Uniformly-Damped Binomial Filters: Five-percent Maximum Overshoot Optimal Response Design

TL;DR

This paper introduces a new class of uniformly-damped binomial filters with a five-percent maximum overshoot, providing a balanced response suitable for applications requiring both filtering and smooth transient response.

Contribution

It extends the binomial theorem to create uniformly-damped binomial filters that optimize maximum overshoot, bridging the gap between Butterworth and standard binomial filters.

Findings

Five-percent uniformly-damped binomial filters offer a compromise between Butterworth and binomial filters.

The proposed filters achieve negligible overshoot with strong filtering and smooth transient response.

Applicable to step-tracking and similar applications requiring fast, smooth responses.

Abstract

In this paper, the five-percent maximum overshoot design of uniformly-damped binomial filters (transfer-functions) is introduced. First, the butterworth filter response is represented as a damped-binomial filter response. To extend the maximum-overshoot response of the second-order butterworth to higher orders, the binomial theorem is extended to the uniformly-damped binomial theorem. It is shown that the five-percent uniformly-damped binomial filter is a compromise between the butterworth filter and the standard binomial filter, with respect to the filter-approximation problem in the time and frequency domain. Finally, this paper concludes that in applications of interest, such as step-tracking, where both strong filtering and a fast, smooth transient-response, with negligible overshoot are desired, the response of the normalized five-percent uniformly-damped binomial form is a candidate replacement for both the butterworth and standard binomial filter forms.