Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Transient and Steady-state Response

Transient and Steady-state Response

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.
These test signals are integral in designing control systems to exhibit two key performance aspects: transient response and steady-state...

Response Surface Methodology

Response Surface Methodology

Response Surface Methodology (RSM) is a collection of statistical and mathematical techniques used to develop, improve, and optimize processes. It is particularly valuable when many input variables or factors potentially influence a response variable.
The process of RSM involves several key steps:

First Order Systems

First Order Systems

First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...

Feedback control systems

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...

Second Order systems II

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.

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

You might also read

Related Articles

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

Sort by

Same journal

Multiscale dynamics of special memristive ion channels in a neural circuit.

Chaos (Woodbury, N.Y.)·2026

Same journal

Symmetry-protected delay spectroscopy in oscillator networks.

Chaos (Woodbury, N.Y.)·2026

Same journal

Mesoscale community organization governs epidemic onset and spread in metapopulations.

Chaos (Woodbury, N.Y.)·2026

Same journal

Topological dependence of viral mutation spread in complex host-interaction networks.

Chaos (Woodbury, N.Y.)·2026

Same journal

Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics.

Chaos (Woodbury, N.Y.)·2026

Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 6, 2025

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

Unsupervised data-driven response regime exploration and identification for dynamical systems.

¹Leo AI Inc., 160 Alewife Brook Parkway, Suite 1095, Cambridge, Massachusetts 02138, USA and Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel.

Chaos (Woodbury, N.Y.)

|December 3, 2024

Summary

This summary is machine-generated.

Data-Driven Response Regime Exploration and Identification (DR2EI) automatically discovers dynamical system behaviors. This method efficiently identifies dominant response regimes using unsupervised learning and active sampling, even with unknown system dynamics.

More Related Videos

Interactive and Visualized Online Experimentation System for Engineering Education and Research

Interactive and Visualized Online Experimentation System for Engineering Education and Research

Published on: November 24, 2021

Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface

Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface

Published on: May 8, 2021

Related Experiment Videos

Last Updated: Jun 6, 2025

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

Interactive and Visualized Online Experimentation System for Engineering Education and Research

Interactive and Visualized Online Experimentation System for Engineering Education and Research

Published on: November 24, 2021

Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface

Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface

Published on: May 8, 2021

Area of Science:

Complex Systems Analysis
Dynamical Systems Theory
Machine Learning Applications

Background:

Characterizing dynamical systems is challenging, especially when equations are unknown or sampling is costly.
Identifying distinct response regimes is crucial for understanding system behavior and for model order reduction.

Purpose of the Study:

Introduce a fully data-driven method for automated response regime identification.
Enable efficient exploration of complex dynamical systems with unknown governing equations.

Main Methods:

Utilizes unsupervised learning for transforming system responses into an embedding space for classification.
Employs an active sequential sampling strategy with Gaussian Process Regression for efficient parameter space exploration.
Validates performance on the mathematical pendulum, Lorenz system, and Duffing oscillator.

Main Results:

Successfully identified diverse response regimes with varying topological and frequency characteristics.
Demonstrated robustness to noise across different magnitudes.
Showcased the method's versatility in capturing a wide range of system behaviors.

Conclusions:

DR2EI offers an automated and efficient approach to discover dominant response regimes in complex dynamical systems.
The method reduces the need for prior knowledge of system equations or behavior.
Provides a valuable tool for order reduction and system exploration.