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Effective proportional–integral–derivative controller tuning is critical for attaining high-performance operation in direct current motor systems, especially when traditional approaches fail under nonlinear or uncertain dynamics. This study conducted a statistically robust comparative analysis of seven evolutionary algorithms for proportional–integral–derivative gain tuning: genetic algorithm, particle swarm optimisation, shuffled frog leaping algorithm, firefly algorithm, artificial bee colony, simulated annealing and invasive weed optimisation algorithm. Simulations were performed in MATLAB/Simulink using two different tuning scenarios: Case 1 (conservative bounds) and Case 2 (aggressive bounds), with the integral time absolute error serving as the primary performance metric. Analysis of variance, Tukey's honestly significant difference and Cohen's d were employed to ensure statistical validity. The results revealed distinct trade-offs among the algorithms. Particle swarm optimisation achieved the best overall performance, with a minimal integral time absolute error mean of 190.54 in Case 2, low volatility and a moderate execution time of 1200.19 s. The invasive weed optimisation algorithm was the fastest algorithm, with execution times of 285.76 and 371.43 s in Cases 1 and 2, respectively, but it exhibited higher integral time absolute error variability. Simulated annealing and the firefly algorithm yielded the lowest integral time absolute error means (158.74 and 160.22, respectively) in Case 1, but they required the highest computational time (up to 20,567.84 s for simulated annealing). In contrast, the artificial bee colony performed the worst, with a Case 2 integral time absolute error mean of 422.38 and significant gain inconsistency. Statistical analysis with analysis of variance, Tukey's honestly significant difference and Cohen's d revealed the significance of the differences. This work provides evidence-based guidance for selecting evolutionary algorithms in proportional–integral–derivative tuning based on system priorities. A hybrid invasive weed optimisation algorithm–particle swarm optimisation framework is proposed as a promising future direction, combining the rapid global search of invasive weed optimisation algorithm with the reliable convergence of particle swarm optimisation for real-time, high-precision control.

DC motors power many everyday systems, from robots to electric vehicles. To control them effectively, engineers use PID controllers, but tuning these controllers can be difficult. This study compared seven computer algorithms inspired by natural processes to find the best way to tune PID settings. Results showed that Particle Swarm Optimisation (PSO) gave the most reliable overall performance, while Invasive Weed Optimisation (IWOA) was fastest but less consistent. The study provides practical guidance on choosing the right method based on priorities.

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Comparative analysis of evolutionary algorithms for optimising proportional–integral–derivative control in direct current motor speed regulation: A statistical evaluation