Comparative performance evaluation of meta-heuristic optimization algorithms for tuning PID gains in dual-axis solar tracking systems

Abstract

This work addresses the growing need for energy-efficient and accurate control in solar tracking systems, where precise alignment with the sun must be achieved without excessive actuator energy consumption. To this end, a novel proportional-integral-derivative (PID) controller tuning framework is proposed based on a dual-objective cost function that simultaneously minimizes both the integral time-weighted absolute error (ITAE) and the control effort, where the first objective is a measure of tracking accuracy, and the latter serves as a normalized approximation of control energy consumption. First, a complete model of the dual-axis solar tracking system is presented. Then, a PID controller is applied to minimize the tracking error. Next, the PID gains tuning is formulated as a multi-objective optimization problem, and five recent metaheuristic algorithms are applied to solve this problem. These algorithms are the Grey Wolf optimizer (GWO), the Aquila Optimizer (AO), the Manta Ray foraging optimization (MRFO), the Harris Hawks Optimization (HHO), and the gradient-based optimizer (GBO). All these algorithms are applied under consistent settings and benchmarked using 50 Monte Carlo simulations. Besides, they are compared based on their ability to achieve the best and mean solutions, standard deviation, computational effort, number of iterations, and convergence behavior. From the perspective of controller performance, the evaluation includes overshoot, settling time, steady-state error, and control energy consumption. Under these criteria, the GWO achieved the best cost values. All algorithms, however, exhibited overshoot limited to below 0.06% and settling times under 2 s. While from the perspective of algorithm performance, AO demonstrated the fastest average run-time and GWO was the lowest standard deviation, while MRFO achieved the lowest overshoot and GBO achieved the minimum energy consumption. The proposed framework outperforms existing approaches by integrating actuator energy into the control objective and validating statistical robustness through extensive simulation, thus offering a reliable, energy-aware strategy for real-time solar tracking deployment.