Parameters Tuning of Fractional-Order Proportional Integral Derivative in Water Turbine Governing System Using an Effective SDO with Enhanced Fitness-Distance Balance and Adaptive Local Search

Supply-demand-based optimization (SDO) is a swarm-based optimizer. However, it suffers from several drawbacks, such as lack of solution diversity and low convergence accuracy and search efficiency. To overcome them, an effective supply-demand-based optimization (ESDO) is proposed in this study. First, an enhanced fitness-distance balance (EFDB) and the Levy flight are introduced into the original version to avoid premature convergence and improve solution diversity; second, a mutation mechanism is integrated into the algorithm to improve search efficiency; finally, an adaptive local search strategy (ALS) is incorporated into the algorithm to enhance the convergence accuracy. The effect of the proposed method is verified based on the comparison of ESDO with several well-regarded algorithms using 23 benchmark functions. In addition, the ESDO algorithm is applied to tune the parameters of the fractional-order proportional integral derivative (FOPID) controller of the water turbine governor system. The comparative results reveal that ESDO is competitive and superior for solving real-world problems.