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

## TL;DR

This paper explores using a physics-based algorithm to improve temperature control in a complex chemical reactor.

## Contribution

The novel use of Kirchhoff’s law algorithm for tuning a 2DOF-PID controller in non-linear thermal systems.

## Key findings

- The KLA-tuned 2DOF-PID controller achieved faster and more stable temperature responses.
- The controller showed minimal steady-state error and improved robustness in non-linear systems.

## Abstract

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.