Repeated Poles

Repeated poles are multiple occurrences of the same root in a system’s characteristic equation or transfer function, and they strongly influence stability and transient behavior. In a linear time-invariant system, a pole repeated with multiplicity produces response terms such as t^(m-1)e^(pt), where m is the pole multiplicity and p is its location in the complex plane; this polynomial factor can amplify or prolong transients. Engineers analyze repeated poles in control-system design to predict settling time, overshoot, damping, and stability, then adjust feedback or compensator parameters to achieve reliable dynamic performance.

Repeated Poles - Related Videos

Education

JoVE Science Education - Engineering

Introduction to the Power Pole Board

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2023

Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT. DC/DC converters are power electronic converters that convert DC voltages and currents from a certain level to another level. Typically, voltage conversion is the main purpose of DC/DC converters and three main types of conversion exist in a single converter: stepping up, stepping down, and stepping up or down. Among the most common step-up converters are boost converters (Refer to this collections...

Pole and System Stability

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2024

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability. Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.

Research

JoVE Journal - Biology

Dissection of Organizer and Animal Pole Explants from Xenopus laevis Embryos and Assembly of a Cell Adhesion Assay

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Cited by 2 •

2007

This video demonstrates the technique used for preparation of organizer and animal pole explants from Xenopus laevis embryos, including the use of the eyebrow knife - a specialized dissection tool made of one's eyebrow. The protocol for assembling an adhesion assay is also given, which probes for the presence of key adhesion molecules present on the surface organizer or animal pole cells that are critical for proper development.

Infinitely Repeated Games

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2025

An infinitely repeated game is a scenario where players repeatedly engage in the same game without a predetermined end. This concept is crucial in understanding long-term interactions in various fields of the social sciences, including economics and international relations. Examples: Firms Setting Prices: Companies continuously adjust prices. Trade Negotiations: Countries consistently negotiate trade terms. Tit-for-Tat Strategy Cooperative Start: Players begin with a cooperative action,...

Finitely Repeated Games

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2025

Repeated games are scenarios where the same game is played multiple times by the same participants. These games are fundamental in understanding how decision-making processes evolve over time. Finitely Repeated Games: These games occur a specific number of times. Consider two software firms that are in competition, releasing updates to their software every quarter. Each quarter, these firms must decide on their strategic approach: they can either invest heavily in developing innovative new...

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