Optimal PID Level Control of a Nonlinear Spherical Tank Using a Hybrid WOA–GA Optimization Approach

Abstract

Level control of spherical tank systems is challenging due to strong process nonlinearity and varying dynamics across different operating regions. Traditional PID tuning methods and standalone optimization techniques often fail to ensure consistent performance under such conditions. In this paper, a novel hybrid Whale Optimization Algorithm–Genetic Algorithm (WOA–GA)–based approach is proposed for PID controller tuning and implemented on a nonlinear spherical tank model. The proposed hybrid optimization strategy combines the rapid exploitation capability of WOA with the global search ability of GA, enabling effective optimization of PID parameters for nonlinear system dynamics. A nonlinear mathematical model of the spherical tank is developed and utilized for both simulation studies and real-time experimental implementation. The performance of the proposed WOAGA–PID controller is evaluated and systematically compared with WOA–PID and GA–PID controllers using standard time-domain performance indices, including ITAE, rise time, settling time, peak time, and maximum overshoot. Both simulation and experimental results demonstrate enhanced transient response, robustness, and reliability, thereby validating the suitability of the proposed method for nonlinear process control applications.