Fast and smooth surface B-spline interpolation for regularly spaced data used in system modeling to make MPC real-time feasible*

Advanced control applications require accurate system models. Obviously, these models must be evaluated sufficiently fast in order for a model-based controller to be real-time feasible. This holds for methods that are based on online optimizations, such as model predictive control (MPC), in particular. It is common to describe nonlinear static parts of system models with interpolated look-up tables, because they are computationally efficient and they can be designed to provide the required accuracy. Since the underlying data are often determined with measurements or simulations, the location of data points can be chosen by the user to some extent. We use data on regular grids and B-splines with uniform knotvectors located at the data grid points, because this results in smooth interpolated look-up tables that can be evaluated very fast. The algorithm for the online evaluation and interpolation can be extended to efficiently provide first and second order derivatives, which are, for example, needed in MPC. We illustrate the use of the implemented methods with the look-up table of the aerodynamic power coefficient of a wind turbine generator and compare computation times for an implementation on a CPU and on an FPGA.