Abstract
This paper examines the stabilization problem and membership function dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> performance analysis for uncertain hydraulic turbine governing systems with stochastic actuator faults and time-varying delays via sampled-data control. At first, the nonlinear hydraulic turbine systems are modeled as Takagi-Sugeno (T-S) fuzzy systems with time-varying delay and bounded external disturbance through membership functions. Then, a novel delay-dependent looped Lyapunov-Krasovskii functional (LKF) is formulated with complete information throughout the sampling interval. In the meantime, a membership function dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> performance index is suggested to diminish the impact of disturbances on the uncertain fuzzy system. Based on the robust control and novel LKF, new delay-dependent stability conditions for the closed-loop system are attained in the framework of linear matrix inequalities (LMIs). At last, the numerical example validates the proposed theoretical contributions in terms of achieving robust stability and minimizing disturbance attenuation levels.
Highlights
D UE to the exponential rate of the population worldwide, hydropower generation is essential to satisfying clean and renewable energy demand
Modeling and dynamic response control have been investigated for hydraulic turbine governing systems (HTGSs) with surge tanks [7]
The stability analysis via sampled-data control design is still open for HTGSs with stochastic actuator fault, which is another motivation for this work
Summary
D UE to the exponential rate of the population worldwide, hydropower generation is essential to satisfying clean and renewable energy demand. Several control approaches have been used to examine the stability behavior of HTGSs, such as adaptive control [11], finite-time H∞ control [20], proportional integral derivative control [23], sliding mode control [24], etc Unlike these control techniques [11], [20], [23], [24], sampled-data control has attracted much attention due to the advantage of low-cost maintenance, easy installation, and digital technology development. The stability analysis via sampled-data control design is still open for HTGSs with stochastic actuator fault, which is another motivation for this work. The authors in [36] proved that the minimum H∞ index was obtained via the MFD H∞ technique compared with the fixed H∞ approach Still, it could not be considered for continuous-time delayed fuzzy systems. Based on the above motivations, this paper presents a TS fuzzy-model-based robust sampled-data controller for HTGSs with stochastic actuator faults and time-varying delays. I=1 i=1 h=1 ψhi(θh(t)) is the grade of membership of θh(t) in ψhi
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