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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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Sliding Mode Control with Dynamical Correction for Time-Delay Piezoelectric Actuator Systems.

Javier Velasco1, Oscar Barambones2, Isidro Calvo2

  • 1Fundación Centro de Tecnologías Aeronáuticas (CTA), Juan de la Cierva 1, 01510 Miñano, Spain.

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Summary

This study introduces a novel control strategy for time-delay micropositioning systems. The proposed method enhances accuracy and response speed, outperforming traditional methods, especially for high-frequency setpoint changes.

Keywords:
dynamical correctionmicropositioning systempiezoelectric actuatorrobust controlsliding mode controltime-delay mechanism

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Area of Science:

  • Control Systems Engineering
  • Mechatronics
  • Robotics

Background:

  • Piezoelectric actuators (PEAs) exhibit nonlinearities, making precise control challenging.
  • Time delays in micropositioning systems degrade the performance of conventional feedback controllers like Proportional-Integral (PI) and Sliding Mode Control (SMC).
  • High controller gains, often required to compensate for delays, can lead to overcompensation, slow, and inaccurate responses.

Purpose of the Study:

  • To develop a novel control strategy for micropositioning systems with time delays.
  • To achieve precise positioning by combining open-loop control with a modified SMC scheme.
  • To mitigate the negative effects of time delays and system nonlinearities on control performance.

Main Methods:

  • An exhaustive analysis of the micropositioning system dynamics was performed.
  • A modified SMC scheme, termed SMC with dynamical correction (SMC-WDC), was developed to adapt control inputs based on the system model.
  • A mixed control strategy combining inverse open-loop control and SMC-WDC was implemented.

Main Results:

  • The proposed SMC-WDC strategy demonstrated superior performance compared to PI and standard SMC.
  • SMC-WDC achieved the fastest response and highest accuracy, particularly for sudden setpoint changes above 10 Hz.
  • Integral control was found to be counterproductive at frequencies above 10 Hz due to increased delay, but acceptable below 1 Hz.

Conclusions:

  • SMC-WDC is an effective strategy for precise micropositioning in the presence of time delays and uncertainties.
  • The novel approach ensures fast and accurate setpoint tracking without undesirable control effects like chattering.
  • The findings provide valuable insights into controller design for time-delayed micropositioning applications.