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In an open-loop system, such as a basic thermostat, the poles of the transfer function influence the system's response but do not determine its stability. However, when feedback is introduced to form a closed-loop system, such as an advanced thermostat that adjusts heating based on room temperature, stability is governed by the new poles of the closed-loop transfer function.
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This study introduces new methods for tuning proportional-integral-derivative (PID) controllers using relay feedback tests. These techniques improve process model accuracy for stable, integrating, and unstable systems.

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Area of Science:

  • Control Systems Engineering
  • Process Identification
  • Automation Technology

Background:

  • Relay (on-off) controllers can stabilize various processes but may cause sustained oscillations.
  • Accurate process models are crucial for effective proportional-integral-derivative (PID) controller tuning.
  • Existing methods may require extensive testing or iterative computations.

Purpose of the Study:

  • To propose improved methods for proportional-integral-derivative (PID) controller tuning.
  • To develop techniques for finding accurate process models using mixed closed-loop tests.
  • To enable efficient controller tuning for diverse process types, including unstable and integrating systems.

Main Methods:

  • Utilizing mixed closed-loop tests combining relay feedback and proportional-derivative (PD) controllers.
  • Applying relay feedback tests to unknown processes from arbitrary initial states.
  • Deriving refined methods to determine exact process frequency responses from cyclic steady states.

Main Results:

  • Sustained oscillations are produced, aiding in process stabilization.
  • Accurate process models are obtained efficiently without saving entire relay feedback responses.
  • Refined methods determine frequency responses using integrals at relay switching times, avoiding iterative computations.

Conclusions:

  • The proposed methods enhance PID controller tuning for a wide range of processes.
  • Full closed-loop operation is beneficial for integrating and unstable processes, and even stable ones.
  • The techniques offer an efficient and accurate approach to process identification and controller tuning.