Seminar : Robust stability limit of delayed dynamical systems
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  • Seminar : Robust stability limit of delayed dynamical systems

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Dániel  Bachrathy

Assistant Professor

Budapest University of Technology and Economics

Department of Applied Mechanics


Multi Dimensional Bisection Method (MDBM)

Several engineering applications need a robust method to find all the roots of a set of nonlinear equations automatically. The proposed method guarantees monotonous convergence, and it can determine whole submanifolds of the roots if the number of unknowns is larger than the number of

equations. The critical steps of the Multi-Dimensional Bisection Method are described and possible solutions are proposed. An efficient computational scheme is introduced. The efficiency of the method is characterized by the box-counting fractal dimension of the evaluated points.

Robust stability limit of delayed dynamical systems

Computation of the stability limit of systems with time delay is essential in many research and industrial applications. Most of the computational methods consider the exact model of the system, and do not take into account the uncertainties. However, the stability charts are highly sensitive to the change of input parameters, such as eigenfrequency and time-delay. In case turning processes at low spindle speeds, the computation of the lower envelope of the dense stability lobe structure is expedient.

A method has been developed to determine the robust stability limits of delayed dynamical systems, which is insensitive to fluctuation of parameters of the dynamic system.


Received PhD degree in 2013 and assistant professor since 2014.Jan. at the Department of Applied Mechanics of the Budapest University of Technology and Economics.

Main research fields are:

- development of stability computation methods of time-delayed mechanical systems

- determining the chatter vibrations in cutting processes (turning and milling)

- analyzing the surface properties of the machined workpiece (milling parts with thin walls)