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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.
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Sampling Theorem

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.

Aliasing

Aliasing

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Related Experiment Video

Updated: Jan 8, 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

Multirate sampled data driven fast rate fault detection of dynamic systems.

Yu Hu¹, Aibing Qiu², Yintao Wang²

¹Nantong University, School of Imformation Science and Technology, Nantong, 226019, China.

ISA Transactions

|December 20, 2025

Summary

This study introduces a fast fault detection method for multirate sampled data (MRSD) systems. The technique enhances diagnostic observer performance and enables rapid residual generation for improved fault detection.

Keywords:

Causality constraint Data driven Diagnostic observer Fault detection Multirate sampling

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Last Updated: Jan 8, 2026

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

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Published on: October 28, 2022

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Automated Analysis of Dynamic Ca2+ Signals in Image Sequences

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Area of Science:

Control Systems Engineering
Signal Processing
Fault Diagnosis

Background:

Multirate sampled data (MRSD) systems are prevalent in modern engineering.
Data asynchrony in MRSD systems due to inconsistent sampling rates hinders effective fault diagnosis, leading to delays and missed detections.

Purpose of the Study:

To propose a novel, fast-rate fault detection scheme specifically designed for dynamic systems driven by MRSD.
To address the challenges of data asynchrony and improve the timeliness of fault detection in MRSD systems.

Main Methods:

The lifting technique is utilized to convert asynchronous MRSD into synchronous, slow-rate sampled data.
A multi-dimensional diagnostic observer is constructed using subspace identification and an auxiliary lifted output to compute a parity vector.
A post-filter is employed to manage causality constraints and enable fast-rate residual generation.

Main Results:

The proposed scheme facilitates fast-rate residual generation, overcoming causality constraints.
A fast-rate residual evaluation strategy is developed for enhanced fault detection.
The effectiveness of the scheme was validated using a heating, ventilation, and air conditioning (HVAC) system example.

Conclusions:

The developed fault detection scheme effectively handles MRSD, enabling faster and more reliable fault diagnosis.
The method demonstrates superiority in addressing data asynchrony issues inherent in MRSD systems.
The approach offers a significant advancement for fault diagnosis in complex engineering systems utilizing MRSD.