Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Higher Derivatives01:29

Higher Derivatives

In calculus, higher-order derivatives extend the idea of differentiation beyond the first derivative to capture successive rates of change. These derivatives provide detailed information about the behavior of functions and have important applications in both mathematics and physics. To illustrate these concepts, consider the example function\begin{equation*}f(x) = x^3 - x\end{equation*}which serves as a useful case study for exploring higher derivatives.The first derivative represents the slope...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Sampling Theorem01:15

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
Derivatives of Inverse Trigonometric Functions01:30

Derivatives of Inverse Trigonometric Functions

A ship tracking an approaching aircraft relies on geometric measurements to find out the aircraft’s position relative to the observer. By measuring the slant distance to the aircraft and the angle of elevation, the horizontal and vertical components of the distance can be obtained using trigonometric relationships. This geometric approach provides a basis for analyzing how the observed angle changes as the aircraft moves closer to the ship.To examine the mathematical behavior of the angle of...
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A switched optimal control strategy in human balancing on a harmonically moving platform.

Journal of biomechanics·2025
Same author

Adjoint sensitivity method for parameter estimation: applications to inverted pendulum and human standing balance.

Journal of the Royal Society, Interface·2025
Same author

Human performance in virtual stabilization of a fractional-order system with reaction delay.

Journal of the Royal Society, Interface·2024
Same author

Pole balancing on the fingertip: model-motivated machine learning forecasting of falls.

Frontiers in physiology·2024
Same author

Controlling stick balancing on a linear track: Delayed state feedback or delay-compensating predictor feedback?

Biological cybernetics·2023
Same author

Transient chaotic behavior of fuzzy controlled polishing processes.

Chaos (Woodbury, N.Y.)·2022
Same journal

Correction to: 'Stokes settling and particle-laden plumes: implications for deep-sea mining and volcanic eruption plumes' (2020), by Mingotti et al.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

A stable hothouse triggered by a tipping mechanism.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Beyond distance: quantifying point cloud dynamics with persistent homology and dynamic optimal transport.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Global stability of the Atlantic overturning circulation: edge state, long transients and boundary crisis under CO2 forcing.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Morse index classification and landscape of Kuramoto system for Hebbian-based binary pattern recognition.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Interpretable and equation-free response theory for complex systems.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
See all related articles

Related Experiment Video

Updated: Jun 17, 2026

Measuring Delay Discounting in Humans Using an Adjusting Amount Task
07:47

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

Delayed feedback of sampled higher derivatives.

Tamas Insperger1, Gabor Stepan, Janos Turi

  • 1Department of Applied Mechanics, Budapest University of Technology and Economics, 1521 Budapest, Hungary. inspi@mm.bme.hu

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|December 17, 2009
PubMed
Summary
This summary is machine-generated.

Advanced functional differential equations (AFDEs) are typically unstable. However, this study shows that sampling in digital control can stabilize a simple AFDE with delayed feedback of the second derivative.

More Related Videos

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

Related Experiment Videos

Last Updated: Jun 17, 2026

Measuring Delay Discounting in Humans Using an Adjusting Amount Task
07:47

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

Area of Science:

  • Dynamical Systems and Control Theory
  • Applied Mathematics
  • Numerical Analysis

Background:

  • Advanced functional differential equations (AFDEs) describe systems where the current state depends on past higher-order derivatives.
  • AFDEs, particularly their linearized forms, are inherently unstable with infinitely many unstable poles, limiting practical applications.
  • The implicit nature of AFDEs poses challenges for analysis and control design.

Purpose of the Study:

  • To investigate the stabilization effect of feedback sampling on a simple linear scalar first-order AFDE.
  • To analyze the impact of delayed feedback of the second derivative in a digitally controlled system.
  • To explain the observed stable behavior in dynamical systems with feedback delays in the highest derivative.

Main Methods:

  • Consideration of a linear scalar first-order advanced functional differential equation.
  • Inclusion of delayed feedback of the second derivative of the state.
  • Analysis of the system under the influence of sampling in the feedback loop (digital control).

Main Results:

  • It is demonstrated that the introduction of sampling in the feedback loop can stabilize the AFDE.
  • Stabilization is shown to be achievable for specific parameter combinations.
  • The findings provide an explanation for the stable behavior observed in certain dynamical systems with highest derivative feedback delays.

Conclusions:

  • Feedback sampling can counteract the inherent instability of advanced functional differential equations.
  • Digital control strategies can be employed to achieve stability in systems described by AFDEs.
  • The study offers insights into the practical stabilization of complex dynamical systems through controlled feedback mechanisms.