Optimal design of proportional integral derivative acceleration controller for higher-order nonlinear time delay system using m-MBOA technique

In general, the parameter adjustment is used to design the proportional-integral-derivative (PID) controllers. Despite that, to enhance the capacity of control performance by adjusting parameters is limited. Therefore, in this paper, an optimal design of proportional integral derivative acceleration (PIDA) controller is proposed for higher-order nonlinear time delay system (TDS) using modified butterfly optimization algorithm (MBOA) with the aim of achieving optimal closed-loop response, which is enhanced with mutualism system (m-MBOA). In the proposed approach, the mutualism stage of symbiotic organisms search (SOS) and butterfly optimization algorithm (BOA) global exploration phase is considered. The major aim of the proposed approach is to "tune the gain of the PIDA controller to get the desired response." It reduces the drawback of the PIDA controller in the higher-order TDS using advanced control limits is the individuality of the proposed approach. Here, the proposed approach is employed to reduce the higher-order delays together with reliability limits, like minor overshoots, time resolution, and fixed stage deficiency. To evaluate the proposed PIDA controller, the execution is done by the MATLAB/Simulink platform, also its efficiency is compared with existing approaches. Moreover, the proposed and existing approaches are analyzed with mean, median, and standard deviations. From the analysis, the proposed approach achieves the stability with minimal delay time and reduces the computational complexity. Finally, the simulation results demonstrate that the proposed approach can efficiently with accurately find the optimal global solutions.