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Related Concept Videos

Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

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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...
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BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Feedback control systems01:26

Feedback control systems

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

Time-Domain Interpretation of PD Control

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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...
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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.
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Control System Problem01:21

Control System Problem

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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.
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Related Experiment Video

Updated: Aug 3, 2025

Experimental Investigation of the Hierarchical Control in DC Microgrids Using a Real-time Simulator
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Decentralized H2 Control for Discrete-Time Networked Systems With Positivity Constraint.

Jason J R Liu, Ka-Wai Kwok, James Lam

    IEEE Transactions on Neural Networks and Learning Systems
    |April 7, 2023
    PubMed
    Summary

    This study addresses decentralized H2 state-feedback control for networked positive systems. A novel primal-dual iterative algorithm provides necessary and sufficient conditions, avoiding local minima for robust control.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Networked Systems

    Background:

    • Decentralized H2 state-feedback control for networked discrete-time systems with positivity constraints is a complex problem.
    • Existing methods often provide only sufficient conditions, potentially leading to suboptimal solutions.
    • The inherent nonconvexity of the problem for single positive systems presents significant challenges.

    Purpose of the Study:

    • To investigate the decentralized H2 state-feedback control problem for networked discrete-time positive systems.
    • To develop necessary and sufficient synthesis conditions, overcoming limitations of existing approaches.
    • To propose a primal-dual iterative algorithm that guarantees convergence to the global minimum.

    Main Methods:

    • Utilizing a primal-dual scheme to derive control synthesis conditions.
    • Formulating equivalent conditions for networked positive systems.
    • Developing a primal-dual iterative algorithm for solving the control problem.
    • Employing simulation examples for validation.

    Main Results:

    • Established necessary and sufficient conditions for decentralized H2 state-feedback control in networked positive systems.
    • Developed a primal-dual iterative algorithm that avoids local minima.
    • Demonstrated the effectiveness of the proposed method through two simulation examples.

    Conclusions:

    • The primal-dual scheme offers a robust framework for solving the challenging decentralized H2 state-feedback control problem.
    • The proposed algorithm ensures convergence to optimal solutions, unlike methods relying solely on sufficient conditions.
    • The findings advance the theory and practice of control for networked positive systems.