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Related Concept Videos

Open and closed-loop control systems01:17

Open and closed-loop control systems

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Control systems are foundational elements in automation and engineering. They are broadly categorized into open-loop and closed-loop systems. These classifications hinge on the presence or absence of feedback mechanisms, significantly influencing the system's performance, complexity, and application.
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal...
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Control System Problem01:21

Control System Problem

165
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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State Space to Transfer Function01:21

State Space to Transfer Function

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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:
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State Space Representation01:27

State Space Representation

274
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...
274
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

120
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,...
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Transfer Function to State Space01:23

Transfer Function to State Space

367
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...
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Related Experiment Video

Updated: Aug 28, 2025

An Experimental Platform to Study the Closed-loop Performance of Brain-machine Interfaces
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Dual closed loop AUV trajectory tracking control based on finite time and state observer.

Xiaoqiang Dai1, Hewei Xu1, Hongchao Ma1

  • 1School of Automation, Jiangsu University of Science and Technology, Zhenjiang 212003, China.

Mathematical Biosciences and Engineering : MBE
|September 20, 2022
PubMed
Summary

This study introduces a novel control method for autonomous underwater vehicles (AUVs) to improve three-dimensional trajectory tracking. The enhanced algorithm ensures faster convergence and higher accuracy despite disturbances like wind and waves.

Keywords:
AUVadaptive finite time controlfilter integral sliding modereduced-order extended state observertrajectory tracking control

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Area of Science:

  • Robotics and Control Systems
  • Ocean Engineering

Background:

  • Autonomous Underwater Vehicles (AUVs) require precise three-dimensional trajectory tracking for mission completion.
  • External disturbances (wind, waves, currents) and internal model uncertainties negatively impact AUV control performance, leading to slow convergence and output saturation.

Purpose of the Study:

  • To develop an advanced control strategy for robust and accurate 3D trajectory tracking in AUVs.
  • To address limitations of existing controllers, including slow convergence, output saturation, and model uncertainties.

Main Methods:

  • Implemented a finite-time control method to accelerate controller convergence speed.
  • Designed an auxiliary dynamic system to compensate for controller output saturation.
  • Utilized a reduced-order extended observer to estimate and compensate for AUV model uncertainties and external disturbances in real-time.

Main Results:

  • Simulations demonstrated superior convergence speed, control accuracy, robustness, and tracking performance compared to conventional methods.
  • Experimental validation on the "sea exploration II" AUV in Suzhou Lake confirmed the algorithm's effectiveness.
  • Achieved mean pitch and heading angle errors below 8 degrees, and mean depth error below 0.1 meters.

Conclusions:

  • The proposed control strategy significantly enhances AUV trajectory tracking capabilities.
  • The method effectively mitigates issues related to slow convergence, output saturation, and model uncertainties.
  • The validated algorithm meets practical AUV navigation and task requirements.