Fuzzy-Based Integral Sliding Mode Control for PMSM With Fractional Stochastic Disturbances

The aim of this study is to focus on proposing the theoretical framework for investigating the stability properties of permanent magnet synchronous motors (PMSMs) considering the stochastic disturbances and parameter uncertainties in the fractional domain. To do this, the aerodynamics of PMSM is chosen as stochastic disturbances, followed by the inherent parameter uncertainties in voltage equations. In addition, for the proposed nonlinear PMSM model, an equivalent linear submodels holding same dynamical properties of PMSM are derived through Takagi–Sugeno (T–S) fuzzy approach. Besides, the derivative of white noise is considered with Hurst parameter known as fractional Brownian motion (FBM) and it holds the properties of conventional Brownian motion when Hurst parameter is chosen as 0.5. The Lyapunov stability theory is employed to derive the sufficient stability conditions that guarantee the global stable performance of the proposed fuzzy-based PMSM model. In this regard, instead of traditional Ito's differential formula, the study utilizes Ito's fractional differential formula to obtain the sufficient conditions. To validate the proposed approach, numerical experiments are performed by considering the experimental range of parameter values and the outcomes are illustrated through time-series, and phase-portraits.