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Related Concept Videos

Feedback control systems01:26

Feedback control systems

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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...
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Gain01:15

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Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
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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.
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Updated: May 2, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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Nonlinear Dynamic Relative Gain Array for control configuration selection in nonlinear MIMO systems.

Shirin Nazem-Zadeh1, Bijan Moaveni1

  • 1Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran 16317-14191, Iran.

ISA Transactions
|April 30, 2026
PubMed
Summary

This study introduces the Nonlinear Dynamic Relative Gain Array (NDRGA) for selecting control configurations in complex nonlinear systems. The NDRGA method effectively analyzes system dynamics and nonlinearities in the frequency domain.

Keywords:
Control configuration selectionGeneralized frequency response functionNonlinear Dynamic Relative Gain ArrayNonlinear MIMO systems

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Area of Science:

  • Control Engineering
  • Nonlinear Systems Analysis
  • Systems and Control Theory

Background:

  • Existing control configuration selection (CCS) methods often struggle with dynamic, nonlinear multi-input multi-output (MIMO) systems.
  • A gap exists in frequency-domain CCS techniques for nonlinear MIMO systems, limiting analysis of system dynamics and nonlinearities simultaneously.

Purpose of the Study:

  • To present the Nonlinear Dynamic Relative Gain Array (NDRGA) as a novel input-output interaction measure for CCS in nonlinear dynamic MIMO systems.
  • To extend the Dynamic Relative Gain Array (DRGA) to incorporate higher-order nonlinear interaction effects.
  • To enable frequency-domain analysis of both system dynamics and nonlinearities for CCS.

Main Methods:

  • The NDRGA is derived by extending the DRGA definition to nonlinear systems.
  • Generalized Frequency Response Functions (GFRFs) for the nominal forward system and its inverse are estimated using a harmonic probing algorithm and Rönnow's recursive method.
  • A frequency-based CCS criterion is developed for nonlinear systems.

Main Results:

  • The NDRGA successfully incorporates higher-order nonlinear interaction effects.
  • The method allows for simultaneous analysis of system dynamics and nonlinearities in the frequency domain.
  • Simulations on two nonlinear systems demonstrate the validity and effectiveness of the NDRGA for CCS.

Conclusions:

  • The proposed NDRGA provides a frequency-domain CCS criterion for nonlinear MIMO systems, filling a current research gap.
  • The NDRGA is effective for control configuration selection in nonlinear dynamic systems, as confirmed by closed-loop simulations.