Economic nonlinear model predictive control of fatigue—Formulation and application to wind turbine control

Abstract

AbstractIn this article, the estimation of fatigue is implemented in the cost function of a gradient‐based model predictive controller (MPC). This is a challenging problem, because calculating fatigue leads to a non‐standard and discontinuous cost function. Based on a brief previous publication, in the present work the method is derived, explained, and assessed in detail. The key enablers of the proposed method are a sequential implementation of MPC, the periodic substitution of discontinuous aspects of the cost function by linear functions, and the assumption of a sufficiently infrequent switching of this substitution. Fatigue cost gradients are obtained efficiently by automatic differentiation. The method is implemented in an economic nonlinear model predictive controller (ENMPC), which optimally balances revenue and fatigue cost. This novel formulation is applicable to a very wide range of domains, and it is demonstrated here on the control of a wind turbine. The proposed ENMPC is fully parameterized by physical and monetary variables, and outperforms a conventional ENMPC based on the literature. The method is assessed by considering various metrics, including frequency spectra, damage estimation, switching, and gradient dynamics, which together provide useful insight into its main characteristics and an initial assessment of its performance.