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Paper details
Number 4 - December 2014
Volume 24 - 2014
Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold
Cheng Zeng, Shan Liang, Yuzhe Zhang, Jiaqi Zhong, Yingying Su
Abstract
Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the
fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling
period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting
sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree
of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed
for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH
even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails
to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample
ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate
approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be
particular cases of the ideas presented here.
Keywords
stability, discretization zeros, Taylor method, signal reconstruction, sampled-data model