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Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

Linear Approximation in Time Domain

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...

Multimachine Stability

Multimachine Stability

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:

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...

Bus Impedance Matrix

Bus Impedance Matrix

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,...

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...

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Related Experiment Video

Updated: May 6, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

A gray-box neural network-based model identification and fault estimation scheme for nonlinear dynamic systems.

Zhaohui Cen¹, Jiaolong Wei, Rui Jiang

¹Department of Electronic and Information Engineering, Huazhong University of Science and Technology, Wuhan, China.

International Journal of Neural Systems

|October 26, 2013

Summary

A new gray-box neural network model (GBNNM) accurately estimates faults in nonlinear systems. This model identifies system dynamics and nonlinearities, enabling precise fault parameter estimation for satellite attitude control systems.

Related Experiment Videos

Last Updated: May 6, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

Area of Science:

Control Systems Engineering
Artificial Intelligence
Aerospace Engineering

Background:

Nonlinear dynamic systems require accurate modeling for reliable operation.
Existing neural network (NN) methods for model identification can be complex and less adaptable.
Fault estimation is crucial for maintaining the integrity of control systems, especially in aerospace applications.

Purpose of the Study:

To propose a novel gray-box neural network model (GBNNM) for model identification and fault estimation (MIFE).
To develop an improved extended state observer using NNs (IESONN) for fault parameter estimation.
To validate the proposed MIFE scheme on reaction wheels within a satellite attitude control system (SACS).

Main Methods:

A GBNNM combining multi-layer perception (MLP) neural networks and integrators is developed.
The GBNNM directly models system dynamics and separately models nonlinearities.
An improved extended state observer (IESONN) is integrated for fault parameter estimation, leveraging NNs from the GBNNM.

Main Results:

The GBNNM accurately approximates nonlinear system dynamics and nonlinearities.
Quantitative residuals generated by the GBNNM effectively indicate fault severity.
The proposed MIFE scheme demonstrated superior performance in estimating fault parameters for partial loss of effect (LOE) faults in RWs.

Conclusions:

The GBNNM offers a more intuitive and effective approach to model identification compared to traditional NN methods.
The integrated IESONN enhances fault parameter estimation accuracy without prior knowledge of system nonlinearities.
The proposed MIFE scheme shows significant promise for fault diagnosis and management in satellite attitude control systems.