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Related Concept Videos

Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

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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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In control systems, test signals are essential for evaluating performance under various conditions. The ramp function is effective for systems undergoing gradual changes, while the step function is suitable for assessing systems facing sudden disturbances. For systems subjected to shock inputs, the impulse function is the most appropriate test signal.
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Related Experiment Video

Updated: Jan 8, 2026

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Quantifying State-Dependent Control Properties of Brain Dynamics from Perturbation Responses.

Yumi Shikauchi1,2, Mitsuaki Takemi3,4, Leo Tomasevic4,5,6

  • 1Graduate School of Arts and Sciences, The University of Tokyo, Tokyo 153-8902, Japan shikauchi-y@med.showa-u.ac.jp c-oizumi@g.ecc.u-tokyo.ac.jp.

The Journal of Neuroscience : the Official Journal of the Society for Neuroscience
|December 19, 2025
PubMed
Summary

This study introduces a new network control theory method to analyze brain dynamics using external perturbations. Controllable directions, derived from this method, better distinguish brain states than overall controllability.

Keywords:
concurrent TMS-EEG measurementdata-driven controlmotor executionmotor imagerynetwork controllabilityresting state

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Area of Science:

  • Neuroscience
  • Control Theory
  • Systems Biology

Background:

  • The brain functions as a dynamic control system, transitioning between various states like rest and motor activity.
  • Network control theory offers tools to analyze brain dynamics, but prior studies often overlooked external perturbations' role in system identification.

Purpose of the Study:

  • To develop a novel method for estimating the controllability Gramian matrix by integrating perturbation inputs with network control theory.
  • To investigate brain state dynamics and their responses to external stimulation using this new framework.

Main Methods:

  • A perturbation input paradigm was combined with network control theory.
  • A novel method for estimating the controllability Gramian matrix was proposed and validated.
  • The method was applied to transcranial magnetic stimulation-induced electroencephalographic (EEG) responses in motor-related and resting states.

Main Results:

  • The proposed method provides insights into brain dynamics, quantifying overall controllability (eigenvalues) and specific controllable directions (eigenvectors).
  • Controllable directions effectively differentiated between resting and motor-related brain states.
  • Certain states, such as motor execution and motor imagery, were not distinguishable using these measures, suggesting shared intrinsic control properties.

Conclusions:

  • Brain states exhibit distinct intrinsic control properties, influencing their dynamic responses to stimulation.
  • The developed methodology offers a quantitative approach to assess brain state differences.
  • This approach has potential applications in characterizing individual response variability and optimizing stimulation efficacy.