Takagi–Sugeno fuzzy sampled‐data model‐based less conservative stability criterion for a Francis hydropower unit's governing system

Abstract

In this study, the stability analysis and controller design of a hydropower unit's governing system (HUGS) were studied based on a Takagi-Sugeno (T-S) fuzzy model and constant sampled-data control. First, according to the T-S fuzzy theory, the non-linear Francis hydro-turbine governing system under rigid water hammer is linearised and then the approximate linear system was obtained. Second, a fuzzy sampled-data controller was designed in the case of periodic sampling, and the closed-loop sampling system was discretised. After constructing the Lyapunov function and using the forward difference method, the stabilisation condition was given with less conservatism in a symmetrical linear matrix inequality form. Finally, the numerical simulation results showed that under four different sampling periods, the HUGS can quickly achieve stability and that it has different stability performance. In addition, the superiority of the controller was verified in comparison with traditional proportional-integral-derivative control and fuzzy control techniques.