Fuzzy inference modeling method based on T-S fuzzy system

Abstract

In this paper, a kind of fuzzy inference modeling method based on T-S fuzzy system is proposed. Firstly, the T-S fuzzy inference rules “If x is A _i and y is B _j , then $z=c_{\mathit{ij}}^0+c_{\mathit{ij}}^{1}x+c_{\mathit{ij}}^{2}y$” are transformed into a fuzzy system $z={\sum }_{k=i}^{i+1}{\sum }_{l=j}^{j+1}{A}_k\left(x\right)B_l\left(y\right)z_{\mathit{kl}}$. Secondly, the variants (y, $\dot{y}$) and $\ddot{y}$ in the second-order freedom movement systems are considered as input variants and output variant respectively, then we obtain a nonlinear differential equation model with variable coefficients. Thirdly, this method is applied to build the mathematical modeling for time-invariant and time-varying second-order freedom movement systems, and new input-output models and new state-space models are obtained respectively. Finally, we have given the approximation accuracy of the constructed differential equation model and shown the effectiveness and superiority of presented method through simulation experiments and comparing the maximum errors.