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Related Concept Videos

State Space Representation01:27

State Space Representation

166
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...
166
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

66
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,...
66
State Space to Transfer Function01:21

State Space to Transfer Function

175
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
175
Transfer Function to State Space01:23

Transfer Function to State Space

197
State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an...
197
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

42
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...
42
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

60
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Parameter-coupled state space models based on quasi-Gaussian fuzzy approximation.

Yizhi Wang1,2, Fengyuan Ma3, Xiaomin Tian3

  • 1College of Intelligent Science and Control Engineering, Jinling Institute of Technology, Nanjing, 210000, China. w_yz@jit.edu.cn.

Scientific Reports
|October 30, 2024
PubMed
Summary

This study introduces quasi-Gaussian fuzzy systems (QGFS) for improved fuzzy control. The new quasi-Gaussian membership function enhances interpretability and approximation accuracy in mechanical system modeling.

Keywords:
Fuzzy ApproximationParameter-Coupled ModelsPharmaceutical EquipmentQuasi-Gaussian Fuzzy SetsState Space Models

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Area of Science:

  • Engineering
  • Computer Science
  • Control Systems

Background:

  • Fuzzy systems are crucial for control system design, but their interpretability and accuracy depend on membership function performance.
  • Existing membership functions offer either sensitivity or interpretability, creating a trade-off in fuzzy system design.

Purpose of the Study:

  • To introduce a novel quasi-Gaussian membership function that combines the sensitivity of triangular functions with the interpretability of Gaussian functions.
  • To develop quasi-Gaussian fuzzy systems (QGFS) for enhanced approximation accuracy and interpretability in mechanical system modeling.
  • To validate the effectiveness of 1-D and 2-D QGFS in approximating complex mechanical models, specifically a depyrogenation tunnel.

Main Methods:

  • Derivation of a two-dimensional (2-D) quasi-Gaussian membership function.
  • Development of a method for establishing quasi-Gaussian fuzzy systems (QGFS) using a rectangular grid.
  • Validation of approximation properties using the sine function and application to mechanical models of a depyrogenation tunnel.

Main Results:

  • The proposed quasi-Gaussian membership function achieves the sensitivity of triangular functions and interpretability of Gaussian functions.
  • One-dimensional (1-D) and 2-D QGFS demonstrated approximation errors within a ±5% range when applied to the sine function.
  • 1-D and 2-D QGFS successfully approximated mechanical models of the depyrogenation tunnel with satisfactory results.
  • The 2-D QGFS effectively described models with coupled parameters.

Conclusions:

  • Quasi-Gaussian fuzzy systems (QGFS) offer a promising approach to enhance both accuracy and interpretability in fuzzy control and system modeling.
  • The developed quasi-Gaussian membership function and QGFS methodology are effective for approximating complex mechanical systems, including those in the pharmaceutical industry.
  • The 2-D QGFS shows particular strength in modeling systems with interconnected parameters, paving the way for more sophisticated control designs.