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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.
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Related Experiment Video

Updated: May 16, 2025

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
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Trajectory tracking control for ships with fixed-time prescribed performance considering input saturation and dead

Yunsong Lei1, Xianku Zhang1, Shihang Gao1

  • 1Key Lab. of Marine Simulation and Control, Navigation College, Dalian Maritime University, Dalian 116026, China.

ISA Transactions
|April 3, 2025
PubMed
Summary

This study introduces a novel fixed-time control method for underactuated ships, enhancing trajectory tracking despite disturbances and actuator issues. The new approach ensures faster, smoother performance and improved stability.

Keywords:
Fixed-time convergenceInput dead zone and saturationPrescribed performance controlTrajectory tracking

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Area of Science:

  • Marine engineering
  • Control systems theory
  • Robotics

Background:

  • Underactuated ships face challenges in trajectory tracking due to external disturbances, model uncertainties, and actuator limitations like saturation and dead zones.
  • Existing control methods often struggle with fixed constraint boundaries and slow convergence rates.
  • Addressing these limitations is crucial for reliable autonomous navigation and operation of underactuated vessels.

Purpose of the Study:

  • To design a fixed-time prescribed performance trajectory tracking control method for underactuated ships.
  • To overcome limitations of traditional methods by using adaptive prescribed performance functions and fixed-time convergence.
  • To ensure robust trajectory tracking under unknown disturbances, uncertainties, and actuator nonlinearities.

Main Methods:

  • Utilized barrier Lyapunov functions and prescribed performance functions to constrain position tracking errors.
  • Employed Radial Basis Function (RBF) neural networks for estimating model uncertainties.
  • Developed an adaptive control law incorporating fixed-time convergence theory and sliding mode surfaces.

Main Results:

  • Proven global fixed-time convergence for velocity tracking errors through Lyapunov stability analysis.
  • Demonstrated successful trajectory tracking in simulations despite actuator saturation and dead zones.
  • Achieved significantly improved performance indicators, including reduced settling time and smoother input curves compared to traditional methods.

Conclusions:

  • The proposed fixed-time control method effectively enables underactuated ships to achieve precise trajectory tracking.
  • The approach offers enhanced robustness against disturbances and actuator nonlinearities.
  • The controller's performance is superior to existing methods, aligning better with practical engineering requirements.