In this chapter, the design of a nonlinear rotor-side controller is described for a variable pitch wind turbine based on nonlinear, H2 optimal control theory. The objective is to demonstrate the synthesis and application of a maximum power point tracking (MPPT) algorithm. In the case of a variable pitch wind turbine, the blade collective pitch angle is controlled to ensure that the turbine is not overloaded. In the case of such turbines the blade pitch may be treated as unknown input and the actual pitch angle is estimated in real time from torque measurements. The algorithm uses a non-linear estimation technique and maximizes an estimate of the actual power transferred from the turbine to the generator. It is validated by simulating the wind-turbine’s dynamics. It is shown that the MPPT algorithm performs within prescribed error bounds both in the case when no disturbances are present, as it is an indicator of the validity of the algorithm and in cases when significant levels of wind disturbances are present.
Part of the book: Wind Turbines
The classical approach to the problem of synthesizing an optimal attitude manoeuver trajectory, involves the use of the calculus of variations and the use Lagrange multipliers or co-states. The nonlinear large attitude manoeuver trajectory is controlled by a set of nonlinear evolving co-states. In this paper, following a review of the methodologies available for trajectory synthesis followed by tracking control, the optimal trajectory for a typical optimal attitude manoeuver is synthesized by solving for the states and co-states defined by a two point boundary value problem. Gravity gradient torques are included as a matter of course. Following the synthesis of the optimal attitude-rate trajectory, tracking control laws are synthesized by re-formulating the optimal control as a feedback law. The approximate linear tracking feedback controls are evaluated by relating the optimal state and co-state vector by a linear relation. The control laws are synthesized numerically. The problem of optimal attitude orientation trajectory synthesis is also addressed. The methodologies are applied to typical sample problems and results are presented. Quantitative comparisons of the results of the methods are made to the results obtained by the application of other linear and nonlinear methods, to illustrate the key features of the methodologies.
Part of the book: Advances in Spacecraft Attitude Control