Abstract
Computation of the stability limits 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 some input parameters, especially to time delays. An algorithm has been developed to determine the robust stability limits of delayed dynamical systems, which is not sensitive to the fluctuations of selected parameters in the dynamic system. The algorithm is combined with the efficient Multi-Dimensional Bisection Method. The single-degree-of-freedom delayed oscillator is investigated first and the resultant robust stability limits are compared to the derived analytical results. For multi-degree-of-freedom systems, the system of equations of the robust stability limits are modified with the aim to reduce the computational complexity. The method is tested for the 2-cutter turning system with process damping.
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