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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.
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Related Experiment Video

Updated: May 23, 2026

Experimental Investigation of the Hierarchical Control in DC Microgrids Using a Real-time Simulator
06:04

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Published on: February 14, 2025

Data-Driven Internal Model Control for Output Regulation.

Wenjie Liu, Yifei Li, Jian Sun

    IEEE Transactions on Cybernetics
    |May 21, 2026
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a data-driven approach for output regulation in unknown systems, even with noisy data. It achieves zero tracking error by integrating the internal model principle with data-based linear matrix inequalities.

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    The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy
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    Published on: October 14, 2017

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    Published on: February 14, 2025

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    The Modular Design and Production of an Intelligent Robot Based on a Closed-Loop Control Strategy

    Published on: October 14, 2017

    Area of Science:

    • Control Theory
    • Data-Driven Control
    • Systems Engineering

    Background:

    • Output regulation is a core control theory problem, traditionally requiring known system models.
    • Data-driven control offers solutions for unknown systems, but struggles with noisy data in existing methods.
    • Existing data-driven output regulator equations (OREs) fail to achieve zero tracking error with noisy data.

    Purpose of the Study:

    • To address the output regulation problem for unknown single and multiagent systems (MASs) using noisy data.
    • To overcome limitations of existing data-driven methods by incorporating the internal model principle.
    • To achieve exact output regulation (zero tracking error) in data-driven control frameworks.

    Main Methods:

    • Leveraging Willems et al.'s fundamental lemma for data-driven control.
    • Applying the internal model principle to robust output regulation.
    • Solving data-based linear matrix inequalities (LMIs) for controller design.
    • Extending the framework to nonlinear systems and multiagent systems (MASs).

    Main Results:

    • Exact output regulation (zero tracking error) is achieved for linear time-invariant (LTI) systems via data-based LMIs.
    • The proposed framework is successfully extended to nonlinear systems and both linear and nonlinear MASs.
    • Numerical tests confirm the efficacy of the developed data-driven controllers.

    Conclusions:

    • The internal model principle, combined with data-based LMIs, provides an effective solution for output regulation with noisy data.
    • This data-driven approach enables precise control of unknown systems, including complex multiagent systems.
    • The study advances data-driven control by enabling zero tracking error in challenging scenarios.