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Related Concept Videos

Block Diagram Reduction01:22

Block Diagram Reduction

The process of deriving the transfer function of a control system often involves reducing its block diagram to a single block. This simplification can be achieved through a series of strategic operations, including relocating branch points and comparators. These operations preserve the overall function of the system while allowing for easier manipulation and combination of blocks.
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Documentation of Nursing Diagnosis01:10

Documentation of Nursing Diagnosis

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Routh-Hurwitz Criterion II01:19

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Related Experiment Video

Updated: May 9, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Fault diagnosis viewed as a left invertibility problem.

R Martínez-Guerra1, J L Mata-Machuca, J J Rincón-Pasaye

  • 1Departamento de Control Automático, CINVESTAV-IPN, Av. IPN 2508, 07360 DF, Mexico. rguerra@ctrl.cinvestav.mx

ISA Transactions
|July 11, 2013
PubMed
Summary

This study introduces novel fault diagnosis properties using differential output rank and left invertibility. Two nonlinear observers were compared for fault estimation in a real-time three-tank system.

Keywords:
Differential output rankFault diagnosisLeft invertibility conditionReduced order observerSliding mode observer

Related Experiment Videos

Last Updated: May 9, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

  • Control Systems Engineering
  • Nonlinear Systems Analysis
  • Fault Diagnosis and Fault-Tolerant Control

Background:

  • Fault diagnosis is critical for system reliability and safety.
  • Estimating fault signals in nonlinear systems presents significant challenges.
  • Left invertibility and differential output rank offer advanced analytical tools.

Purpose of the Study:

  • To investigate new properties for fault diagnosis using left invertibility and differential output rank.
  • To compare the performance of two distinct nonlinear observer schemes for fault signal estimation.
  • To validate the proposed methodology through real-time implementation.

Main Methods:

  • Utilizing the concept of differential output rank to uncover new properties related to left invertibility.
  • Developing and implementing two nonlinear observer schemes: a proportional reduced-order observer and a sliding mode observer.
  • Conducting a real-time implementation on a three-tank system to assess observer performance.

Main Results:

  • New theoretical properties for fault diagnosis were identified based on left invertibility conditions.
  • Comparative analysis demonstrated the effectiveness of both observer types in estimating fault signals.
  • Successful real-time validation of the fault diagnosis methodology on the experimental setup.

Conclusions:

  • The differential output rank and left invertibility conditions provide a robust framework for fault diagnosis.
  • Both proportional reduced-order and sliding mode observers are viable for fault estimation in nonlinear systems.
  • The real-time implementation confirms the practical applicability of the developed fault diagnosis approach.