A challenging topic arising in dynamic wind turbine wake is modeling, especially the low-order approximation. The central problem is the fact that it has high-dimensional and nonlinear wake characteristics. In this paper, a Koopman-linear flow estimator is designed according to the Koopman operator theory. Different from the conventional flow reconstruction with the linear stochastic estimation method, a dynamic state-space model with physical states is constructed. The wake dynamics are approximated using a limited number of measurable physical parameters by the dynamic part; then, the full wake flow is reconstructed from the low-order states by the estimation part. The flow estimator is designed into three different forms following Extended Dynamic Mode Decomposition (EDMD) method. Each form has its unique advantages. Precisely, probe sensors are placed in the studied space and provide direct information of the wake, and a few in-directly physical parameters are also included. Nonlinear integer programming is further adopted using a heuristic optimization algorithm, by which the sensor configurations are optimized. Comparisons with the standard Dynamic Mode Decomposition (DMD)-based wake model are adopted in time domain and frequency domain to verify the effectiveness of the proposed flow estimators. The results show acceptable accuracy in typical modeling cases and maintain good estimation accuracy when the measurement noises are involved. Finally, the proposed Koopman-linear flow estimator is compared with related stochastic estimation methods, in which the connections of the proposed estimator with stochastic ones are also discussed.

This paper proposes a controller design for the electric pump of a deep-throttling rocket engine. The nonlinearity of the system is taken into consideration by analyzing the gap metric. Then, proportional-integral-derivative controller and gain-scheduling linear quadratic regulator are designed. Analyzing the amplitude- and phase-frequency characteristics as well as the pole-zero distribution of the system, the results show that the designed controllers can stabilize the linearized equations in incremental form at different operating points. This indicates that these two controllers are available for the original system in the whole range of working conditions and this is verified in the simulation. Meanwhile, the comparison between proportional-integral-derivative controller and gain-scheduling linear quadratic regulator is presented. It demonstrates that the proportional-integral-derivative controller is better at tracking both step and ramp signals but with worse control signals. It means that the proportional-integral-derivative controller seems less suitable for real use due to severe oscillations. Meanwhile, the parameter tuning of a proportional-integral-derivative controller depends on more extensive manual tuning. Therefore, the gain-scheduling linear quadratic regulator is preferred. 

For the study of wind farm and wake effect, the steady-state wake models like FLORIS were proposed and used during wind farm operations to achieve higher wind power utilization and conversion. However, the dynamic performance of the wake should also be involved in favor of better optimizations. In this paper, a data-driven analysis and modeling method, dynamic mode decomposition (DMD), is used to construct dynamic flow model with high-fidelity flow data. Two DMD-derived models are constructed based on flow data in three-dimensional and two-dimensional spaces, respectively. The obtained models and respective flows are compared in the time and frequency domain. Results show that both models have apparent differences in the frequency domain, but the dominant wake characteristics' consistency is maintained.