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

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.