Hybrid golden jackal and golden sine optimizer for tuning PID controllers

In the domain of control engineering, effectively tuning the parameters of proportional-integral-derivative (PID) controllers has persistently posed a challenge. This study proposes a hybrid algorithm (HGJGSO) that combines golden jackal optimization (GJO) and golden sine algorithm (Gold-SA) for tuning PID controllers. To accelerate the convergence of GJO, a nonlinear parameter adaptation strategy is incorporated. The improved GJO is combined with Gold-SA, capitalizing on the expedited convergence speed offered by the improved GJO, coupled with the global optimization and precise search capabilities of Gold-SA. HGJGSO maximizes the strengths of two algorithms, facilitating a comprehensive and balanced exploration and exploitation. The effectiveness of HGJGSO is assessed through tuning the PID controllers for three typical systems. The results indicate that HGJGSO surpasses the comparison tuning methods. To evaluate the applicability of HGJGSO, it is used to tune the cascade PID controllers for trajectory tracking in a quadrotor UAV. The results demonstrate the superiority of HGJGSO in addressing practical challenges.