a b s t r a c tHigh performance and reliability are required for wind turbines to be competitive within the energy market. To capture their nonlinear behavior, wind turbines are often modeled using parameter-varying models. In this paper we design and compare multiple linear parameter-varying (LPV) controllers, designed using a proposed method that allows the inclusion of both faults and uncertainties in the LPV controller design. We specifically consider a 4.8 MW, variable-speed, variable-pitch wind turbine model with a fault in the pitch system.We propose the design of a nominal controller (NC), handling the parameter variations along the nominal operating trajectory caused by nonlinear aerodynamics. To accommodate the fault in the pitch system, an active fault-tolerant controller (AFTC) and a passive fault-tolerant controller (PFTC) are designed. In addition to the nominal LPV controller, we also propose a robust controller (RC). This controller is able to take into account model uncertainties in the aerodynamic model.The controllers are based on output feedback and are scheduled on an estimated wind speed to manage the parameter-varying nature of the model. Furthermore, the AFTC relies on information from a fault diagnosis system.The optimization problems involved in designing the PFTC and RC are based on solving bilinear matrix inequalities (BMIs) instead of linear matrix inequalities (LMIs) due to unmeasured parameter variations. Consequently, they are more difficult to solve. The paper presents a procedure, where the BMIs are rewritten into two necessary LMI conditions, which are solved using a two-step procedure.Simulation results show the performance of the LPV controllers to be superior to that of a reference controller designed based on classical principles.

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This paper presents a converse barrier certificate theorem for a generic dynamical system. We show that a barrier certificate exists for any safe dynamical system defined on a compact manifold.Other authors have developed a related result, by assuming that the dynamical system has no singular points in the considered subset of the state space. In this paper, we redefine the standard notion of safety to comply with generic dynamical systems with multiple singularities. Afterwards, we prove the converse barrier certificate theorem and illustrate the differences between ours and previous work by simple examples.

This paper proposes a compositional method for verifying the safety of a dynamical system, given as an interconnection of subsystems. The safety verification is conducted by the use of the barrier certificate method; hence, the contribution of this paper is to show how to obtain compositional conditions for safety verification.We show how to formulate the verification problem, as a composition of coupled subproblems, each given for one subsystem. Furthermore, we show how to find the compositional barrier certificates via linear and sum of squares programming problems.The proposed method makes it possible to verify the safety of higher dimensional systems, than the method for centrally computed barrier certificates. This is demonstrated by verifying the safety of an emergency shutdown of a wind turbine.