Since pH neutralization processes have extremely nonlinear characteristics, controlling it might be difficult. Therefore, a special controller design is needed to handle the high nonlinearities of the process. In this study, an inverse neuro-fuzzy model-based controller (NFMBC) design is presented for control of a pH neutralization process (NP). Input-output (IO) data set of the process is collected by applying a proper excitation signal. Then, forward and inverse neuro-fuzzy models of the process are constructed by using this data set after a training process. In terms of design simplicity, a two-input-one-output model structure is chosen for both neuro-fuzzy models. These forward and inverse neuro-fuzzy models are used in a nonlinear internal model control (NIMC) structure in order to provide robustness against disturbances and model mismatches. To examine the proposed controller's performance, simulation studies are carried out under setpoint variation and disturbance conditions. Additionally, the performance of the inverse NFMBC is compared to that of a fuzzy proportional integral derivative (FPID) controller with a 7x7 rule base. The results demonstrate that the designed controller provides more effective control performance for setpoint variations and also exhibits higher robustness against disturbances in the acid flow rate than the FPID controller.

Recent advances in transportation technologies highlight the demand for faster and more efficient systems. Magnetic levitation has emerged as a key enabler in high-speed concepts such as the Hyperloop by eliminating mechanical contact, reducing friction, and improving stability. Among the different approaches, electrodynamic suspension (EDS) with Halbach array permanent magnets offers a promising solution for contactless high-speed travel, yet accurately modeling its nonlinear levitation dynamics remains challenging. This study compares a physics-based analytical model with a data-driven fuzzy logic model for a rotating Halbach array EDS system. An analytical lift-force expression is derived from electromagnetic principles and validated via three-dimensional (3D) finite-element simulations and static experiments, and a dynamic model is formulated to relate levitation gap to rotor speed. In parallel, an adaptive neuro-fuzzy inference system (ANFIS) is trained on experimental input–output data. Experimental evaluation on an independent test record shows that the fuzzy model achieves a lower root mean square error (RMSE) than the analytical model (0.0298 mm vs. 0.1064 mm). This gap reflects limits of analytical models using simplified assumptions (e.g., uniform magnetization and idealized conductivity), missing nonlinear, frequency-dependent effects. By learning directly from experimental measurements, the ANFIS model captures the aggregate influence of unmodeled nonlinearities and experimental effects within the investigated operating range. Consequently, the ANFIS-based model provides a more accurate representation of the measured levitation dynamics under the tested conditions, indicating its potential for real-time modeling and control applications in EDS systems.