Implicit Integrators for Linear Dynamics Coupled to a Nonlinear Static Feedback and Application to Wind Turbine Control*

Efficient integration schemes with sensitivity propagation are crucial for deploying real-time Nonlinear Model Predictive Control on systems described by continuous time dynamics. Implicit integration schemes are preferred when stiff modes are present in the model equations, or when the equations are implicit. We consider here a class of models, where the dynamics are linear, but coupled to a general static nonlinear feedback function. We propose a collocation-based implicit integration scheme where a lifting-condensing approach is used to exploit this specific structure to reduce the size of the linear algebra underlying the integrator. This technique yields a significant reduction in the computational complexity of performing the system integration and sensitivity analysis, when the static nonlinearity is of much smaller dimensions than the complete dynamics. The proposed method is illustrated on a complex wind turbine model, resulting in a significant gain of computational time in the linear algebra, and an overall gain of computational time of a factor 2.