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State Space Representation01:27

State Space Representation

158
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...
158
Transfer Function to State Space01:23

Transfer Function to State Space

181
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
181
Node Analysis for AC Circuits01:14

Node Analysis for AC Circuits

273
Consider an angioplasty system featuring a catheter equipped with a turbine, a critical tool for removing plaque deposits from coronary arteries. This intricate medical device operates using a circuit model reminiscent of a dual-node RLC circuit powered by a current-controlled voltage source.
To unravel the complexities of this system, nodal analysis is employed, a powerful technique founded on Kirchhoff's current law (KCL), which remains valid for phasors. AC circuits can effectively be...
273
Bus Impedance Matrix01:24

Bus Impedance Matrix

95
Calculating subtransient fault currents for three-phase faults in an N-bus power system involves using the positive-sequence network. When a three-phase short circuit occurs at a specific bus, the analysis uses the superposition method to evaluate two separate circuits.
In the first circuit, all machine voltage sources are short-circuited, leaving only the prefault voltage source at the fault location. The positive-sequence bus impedance matrix can be determined by solving the nodal equations,...
95
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

127
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
127
Multimachine Stability01:25

Multimachine Stability

128
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
128

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Updated: May 22, 2025

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
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Predicting critical transitions induced by the saddle-node bifurcation in electronic circuits using parameter space

Y Itoh1

  • 1Department of Electrical and Electronic Engineering, Hokkaido University of Science, Hokkaido 006-8585, Japan.

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PubMed
Summary
This summary is machine-generated.

This study predicts critical transitions in electronic circuits using parameter space estimation from time-series data. This method enables early warning signals for saddle-node bifurcations, crucial for system stability.

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Area of Science:

  • Complex Systems Science
  • Nonlinear Dynamics
  • Electronic Engineering

Background:

  • Critical transitions, often driven by bifurcations like the saddle-node bifurcation, pose risks in various systems, including electronic circuits.
  • Predicting these transitions from observational data is challenging but essential for system stability and management.

Purpose of the Study:

  • To develop a method for predicting critical transitions in electronic circuits solely from time-series data.
  • To estimate the parameter space of an unknown system and plot its bifurcation diagram and Lyapunov exponents.
  • To enable early warning signals for saddle-node bifurcations.

Main Methods:

  • Parameter space estimation using time-series data preceding critical transitions.
  • Utilizing the universal property of Lyapunov exponents approaching zero at critical transitions.
  • Employing an extreme learning machine for extracting system dynamics from noisy data.
  • Applying the method to electronic circuits modeling one-dimensional and two-dimensional biomass models.

Main Results:

  • Accurate prediction of critical transitions in electronic circuits from time-series data.
  • Successful estimation of parameter space, bifurcation diagrams, and Lyapunov exponents for unknown systems.
  • Demonstrated robustness against dynamical and observational noise.
  • Feasibility of predicting parameter value changes for continuous system monitoring.

Conclusions:

  • Parameter space estimation is a powerful, generalized tool for predicting critical transitions in complex systems.
  • The developed method offers a robust approach for early warning signals in electronic circuits and potentially other dynamical systems.
  • Predicting parameter shifts enhances continuous monitoring and timely intervention capabilities.