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On the delay margin of dead-time compensators. (English) Zbl 1133.93318

Summary: Dead-time compensators (DTCs) are frequently regarded as being excessively sensitive to uncertainty in the loop delay. Yet this claim is based mostly on empirical studies rather than on any rigorous analysis. In particular, despite existing literature on calculating the delay margin, \(\mu_{d}\), there appears to be no study of the underlying reasons of such a sensitivity. In this paper we address the latter issue. By applying Nyquist criterion arguments, we demonstrate that substantial deterioration of \(\mu_{d}\) is caused by the crossover proliferation phenomenon, which, in turn, may be triggered by the use of DTC, especially when aggressive control strategies are used. We also show that crossover proliferation may give rise to the discontinuity of \(\mu_{d}\) as a function of system parameters. We argue that the sensitivity of DTCs to delay uncertainty shows mainly through these discontinuity points, so that the robustness can be improved if the discontinuities are avoided.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93C41 Control/observation systems with incomplete information
Full Text: DOI

References:

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