Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold

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.

The limiting zero dynamics of discrete-time system based on forward triangle sample-and-hold

“…Remark 4 : Generally speaking, the relative degree of many linear or nonlinear mechanical systems in practical field is two [ 27 , 28 ]. As the results in Theorem 4 shown, one can find the feasible solution of the variable parameter of FTSH to ensure the corresponding discrete-time limiting zeros are stable.…”