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Related Concept Videos

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.
Feedback control systems01:26

Feedback control systems

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...
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:
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...
First Order Systems01:21

First Order Systems

First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
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...

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Related Experiment Videos

Identification of nonlinear dynamic systems using functional link artificial neural networks.

J C Patra1, R N Pal, B N Chatterji

  • 1Dept. of Appl. Electron. & Instrum. Eng., Regional Eng. Coll., Orissa.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|February 7, 2008
PubMed
Summary

A new functional link artificial neural network (FLANN) offers an alternative for nonlinear dynamic system identification. This enhanced structure can perform as well as or better than multilayer perceptrons (MLPs).

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Area of Science:

  • * Computational intelligence and machine learning.
  • * Artificial neural networks (ANNs) and their applications.
  • * System identification and control engineering.

Background:

  • * Traditional feedforward artificial neural networks, such as multilayer perceptrons (MLPs), are widely used for system identification.
  • * Capturing complex nonlinear dynamics often requires intricate network architectures.
  • * Exploring alternative ANN structures can lead to more efficient and effective identification methods.

Purpose of the Study:

  • * To introduce and evaluate a functional link artificial neural network (FLANN) as an alternative to traditional ANNs for nonlinear dynamic system identification.
  • * To demonstrate the efficacy of FLANNs in handling nonlinear system dynamics.
  • * To compare the performance of FLANNs against established MLP structures.

Main Methods:

  • * Development of a functional link artificial neural network (FLANN) architecture.
  • * Utilization of the backpropagation algorithm for training the FLANN.
  • * Enhancement of the input pattern with nonlinear functional expansion to introduce nonlinearity.
  • * Comparative analysis against multilayer perceptron (MLP) structures.

Main Results:

  • * The FLANN, a single-layer structure, effectively introduces nonlinearity through functional expansion.
  • * FLANNs demonstrate comparable performance to MLPs in nonlinear dynamic system identification.
  • * In certain cases, FLANNs exhibit superior performance compared to MLPs.

Conclusions:

  • * The functional link artificial neural network (FLANN) presents a viable and efficient alternative for nonlinear dynamic system identification.
  • * FLANNs offer a simplified structure with the capability to model complex nonlinear systems effectively.
  • * The choice of functional expansion is crucial for optimizing FLANN performance.