<![CDATA[This paper presents a comparative study of the Grasshopper Optimization Algorithm (GOA) with three suggested modified versions—Levy Flight GOA (LFGOA), Dynamic Attraction-Repulsion GOA (DARGOA), and Chaotic GOA (CHGOA)—for tuning Proportional-Integral-Derivative (PID) controller parameters in a nonlinear Single-Input Single-Output (SISO) system. The research contribution is the development and evaluation of CHGOA, which aims to improve convergence speed and transient response stability. The methodology employs exploratory and exploitative mechanisms of each algorithm to optimize PID parameters based on six objective functions. Performance metrics include rise time, settling time, overshoot, peak value, and best fitness obtained from MATLAB/Simulink simulations. A second-order Mass-Spring-Damper (MSD) system is used as a representative nonlinear SISO system. Simulation results indicate that the proposed CHGOA consistently achieves lower fitness values, faster convergence, and stable transient responses compared to LFGOA, DARGOA, and standard GOA, under the tested objective functions. While LFGOA and DARGOA show competitive performance in traditional error metrics, standard GOA exhibits slower convergence in simulation scenarios. In this paper, the performance of the MSD system controlled by the proposed optimal PID with GOAs was also compared with the performance of this system with Nonlinear PIDs (NPIDs) which proposed by previous studies. The comparison results showed the efficiency of our proposed controllers in improving the performance of the MSD system, especially the CHGOA. Overall, the proposed CHGOA provides an effective balance between error minimization, convergence speed, and transient response performance, making it suitable for high-precision real-time applications.]]>
