Optimized fractional-order PID (FOPID) controller for two-wheeled self-balancing robots(TWSBR) using Multi-strategy improved Beluga Whale optimization algorithm(MSBWO)

In recent years, fractional-order controllers have seen a rise in popularity. These controllers provide researchers with increased flexibility in design, with intelligent optimization algorithms playing a critical role in parameter tuning. This study employs FOPID controllers for the control of a TWSBR. To ensure optimal performance, all controllers are optimized using intelligent algorithms. FOPID controllers introduce two additional parameters, $\lambda$ and $\mu$, resulting in a total of five parameters to optimize. The performance of each algorithm is influenced not only by its distinct structure but also by the specific characteristics of the optimization problem. Therefore, this paper introduces a Multi-strategy Improved Beluga Whale Optimization (MSBWO) algorithm and conducts a comprehensive performance evaluation. The parameters of the FOPID controller are fine-tuned using various popular algorithms, and the resultant system performances are compared. The results indicate that the FOPID controller, when optimized by MSBWO, outperforms other algorithms and consistently surpasses the performance of the integer-order PID controller under identical conditions. Mathematics Subject Classification (2020) 93C10 · 93C40 · 49M37 · 26A33