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Related Concept Videos

Properties of the Root Locus01:05

Properties of the Root Locus

The root locus method is an invaluable tool for analyzing higher-order systems without needing to factor the denominator of the transfer function. A pole of the system is identified when the characteristic polynomial in the transfer function's denominator equals zero.
To determine if a point lies on the root locus, the criterion involves the sum of angles contributed by all poles and zeros to that point. Specifically, this sum must be an odd multiple of 180 degrees. The gain at any point on the...
Plotting and Calibrating the Root Locus01:19

Plotting and Calibrating the Root Locus

Root loci often diverge as system poles shift from the real axis to the complex plane. Key points in this transition are the breakaway and break-in points, indicating where the root locus leaves and reenters the real axis. The branches of the root locus form an angle of 180/n degrees with the real axis, where n is the number of branches at a breakaway or break-in point.
The maximum gain occurs at the breakaway points between open-loop poles on the real axis, while the minimum gain is observed...
Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
Root-Locus Method01:19

Root-Locus Method

A cruise control system in a car is designed to maintain a specified speed automatically by adjusting the gas pedal. The system continuously measures the vehicle's speed and makes fine adjustments to the pedal to achieve this goal. The root locus method is particularly useful for understanding how the cruise control system's behavior changes under varying conditions, such as when the car goes uphill, downhill, or faces strong wind resistance.
This system can be represented by a block diagram,...
Construction of Root Locus01:15

Construction of Root Locus

The construction of a root locus involves several key steps to analyze and visualize the behavior of a system's poles with varying gain. The number of branches in the root locus equals the number of closed-loop poles and is symmetrical about the real axis.
For positive gain values, the root locus exists on the real axis to the left of an odd number of finite open-loop poles or zeros. The root locus starts at the open-loop poles and traces the paths of the closed-loop poles as the gain increases.
Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

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Related Experiment Video

Updated: May 16, 2026

A Simple Protocol for Mapping the Plant Root System Architecture Traits
11:09

A Simple Protocol for Mapping the Plant Root System Architecture Traits

Published on: February 10, 2023

Toward a systems analysis of the root.

P N Benfey1

  • 1Department of Biology, Duke Center for Systems Biology, Duke University, Durham, North Carolina 27708, USA. philip.benfey@duke.edu

Cold Spring Harbor Symposia on Quantitative Biology
|December 14, 2012
PubMed
Summary

Researchers explored plant root development using molecular genetics, genomics, and systems biology. Key findings include identifying a transcription factor regulating root patterning and a clock-like process controlling lateral root formation.

Area of Science:

  • Plant biology
  • Molecular genetics
  • Genomics
  • Systems biology

Background:

  • Root development is crucial for plant growth and survival.
  • Understanding root system architecture is essential for improving crop yields.
  • Previous research has laid the groundwork for investigating root development at multiple biological levels.

Purpose of the Study:

  • To investigate root development through the integration of molecular genetics, genomics, and systems biology.
  • To identify key regulators of root radial patterning and lateral root formation.
  • To elucidate the genetic basis of root system architecture.

Main Methods:

  • Characterization of mutations affecting root radial patterning.
  • Cell sorting combined with microarray analysis for genome-wide expression profiling.

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Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
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Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data

Published on: April 26, 2016

Lateral Root Inducible System in Arabidopsis and Maize
09:23

Lateral Root Inducible System in Arabidopsis and Maize

Published on: January 14, 2016

Related Experiment Videos

Last Updated: May 16, 2026

A Simple Protocol for Mapping the Plant Root System Architecture Traits
11:09

A Simple Protocol for Mapping the Plant Root System Architecture Traits

Published on: February 10, 2023

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
09:37

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data

Published on: April 26, 2016

Lateral Root Inducible System in Arabidopsis and Maize
09:23

Lateral Root Inducible System in Arabidopsis and Maize

Published on: January 14, 2016

  • Analysis of gene regulatory networks and clock-like processes.
  • Automated imaging of growing root systems to dissect genetic basis of architecture.

    • Main Results:

    • Identification of a transcription factor involved in root radial patterning and development.
    • Discovery of extensive tissue-specific gene expression responses under various conditions.
    • Elucidation of a gene regulatory network and a clock-like mechanism controlling lateral root positioning.
    • Progress in dissecting the genetic underpinnings of root system architecture.

    Conclusions:

    • The integration of molecular genetics, genomics, and systems biology provides a powerful framework for studying complex biological processes like root development.
    • Key molecular players and regulatory mechanisms have been identified that govern root patterning and architecture.
    • This research contributes to a deeper understanding of plant development with implications for agriculture and crop improvement.