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Related Concept Videos

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...
Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
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...
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.
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...

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Related Experiment Videos

Fuzzy neural-based control for nonlinear time-varying delay systems.

Chih-Lyang Hwang1, Li-Jui Chang

  • 1Department of Electrical Engineering, Tamkang University, Tamsui 25137, Taiwan, ROC. clhwang@mail.tku.edu.tw

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|January 9, 2008
PubMed
Summary

This study introduces a novel fuzzy neural control for nonlinear dynamic systems with time-varying delays. The adaptive robust control compensates for system uncertainties and ensures stability without delay bound assumptions.

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Fuzzy Logic Systems

Background:

  • Nonlinear dynamic systems with time-varying delays present significant control challenges.
  • Approximation of such systems using fuzzy-based linear subsystems is a common strategy.
  • Designing controllers that handle uncertainties and time delays is crucial for system performance.

Purpose of the Study:

  • To develop a fuzzy neural-based control strategy for nonlinear dynamic systems with time-varying input and state delays.
  • To design a controller that can adaptively compensate for approximation errors and system uncertainties.
  • To ensure system stability and smooth control input transitions between robust and adaptive control modes.

Main Methods:

  • Approximation of the nonlinear system by N fuzzy-based linear subsystems with average delay.
  • Design of a fuzzy neural-based control using a radial-basis function neural network to learn uncertainties.
  • Implementation of adaptive control with uncertainty compensation and robust control without compensation, featuring a transition mechanism.
  • Stability verification using Lyapunov stability theory.

Main Results:

  • The proposed fuzzy neural control effectively learns and compensates for uncertainties arising from approximation errors and time-varying delays.
  • The control strategy seamlessly transitions between adaptive and robust control modes, ensuring smooth control input.
  • Stability of the overall closed-loop system is rigorously proven using Lyapunov stability theory.
  • Simulation results demonstrate superior performance compared to linear transformed state feedback with integration control.

Conclusions:

  • The developed fuzzy neural control is effective for nonlinear systems with time-varying delays, offering adaptive and robust control capabilities.
  • The method does not require prior knowledge of delay upper bounds, simplifying controller design.
  • The approach provides a stable and robust solution for complex dynamic systems, validated through simulations.