Time-delay systems with a controlled time-varying delay Stability analysis and applications

Wim Michiels (1) , V. van Assche (2) , Silviu-Iulian Niculescu (3)

1 Department of Computer Science - K.U.Leuven
2 UPJV - Université de Picardie Jules Verne
3 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

We study the stability of a linear system with a point-wise, time-varying delay. We assume that the delay varies around a nominal value in a deterministic way and investigate the influence of this variation on stability. More precisely we are interested in characterizing situations where the time-varying delay system is stable, whereas the system with constant delay is unstable. Our approach consists of relating the stability properties of a system with a fast varying point-wise delay with these of a time-invariant system with a distributed delay. Then we can use frequency domain methods to analyze the problem and to derive stability criteria. The results are first illustrated with two theoretical example. Then we study a model of a variable speed rotating cutting tool. Based on the developed theory, we thereby provide both a theoretical explanation and a quantitative analysis tool for the beneficial effect of a variation of the machine speed on enhancing stability properties, which was reported in the literature.

Mots clés: Cutting tools; Eigenvalues and eigenfunctions; Frequency domain analysis; Frequency modulation; Linear systems; Lyapunov methods; Mathematical models; Mechanical engineering; Natural frequencies; Quenching; Set theory; System stability; Theorem proving; Quantitative analysis tools; Rotating cutting tool; Time invariant systems; Time-delay systems; Time varying systems

Domaines: Automatique / Robotique

Wim Michiels, V. van Assche, Silviu-Iulian Niculescu. Time-delay systems with a controlled time-varying delay Stability analysis and applications. 2004 43rd IEEE Conference on Decision and Control (CDC), Dec 2004, Nassau, Bahamas. pp.4521-4526. ⟨hal-02294294⟩