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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.
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
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 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...
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:
Control System Problem01:21

Control System Problem

In an open-loop system, such as a basic thermostat, the poles of the transfer function influence the system's response but do not determine its stability. However, when feedback is introduced to form a closed-loop system, such as an advanced thermostat that adjusts heating based on room temperature, stability is governed by the new poles of the closed-loop transfer function.
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...

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Related Experiment Videos

A constructive approach for nonlinear system identification using multilayer perceptrons.

J Y Choi1, H F Van Landingham, S Bingulac

  • 1Bradley Dept. of Electr. Eng., Virginia Polytech. Inst. & State Univ., Blacksburg, VA.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|January 1, 1996
PubMed
Summary
This summary is machine-generated.

This study introduces a novel nonlinear system identification method by integrating traditional multivariable techniques with dynamic multi-layer perceptrons (MLPs). The approach accurately models complex nonlinear systems, extending linear models to capture dynamic behaviors.

Related Experiment Videos

Area of Science:

  • Control Engineering
  • Computational Intelligence
  • Nonlinear Dynamics

Background:

  • Traditional system identification often relies on linear models, which are insufficient for many real-world nonlinear systems.
  • Existing nonlinear methods can be complex and computationally intensive.
  • Accurate modeling of nonlinear systems is crucial for control and prediction.

Purpose of the Study:

  • To develop a constructive method for nonlinear system identification.
  • To combine conventional multivariable system identification with dynamic multi-layer perceptrons (MLPs).
  • To create an accurate discrete-time nonlinear model from a MIMO linear model.

Main Methods:

  • Integration of a conventional multivariable system identification technique.
  • Utilization of a dynamic multi-layer perceptron (MLP) architecture.
  • Assumption of nominal operation around an equilibrium point with an existing linearized model.

Main Results:

  • A constructive method for nonlinear system identification was achieved.
  • An accurate discrete-time nonlinear model was developed.
  • The model successfully captures the nonlinear behavior of the system, extending from a MIMO linear model.

Conclusions:

  • The proposed method effectively identifies and models nonlinear systems.
  • This approach offers an accurate extension of linear models for complex dynamic behaviors.
  • The combination of conventional and MLP methods provides a robust nonlinear system identification technique.