Time delays often occur in engineering systems related to mechanical contact tasks and/or control tasks with relevant information processing and transmission time. Parametric excitation is also a typical vibration phenomenon in many well-known engineering applications. There are not many models, however, that combine delay and time-periodic coefficients, in spite of the fact that machine tool vibrations and many control problems, especially digital control tasks, may often lead to time-periodic delay differential equations with discrete delays or even with distributed ones. A paradigm for such delayed time-periodic systems is the delayed Mathieu equation, the stability analysis and stability charts of which will be presented. Then the numerical method called semi-discretization is introduced as a time-periodic perturbation of the time delay. Among the applications, the milling process and turning with spindle-speed variation is mentioned, while the so-called “act-and-wait” control is presented for robotic force control problems.
|Title of host publication||Advances in Analysis and Control of Time-Delayed Dynamical Systems|
|Publisher||World Scientific Publishing Co.|
|Number of pages||15|
|ISBN (Print)||9789814525503, 9789814522021|
|Publication status||Published - Jan 1 2013|
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