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Related Concept Videos

Effects of feedback01:24

Effects of feedback

Feedback in control systems plays a critical role in shaping various operational parameters, extending beyond simple error reduction to influence stability, bandwidth, gain, impedance, and sensitivity. Understanding these effects requires examining a basic feedback system characterized by defined input, output, error, and feedback signals.
Feedback significantly modifies the gain of a control system. The gain of a system without feedback is altered by a factor of one plus GH, where G represents...
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Linear time-invariant Systems

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Animal organs and organ systems constantly adjust to internal and external changes through a process called homeostasis ("steady state"). Examples of these changes include regulation of the level of glucose or calcium in the blood or internal responses to external temperatures. Homeostasis requires  maintaining an internal dynamic equilibrium:
Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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Ultra-high-frequency piecewise-linear chaos using delayed feedback loops.

Seth D Cohen1, Damien Rontani, Daniel J Gauthier

  • 1Department of Physics, Duke University, Durham, North Carolina 27708, USA.

Chaos (Woodbury, N.Y.)
|January 3, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a novel ultra-high-frequency chaotic electronic system. It generates both analog and digital chaos, enabling symbolic dynamics for advanced communication and radar applications.

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Area of Science:

  • Electronics
  • Chaos Theory
  • Signal Processing

Background:

  • Chaos systems are complex and have potential applications in secure communications and radar.
  • Existing chaotic systems often require specialized components or complex designs.

Purpose of the Study:

  • To design and demonstrate an ultra-high-frequency chaotic system using low-cost electronic components.
  • To achieve simultaneous generation of analog and digital chaos.
  • To lay the foundation for symbolic dynamics in chaotic systems.

Main Methods:

  • Developed a piecewise-linear chaotic system with two electronic time-delayed feedback loops.
  • Utilized a primary analog loop for multi-mode oscillations around 2 GHz.
  • Employed a secondary loop to switch variable gain using a digital-like signal.

Main Results:

  • Successfully generated ultra-high-frequency chaos (>1 GHz).
  • Demonstrated simultaneous analog and digital chaos generation.
  • Showcased digital chaos's ability to partition the system's attractor.

Conclusions:

  • The designed system offers a novel approach to generating hybrid analog-digital chaos.
  • This hybrid chaos is suitable for creating symbolic dynamics.
  • Potential applications include noise-resilient communications and radar systems.