What question did this study set out to answer?

The aim is to optimize the gains of a 2-DOF PID controller for effective load frequency control in a nonlinear thermal system.

May 3, 2026Open Access

Optimal 2-DOF PID controller design for load frequency control with various nonlinearities

Key Points

The aim is to optimize the gains of a 2-DOF PID controller for effective load frequency control in a nonlinear thermal system.
Used Differential Evolution - Particle Swarm Optimization (DE-PSO) for controller gain optimization.
Considered Integral Time Absolute Error (ITAE) as the optimization criterion.
Implemented generation rate constraints to address the nonlinearities in the system.
The DE-PSO method outperforms previous approaches in optimizing PID controller gains.
Demonstrated improved settling time and reduced undershoot and overshoot compared to other controllers.
Robustness verified by introducing time delay as an additional source of nonlinearity.

Abstract

This article includes an efficient and effective hybrid optimization technique called as Differential Evolution - Particle Swarm Optimization (DE-PSO) is used to optimize the controller gains parameters of two-degree of freedom-proportional-integral-derivative controller (2-DOF-PID) by considering the Integral time absolute error (ITAE) in load frequency control of three area non-linear interconnected reheat thermal system. The nonlinearities of the system are implemented by generation rate constraints (GRC) in each of the control areas. The incompara-bility of the suggested method is recognized above some pre-published outputs. The domination of 2-DOF-PID controller in conditions of responses of the settling time, minimum undershoots & overshoot over other controllers is proved on the nonlinear system. For the verifica-tion of the robustness of the mentioned controller a time delay is introduced in the scrutinized system as a second source of nonlinearity.

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