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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.
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Related Experiment Video

Updated: Jun 7, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

Flexible Prescribed-Time Optimal Control With Adaptive State-Input Constraint Bounds via Actor-Critic Learning.

Junkai Tan, Shuangsi Xue, Hui Cao

    IEEE Transactions on Neural Networks and Learning Systems
    |June 5, 2026
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel framework for optimal tracking in nonlinear systems, ensuring prescribed-time (PT) convergence despite state and input constraints. The method enhances safety and operational flexibility by adaptively managing constraint boundaries.

    Related Experiment Videos

    Last Updated: Jun 7, 2026

    WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
    08:18

    WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

    Published on: August 15, 2020

    Area of Science:

    • Control Systems Engineering
    • Nonlinear System Analysis
    • Optimal Control Theory

    Background:

    • Traditional control systems often struggle with simultaneous state and input constraints.
    • Achieving optimal tracking within a prescribed time (PT) under constraints is a significant challenge.
    • Existing methods can be conservative, limiting operational regions and safety margins.

    Purpose of the Study:

    • To develop a flexible prescribed-time (PT) optimal tracking framework for nonlinear systems.
    • To address concurrent state and input constraints effectively.
    • To guarantee user-assigned convergence accuracy and time, independent of initial conditions.

    Main Methods:

    • A time-varying auxiliary function for PT error transformation.
    • A state-triggered adaptation law for online adjustment of state/input performance envelopes.
    • An actor-critic adaptive dynamic programming (ADP) scheme to solve the Hamilton-Jacobi-Bellman (HJB) equation.

    Main Results:

    • Demonstrated a flexible constraint-handling mechanism that reduces conservatism and enlarges feasible operation regions.
    • Achieved uniform ultimate boundedness of all closed-loop signals.
    • Proved prescribed-time (PT) convergence of the tracking error with user-assigned accuracy and time.

    Conclusions:

    • The proposed PT optimal tracking framework offers superior transient tracking and reliable convergence performance.
    • The adaptive constraint-handling mechanism preserves safety margins while enhancing operational flexibility.
    • Validated through simulations on nonlinear systems and fault-tolerance scenarios, outperforming baseline methods.