Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Time Domain01:21

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, the...
Linear Approximation in Frequency Domain01:26

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 time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A novel robust discrete-time integral sliding mode tracking control design for time-varying delay MIMO systems with unknown uncertainties.

ISA transactions·2023
Same author

ARX model decomposed on Meixner-Like orthonormal bases.

ISA transactions·2019
Same author

Robust adaptive sliding mode control for uncertain systems with unknown time-varying delay input.

ISA transactions·2018
Same author

New methods of Laguerre pole optimization for the ARX model expansion on Laguerre bases.

ISA transactions·2017
Same author

Adaptive MPC based on MIMO ARX-Laguerre model.

ISA transactions·2016
Same author

Moving window KPCA with reduced complexity for nonlinear dynamic process monitoring.

ISA transactions·2016

Related Experiment Video

Updated: May 15, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Nonlinear system modeling based on bilinear Laguerre orthonormal bases.

Tarek Garna1, Kais Bouzrara, José Ragot

  • 1Unité de Recherche Automatique, Traitement de Signal et d'Image, Ecole Nationale d'Ingénieurs de Monastir, Rue Ibn Eljazzar, 5019 Monastir, Tunisia. tarek.garna@enim.rnu.tn

ISA Transactions
|January 8, 2013
PubMed
Summary

This study introduces a novel bilinear-Laguerre model for system representation, significantly reducing parameters. An optimization algorithm enhances model accuracy, validated on a Continuous Stirred Tank Reactor (CSTR) system.

More Related Videos

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

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

Related Experiment Videos

Last Updated: May 15, 2026

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

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
  • Signal Processing
  • Mathematical Modeling

Background:

  • Classical bilinear models often require a large number of parameters.
  • Efficient representation and parameter reduction are crucial for complex system modeling.

Purpose of the Study:

  • To propose a new discrete bilinear model representation using Laguerre orthonormal bases.
  • To develop a pole optimization algorithm for improved model performance.

Main Methods:

  • Developing coefficients for input, output, and cross-product terms on Laguerre bases.
  • Extending an existing pole optimization algorithm (Tanguy et al.) for Laguerre pole selection.
  • Simulating and validating the bilinear-Laguerre model on a Continuous Stirred Tank Reactor (CSTR) system.

Main Results:

  • The proposed bilinear-Laguerre model achieves significant parameter reduction compared to classical models.
  • The model offers a simpler recursive representation.
  • The pole optimization algorithm effectively determines optimal Laguerre poles.

Conclusions:

  • The bilinear-Laguerre model provides an efficient and reduced-parameter alternative for discrete bilinear system representation.
  • The developed pole optimization algorithm is effective for enhancing model accuracy.
  • The model and algorithm are validated on a practical CSTR system.