Controlling A Meandering Wake

Abstract

In this thesis we present a technique to design measurement feedback H_2 controllers for high-order nonlinear systems. The approach presented in this thesis allows insights into choosing potential measurement locations for designing measurement feedback controllers for the high-order nonlinear systems. This approach is fairly general and only requires that snapshots of system state, inputs and outputs can be collected. In this thesis, the proposed control design technique is validated on a simplified wind farm model to reduce wake meandering behind wind turbines. The control design and analysis proceeds in multiple steps. First, a linear reduced order model of the turbine is obtained using snapshots from a higher-order nonlinear 2D actuator disk model. A static full-information feedback H_2 controller is synthesized for the reduced order linear model by solving a set of linear matrix inequalities. The full-information controller has access to all the reduced-order model states as well as disturbance. The state feedback gains from full-information feedback control design are lifted to approximate the state feedback gains for the full-order system states. The magnitude of these lifted gains provides information about the full-order states most important to the controller. The measurement points for a measurement-feedback design are then determined using these state locations. Another reduced-order model is obtained for measurement feedback design and a dynamic measurement feedback H_2 controller is designed for it. The control performance is evaluated by simulations on the higher order nonlinear model. The approach to design a measurement feedback controller is also extended to parameter varying models using gain-scheduling.