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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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Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...
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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
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Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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Effects of error on fluctuations under feedback control.

Sosuke Ito1, Masaki Sano

  • 1Department of Physics, The University of Tokyo-Hongo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8654, Japan. sosuke@daisy.phys.s.u-tokyo.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2011
PubMed
Summary

We studied feedback control for Brownian motion, finding that measurement errors bound the violation of the fluctuation-dissipation theorem (FDT). Analytical models show cooling limits analogous to Carnot efficiency.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Stochastic Processes

Background:

  • The fluctuation-dissipation theorem (FDT) typically holds for systems in thermal equilibrium.
  • Driven systems under non-equilibrium conditions often exhibit violations of the FDT.
  • Understanding these violations is crucial for analyzing feedback-controlled systems.

Purpose of the Study:

  • To investigate the impact of non-equilibrium feedback control on Brownian motion.
  • To quantify the bounds on FDT violation in the presence of measurement errors.
  • To explore cooling processes and their theoretical limits in feedback-controlled systems.

Main Methods:

  • Analysis of one-dimensional Brownian motion subjected to non-equilibrium feedback control.
  • Derivation of bounds on FDT violation using mutual information from the feedback system.
  • Introduction and analysis of two models illustrating feedback cooling.
  • Derivation of analytical results for cooling limits and effective temperature bounds.

Main Results:

  • The degree of FDT violation is limited by the mutual information of the feedback system, even with measurement errors.
  • Two models demonstrate cooling processes achievable through feedback control.
  • Analytical results provide the cooling limit for these systems.
  • In steady states, effective temperatures are bounded by an inequality resembling Carnot efficiency.

Conclusions:

  • Feedback control in non-equilibrium systems leads to a bounded violation of the FDT, influenced by measurement accuracy.
  • The study provides a theoretical framework for understanding and achieving cooling in Brownian systems via feedback.
  • The findings establish a connection between feedback control, FDT violation, and thermodynamic limits like the Carnot efficiency.