Nonlinear Control of Floating Offshore Wind Turbines Using Input/Output Feedback Linearization and Sliding Control

Input/ output feedback linearization and smoothed sliding control methods are used to control a floating offshore wind turbine on a barge platform in high wind speed in order to regulate the power capture. The model of the turbine has the blade pitch angle as the input, generator speed, platform pitch angle and its derivative as the measurements, and wind speed as a disturbance. The designed controllers have been applied to the simplified model of the plant which is used for controller design and also a more complex model which considers all six degrees of freedom for platform movements. Moreover, their performance is compared with the baseline controller for floating offshore wind turbines [1]. Both nonlinear controllers have improved the power regulation compared to the baseline controller. Also, sliding control has been shown to have better performance than the input/ output controller, since it can consider the uncertainty of the disturbance signal in the controller design. INTRODUCTION Wind energy, as a renewable energy, is becoming more and more popular due to its cleanness and sustainability [2]. There are vast areas of sea in addition to land, available for installation of wind turbines. The reasons for offshore installation are stronger, more stable wind at sea and also less noise and visual impact compared to onshore installation. The offshore installation is realizable using a floating platform [1]. To make wind energy competitive with fossil fuel energy, the price of electricity produced by wind turbines should be reduced. The wind energy price can be reduced by increasing energy efficiency, increasing the lifetime of this expensive device, as well as reducing maintenance costs. One of the most economical ways for achieving these objectives without involving any additional hardware or modification to the structure is using feedback control. Increasing the energy efficiency for low wind speed, and regulating the energy capture for high wind speed is one of the control objectives. The other objective is reducing the platform movement; This movement induces large structural load on the system that can reduce the lifetime of the turbine as well as increasing the maintenance costs. In this paper, the high wind speed condition is considered and the objective of reduction in platform movement is not explicitly considered in the design, but it is analyzed for the obtained controllers. The mathematical model needed for designing a controller for floating offshore wind turbine is developed in [1, 3, 4]. This model is implemented in software called FAST (Fatigue, Aerodynamics, Structures, and Turbulences)1 which was developed at the National Renewable Energy Laboratory (NREL) in US [5]. A common control method for high wind speed is using a PI gain-scheduled controller to control the blade pitch angle, this method is used as a baseline controller to compare the performance; this controller can not guarantee stability [1]. Several other controllers are designed for floating offshore wind turbines; see [4, 6–8]. In this paper, two nonlinear controllers using input/output feedback linearization and smoothed sliding control are designed. The simulations are conducted using both the simplified 1http://wind.nrel.gov/designcodes/simulators/fast/. 1 plant model (used in controller design) and also the complete nonlinear model in the software FAST. The objective of these controllers is defined to regulate the power capture, and these controllers were successful in achieving this objective and they could outperform the performance of the baseline controller. This paper is organized by first obtaining the model of the system used in controller design. Then, having the control objective defined and examining the accessibility of the system, the nonlinear controllers are then designed. In the next section, these nonlinear controllers are applied to both the simplified model and the more complex model. MODELING To design a controller, it is important to acquire an accurate mathematical model for the plant. An accurate mathematical model for a floating offshore wind turbine is described in [1] which is implemented in the software FAST [5] by Jonkman. This nonlinear model has large numbers of degrees of freedom which is computationally expensive for the controller design stage, therefore, a simplified model of the turbine is obtained where the states and control inputs are defined as: x =: [Plat f ormpitchangle (p), plat f ormpitchanglerate (ṗ), rotorspeed (ωr)], u =: [Bladepitchangle(β)], d =: [windspeed]. (1) A typical floating offshore wind turbine is illustrated in figure 1. Wind can affect platform pitch movement more than other platform degrees of freedom, also this movement can degrade the power capture by deviating the relative direction of wind with respect to the rotor plane. Therefore, this degree of freedom is considered in the simplified model. Linear parameter varying (LPV) model The simplified linearized model of the turbine at different operating points, specified by different blade pitch angles, can be obtained from the software. Using these models at different blade pitch angles, the LPV model as a function of blade pitch angle (β) is obtained utilizing curve fitting techniques. ẋ = A(β)x+B(β)u+Bd(β)d (2) The parameters in (2) are parameterized as: A(β) =: A0+A1β+A2β, B(β) =: B0+B1β+B2β, (3) Bd(β) =: Bd0+Bd1β+Bd2β, Figure 1. An illustration of a floating offshore wind turbine system.