The Design Process of a 2-DOF PID Controller Applying  the Salp Swarm Algorithm for Position Control of a Linear DC Motor

Sitthisak Audomsi; Palapol Sawatphol; Thanawat Prakhongwong; Supakorn Ukumphan; Worawat Sa-Ngiamvibool; Buncha Wattana

doi:10.55674/ias.v15i2.269161

Authors

Sitthisak Audomsi, Ph.D. Faculty of Engineering, Mahasarakham University, Maha Sarakham, 44150, Thailand.
Palapol Sawatphol Faculty of Engineering, Mahasarakham University, Maha Sarakham, 44150, Thailand.
Thanawat Prakhongwong Faculty of Engineering, Mahasarakham University, Maha Sarakham, 44150, Thailand.
Supakorn Ukumphan Department of Electrical Engineering, Faculty of Engineering, Rajamangala University of Technology Lanna, Nan 55000, Thailand.
Prof. Worawat Sa-Ngiamvibool, Ph.D. Faculty of Engineering, Mahasarakham University, Maha Sarakham, 44150, Thailand.
Assistant Professor Buncha Wattana, Ph.D. Faculty of Engineering, Mahasarakham University, Maha Sarakham, 44150, Thailand.

DOI:

https://doi.org/10.55674/ias.v15i2.269161

Keywords:

2-DOF PID Controller, Controller Optimization, Linear DC Motor, Position Control, Salp Swarm Algorithm

Abstract

Conventional single-degree-of-freedom PI and PID controllers face a trade-off between fast tracking and low overshoot in precision position control. This paper investigates the design of a two-degree-of-freedom proportional-integral-derivative (2-DOF PID) controller for position control of a Linear DC Motor. The Salp Swarm Algorithm (SSA) is employed to tune the controller parameters, including the proportional gain, integral gain, derivative gain, proportional set-point weight, and derivative set-point weight. To provide a fair controller-structure comparison, the same SSA procedure is also applied to conventional PID and PI controllers under identical simulation conditions. The controller performance is evaluated in MATLAB/Simulink using a step reference input and a load disturbance of 0.10 N applied at t = 10 s over 30 independent runs. Two objective functions are considered: the integral of time-weighted absolute error (ITAE) and the integral of absolute error (IAE). The results show that the SSA-tuned 2-DOF PID controller provides the lowest objective function values for both tuning criteria. Under ITAE-based tuning, the proposed controller achieves an ITAE value of 1.5341, which is 53.02% lower than the PID controller and 54.34% lower than the PI controller. Under IAE-based tuning, it achieves an IAE value of 0.3096, which is 70.17% lower than the PID controller and 77.37% lower than the PI controller. The mean values over all runs are also the lowest among the three controllers. In addition, the proposed controller reduces overshoot (to 1.15% and 1.50% under ITAE and IAE, respectively) and undershoot compared with the SSA-tuned PID and PI controllers, with a fast rise time of 0.73 s and 0.30 s. These results demonstrate that the additional set-point weighting parameters of the 2-DOF PID structure improve the tracking performance of the Linear DC Motor position control system.

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