Nonfragile Sampled-Data Control for Interval Type-2 Fuzzy Modeling of Permanent Magnet Synchronous Generator-Based Wind Turbine Systems

The primary objective of this article is to develop an interval type-2 (IT-2) fuzzy controller scheme for analyzing the stability properties of nonlinear permanent-magnet synchronous generator (PMSG)-based wind turbine system (WTS) under external disturbances and parameter uncertainties. More specifically, an IT-2 fuzzy nonfragile sampled-data controller (FNSDC) scheme is presented to reduce the impact of controller uncertainties and save information processing resources. First, the dynamics of PMSG-based WTS are represented by an IT-2 fuzzy modeling technique due to the nonlinearities in the proposed wind turbine model. Second, a new Auxiliary Polynomial-Based Integral Inequality (APBII) is introduced to estimate the quadratic integral terms involving the sampling-related information. Also, a relaxed APBII (RAPBII) is proposed as a special case of APBII to provide extra flexibility. Meanwhile, a novel double-sided looped Lyapunov functional (DSLLF) is constructed to reduce model conservatism, which utilizes the full advantage of actual sampling pattern characteristics. The main challenge of the study is how to design the FNSDC to guarantee the asymptotic stability conditions under the maximal sampling-data period for the addressed WTS in the presence of external disturbances and parameter uncertainties. For this purpose, by combing the DSLLF with the proposed integral inequalities, some less conservative sufficient criteria are derived in the context of the linear matrix inequalitys (LMIs) frameworks, and simultaneously, disturbance reduction is confirmed via an
$H_{\infty }$
control theory. Finally, to prove the effectiveness and applicability of the proposed theoretical observations, the numerical simulations of PMGS-based WTS are validated numerically by considering the experimental range of parameter values. And then, a comparative example is also given to emphasize the superiority and relevance of the proposed method. In addition to comparing with the existing literature, a maximal sampling-data period can be able to attain by this method.