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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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Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
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Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
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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.
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Updated: Sep 4, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Recoil attenuation for deepwater drilling riser systems via delayed H∞ control.

Wei Zhang1, Bao-Lin Zhang1, Qing-Long Han2

  • 1College of Automation and Electronic Engineering, Qingdao University of Science & Technology, Qingdao, Shandong 266061, China.

ISA Transactions
|July 21, 2022
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Summary

This study introduces active H∞ control with delayed states to suppress recoil in deepwater drilling riser systems. Proper time-delays enhance recoil suppression, offering effective control options.

Keywords:
controlRecoil controlRecoil responseRiserTime-delay

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Area of Science:

  • Ocean Engineering
  • Control Systems Engineering
  • Robotics and Automation

Background:

  • Deepwater drilling riser systems face significant recoil challenges.
  • Existing control methods may not adequately address dynamic recoil forces.
  • Platform heave motion and drilling fluid friction exacerbate riser instability.

Purpose of the Study:

  • To develop and analyze an active H∞ control strategy for deepwater drilling riser recoil suppression.
  • To investigate the impact of incorporating delayed states and artificial time-delays into the control system.
  • To optimize artificial time-delays for improved recoil control performance.

Main Methods:

  • Established an incremental dynamic equation for a three degrees of freedom spring-mass-damping riser model.
  • Designed a delayed state feedback H∞ controller utilizing both current and delayed states.
  • Formulated optimal artificial time-delay design as a minimization problem of quintic algebraic polynomials.

Main Results:

  • Delayed H∞ controllers significantly controlled riser recoil responses.
  • Delay-free H∞ control showed a faster decay rate but incurred higher control costs.
  • Optimized time-delays positively influenced recoil suppression, providing flexible control solutions.

Conclusions:

  • Active H∞ control with delayed states is effective for deepwater drilling riser recoil suppression.
  • Artificial time-delays can be strategically employed to enhance control performance and reduce costs.
  • The proposed control schemes offer valuable options for managing riser dynamics in offshore operations.