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Related Concept Videos

Feedback control systems01:26

Feedback control systems

264
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...
264
Second Order systems II01:18

Second Order systems II

76
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
76
Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

85
The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
The construction rules for the root locus in positive feedback systems are similar to those in...
85
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

59
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,...
59
State Space Representation01:27

State Space Representation

158
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...
158
Control System Problem01:21

Control System Problem

94
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...
94

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Distributed extended state observer design for strict-feedback nonlinear leader system.

Jixing Lv1, Changhong Wang1, Yonggui Kao2

  • 1School of Astronautics, Harbin Institute of Technology, Harbin 150001, China.

ISA Transactions
|May 21, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for estimating the state and uncertainty of a leader system for leader-following control. The proposed distributed observers ensure accurate state reconstruction within a guaranteed time frame, even with limited communication.

Keywords:
Distributed estimationDistributed extended state observerLeader-following controlPrescribed-time stabilityStrict-feedback nonlinear system

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Area of Science:

  • Control Theory
  • Nonlinear Systems
  • Distributed Estimation

Background:

  • Accurate leader state and dynamics estimation is essential for effective leader-following control systems.
  • Existing methods often struggle with nonlinear systems, uncertain dynamics, and directed communication constraints.
  • The need for efficient distributed estimation schemes that minimize communication load is critical.

Purpose of the Study:

  • To develop a distributed state and uncertainty estimation scheme for nonlinear leader systems.
  • To address challenges posed by Hölder-growing nonlinearities, matched uncertainty, and directed communication topologies.
  • To enable followers to accurately estimate the leader's state and uncertainty within a prescribed time.

Main Methods:

  • Proposal of a novel prescribed-time distributed estimation scheme utilizing two distributed extended state observers (DESOs).
  • Development of a prescribed-time DESO (PTDESO) for accurate leader state and uncertainty reconstruction within a user-defined time.
  • Construction of a high-gain DESO (HGDESO) for asymptotic convergence and bounded observation errors post-prescribed time.

Main Results:

  • Each follower reconstructs the leader's state and uncertainty using limited one-dimensional output estimates from neighbors and the leader.
  • The PTDESO guarantees state and uncertainty estimation within a prescribed time, independent of initial conditions.
  • The HGDESO ensures asymptotic convergence and maintains observation errors within a small neighborhood of the origin after the prescribed time.

Conclusions:

  • The proposed distributed estimation scheme effectively addresses state and uncertainty estimation for nonlinear leader systems under directed topologies.
  • The observers significantly reduce communication load by requiring only one-dimensional output estimates.
  • Validated through practical examples with multiple manipulators and marine surface vehicles, demonstrating robust performance.