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<p>This study examines the use of Kirchhoff’s law algorithm (KLA) to calibrate a two-degree-of-freedom PID (2DOF-PID) controller for temperature regulation in a non-linear continuous stirred tank reactor (CSTR). The reactor model shows strong thermal nonlinearity. It also shows a noticeable time delay. This is based on the coupled mass and energy balance equations. This makes accurate temperature control much more difficult. These effects were addressed by KLA, which is formulated as a physics-based optimization method rather than a learning or data-driven method. The algorithm produced a set of controller gains that yielded faster, more stable responses by treating the current–voltage equilibrium of electrical circuits as an energy-balanced search method. The optimally tuned 2DOF-PID controller has lower rise and settling times, and minimal steady-state error, compared with the other standard optimizers tested in an identical manner. The results show that combining KLA with controller design can improve both robustness and control accuracy for non-linear thermal systems.</p>

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Enhanced control of continuous stirred tank reactor with two-degree-of-freedom PID driven by Kirchhoff’s law algorithm

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月27日

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  • Gökhan Yüksek,
  • Serdar Ekinci,
  • Musa Yılmaz

摘要

This study examines the use of Kirchhoff’s law algorithm (KLA) to calibrate a two-degree-of-freedom PID (2DOF-PID) controller for temperature regulation in a non-linear continuous stirred tank reactor (CSTR). The reactor model shows strong thermal nonlinearity. It also shows a noticeable time delay. This is based on the coupled mass and energy balance equations. This makes accurate temperature control much more difficult. These effects were addressed by KLA, which is formulated as a physics-based optimization method rather than a learning or data-driven method. The algorithm produced a set of controller gains that yielded faster, more stable responses by treating the current–voltage equilibrium of electrical circuits as an energy-balanced search method. The optimally tuned 2DOF-PID controller has lower rise and settling times, and minimal steady-state error, compared with the other standard optimizers tested in an identical manner. The results show that combining KLA with controller design can improve both robustness and control accuracy for non-linear thermal systems.