Fractional Order Proportional Integral Derivative Controller for Effective Liquid Level Control in Spherical Tanks Using a Hybrid Approach

Liquid Level (LL) regulation in spherical tank systems involves controlling the liquid height to ensure stable operation, but its drawback is the difficulty of accurately measuring and controlling the level due to the tank’s non-cylindrical shape. This paper describes a hybrid approach for the Fractional Order Proportional Integral Derivative (FOPID) Controller to reach the LL in a spherical tank. The proposed hybrid approach, also known as the EOO-MSNN strategy, combines the capabilities of the Mix Style Neural Network (MSNN) and the Eurasian Oystercatcher Optimizer (EOO). The primary goal of the proposed technique is to reduce external disturbances, improve the efficiency of liquid level control and minimize overshoot and settling time. The MSNN is utilized to forecast the liquid level and additive concentration in the liquid, while the EOO is used to adjust the parameters of the FOPID controller. Subsequently, the proposed method’s performance is evaluated using the MATLAB platform and compared with other approaches currently in use. Simulation results demonstrate that the proposed controller achieves a rise time of 0.047[Formula: see text]ms, settling time of 1.163[Formula: see text]ms and zero overshoot, while minimizing error indices with ITSE of 0.00006 under nominal conditions. Robustness tests confirm stable operation under [Formula: see text]10% inlet disturbances and [Formula: see text]% valve coefficient variations, where the proposed method shows only marginal increases in error indices but maintains stability and convergence to the set point without overshoot. Compared with conventional optimization methods like Cuckoo Search Algorithm, Particle Swarm Optimization and Harmony Search Optimization, the proposed EOO–MSNN framework demonstrates superior accuracy, faster response and stronger robustness, highlighting its potential for real-time industrial applications.