUB-WERK),
2.d. Modelling and control of mechanical systems with time-varying parameters (VUB-ELEC, KUL-PMA),
where each time all the fundamental questions raised in the introduction are tackled.
It is clear that there will be a strong interaction between on the one hand the applications and on the other hand the developement of the general measurement procedure. Note also that each application means a break through in its field.
Effective start/end date1/10/0730/09/11

Flemish discipline codes

  • Mechanical and manufacturing engineering
  • Electrical and electronic engineering


  • weakly nonlinaer
  • modelling
  • measurement