On the delay margin of dead-time compensators

Abstract

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, μ 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 μ 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 μd 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.