Analysis and design of Coleman transform-based individual pitch controllers for wind-turbine load reduction

As the size of wind turbines increases, the effects of dynamic loading on the turbine structures become increasingly significant. There is therefore a growing demand for turbine control systems to alleviate these unsteady structural loads in addition to maintaining basic requirements such as power and speed regulation. This has motivated the development of blade individual pitch control (IPC) methodologies, many of which employ the Coleman transformation to simplify the controller design process. However, and as is shown in this paper, the Coleman transformation significantly alters the rotational system dynamics when these are referred to the non-rotating frame of reference, introducing tilt-yaw coupling in the process. Unless this transformation is explicitly included in the model employed for IPC design, then the resulting controllers can yield poor performance. Therefore, in this paper, we show how to model the Coleman transformation in a form that is amenable to IPC analysis and synthesis. This enables us to explain why traditional design parameters of gain and phase margin are poor indicators of robust stability and hence motivate the need for a multivariable design approach. The robust multivariable IPC approach advocated in this paper is based upon H∞ loop shaping and has numerous desirable properties, including reliable stability margins, improved tilt-yaw decoupling and simultaneous rejection of disturbance loads over a range of frequencies. The design of a robust multivariable IPC is discussed, and simulation results are presented that demonstrate the efficacy of this controller, in terms of load reduction on both rotating and non-rotating turbine parts.