Parameter-coupled state space models based on quasi-Gaussian fuzzy approximation

Abstract

The accuracy of a fuzzy system’s approximation is closely tied to the performance of fuzzy control systems design, while this system’s interpretability depends on the description of a mechanical model using human language. This research introduces a quasi-Gaussian membership function characterized by a pair of parameters to achieve the sensitivity of a triangular membership function along with the interpretability of Gaussian membership functions. Consequently, a two-dimensional (2-D) quasi-Gaussian membership function is derived, and a method for establishing quasi-Gaussian fuzzy systems (QGFS) using a rectangular grid is proposed. After validating the approximation properties using the sine function for the one-dimensional (1-D) and 2-D QGFS, the systems are applied to approximate the depyrogenation tunnel, a significant piece of equipment in the pharmaceutical industry with various mechanical designs. Validation results indicate that the 1-D and 2-D QGFS can achieve an approximation error varying within a ± 5% range. Meanwhile, the 1-D and 2-D QGFSs are applied to mechanical models of the depyrogenation tunnel with satisfactory final approximation results. Lastly, the 2-D QGFS is capable of demonstrating an excellent description of models with coupled parameters.