Robust adaptive super-twisting control for floating wind turbines in region III

Wind Energy Science Conference 24-27 June 2025 Nantes, France Robust adaptive super-twisting control for floating wind turbines in region III Moein Sarbandia,Mohammad Mohammadi Shahira,Mohamed Assaad Hamidaa, and Franck Plestana aNantes Universit´ e, ´ Ecole Centrale Nantes, CNRS, LS2N, UMR 6004, F-44000 Nantes, France E-mail: [email protected] Keywords: Floating offshore wind turbine, nonlinear control, super-twisting algorithm. 1 Introduction In this paper, a robust adaptive control strategy based on the super-twisting sliding mode algorithm has been used for the control of floating offshore wind turbines (FOWTs) in above-rated wind speed. FOWTs are highly nonlinear systems, characterised by uncertainty and unmodeled dynamics. The primary objectives are to regulate power output and reduce fatigue loads on the system through a collective blade pitch control. The proposed controller effectively addresses the above-mentioned challenges without requiring prior knowledge of system uncertainties or their bounds. The performance of the robust adaptive controller was evaluated using the OpenFAST simulator. Simulation results demonstrate the efficiency of the examined method by comparing it with the reference opensource controller (ROSCO) [1], which is renowned for its reliable performance. 2 Wind turbine dynamics and modelling The present study focuses on the NREL 5-MW FOWT, which is supported by a semi-submersible floating platform and modelled using OpenFAST [2]. The aerodynamic power Pagenerated by the rotor is expressed as Pa=1 2ρπR2Cp(λ,β)v3,(1) where ρis the air density, Ris the rotor radius, vis the wind speed, and Cpis the power coefficient. The power coefficient is a function of the tip speed ratio (TSR), λ, and blade pitch angle, β. The TRS is defined as λ=ωR /v, where ωis the rotor speed. Assuming a rigid rotor and ignoring shaft friction, the nonlinear control-oriented model is defined as J˙ ω=τa−Ngτg+δ,(2) with Jthe total inertia of the turbine, τaand τgthe aerodynamic and generator torque, respectively, and Ngrepresenting the gearbox ratio, and δaccounts for the unknown bounded uncertainty. 3 Control design In region III, the objective is to maintain the power at its rated value while simultaneously decreasing the variations of the floating platform that could result in negative damping. It should be noted that, when the number of control objectives exceeds the number of available control inputs, as it is the case for control input u=βin this scenario, the problem is classified as underactuated; consequently, a trade-off between rotor speed and platform pitch oscillation is considered. To address this, the sliding variable σis defined as σ=ω−(ω∗−κ˙ φ),(3) Wind Energy Science Conference 24-27 June 2025 Nantes, France where κ>0 is a constant, ω∗represents the rated rotor speed (12.1 rpm), and ˙ φdenotes the platform pitch rate. The control law is expressed as β=βeq +βastw,(4) where βeq is the equivalent part of the controller, and βastw is the adaptive super-twisting part of the controller. 3.1 Equivalent controller By leveraging the nominal parts of turbine’s control-oriented model (2), βeq is computed when ˙ σ=0. However, due to the nonlinear behaviour of Cp, it is not possible to calculate βdirectly. Various authors have proposed nonlinear approximations using polynomial, sinusoidal, and exponential equations [3]. This study considers the linear polynomial function as Cp(λ,β)≃f(λ)β+g(λ),(5) where f(λ)and g(λ)are polynomial functions of λ, given by f(λ) = ∑5 i=0αiλiand g(λ) = ∑4 j=0γjλj. To determine βeq, we differentiate the sliding variable σwith respect to time. By calculating the time derivative of the sliding variable, considering equations equations (1–3), ˙ σ=1 JρπR3v2 2λ(f(λ)β+g(λ))−ngτg+k¨ φ, and then setting ˙ σ=0, the equivalent control input is obtained as βeq =2λNgτg−Jk ¨ φ ρπR3v2f(λ)−g(λ) f(λ).(6) 3.2 Adaptive super-twisting controller The dynamic model of the FOWT incorporates significant nonlinearities, which pose challenges for modelling and control design. Therefore, a simplified nonlinear model (2) is employed for control purposes, as it captures the essential dynamics while reducing computational complexity. To mitigate unmodeled dynamics and disturbances, an adaptive super-twisting controller is used based on [4]. This controller achieves σ=˙ σ=0 in finite time while mitigating chattering effects typically associated with conventional sliding mode control. Additionally, the adaptive algorithm of the controller allows it to dynamically adjust the control gains, improving performance in realistic conditions. The adaptive control law βastw is described as βastw =−(k1+c1)p|σ|sgn(σ)−Zt 0 (k2+c2)sgn(σ)dτ,(7) with the adaptation dynamics for k1and k2defined ˙ ki=(α fi(σ),|σ|>ε −ki,|σ| ≤ ε,for i=1,2,(8) given f1(σ) = | − ˆ ˙ σ|+εand f2(σ) = 2p|σ|, with c1,c2,α, and εare positive design parameters and ˆ ˙ σis an estimation of the first time derivative of σ. 4 Simulation Results In this section, the performance of the proposed method and ROSCO is compared. Simulations are conducted under the same conditions as shown in Fig. 1(d), using turbulent wind speed profiles generated by TurbSim with a mean velocity of 18 ms−1and an irregular wave with a significant height of 1.27 m. It should be mentioned that, although the control strategy was developed based on a simplified model (2), all 24 degrees of freedom are activated in the OpenFAST simulation. The simulation results, depicted in Fig. 1, provide a comparative analysis of the proposed controller and the ROSCO. For a more accurate comparison, the controller’s performance is evaluated using criteria such as root mean square (RMS) and variation (VAR), as shown in Fig. 1(e). In terms of power error, which is the most critical objective for FOWTs, the proposed method outperforms ROSCO by 18% in RMS. However, it shows 8% and Wind Energy Science Conference 24-27 June 2025 Nantes, France Figure 1: Comparison of the proposed controller and the ROSCO. (a) generated power, (b) rotor speed, (c) blade pitch angle, (d) wind speed (left axis) and wave height (right axis), and (e) performance metrics. 9% lower RMS in rotor speed error and blade pitch angle, respectively. Regarding fatigue analysis, the RMS values for platform roll, pitch, and yaw are lower with the proposed controller, indicating improved performance. Additionally, the tower base (TB) moments (fore-aft, side-to-side, and torsional), blade root (BR) moments (flapwise and edge-wise), and the variation of blade pitch and platform pitch rate are compared. The results reveal that the performances are somewhat similar, with better values in most metrics but without a significant difference. However, the proposed controller also offers the advantage of reduced computational complexity, as ROSCO uses a GSPI controller that relies on linearisation at various operating points. 5 Conclusion This study highlights the efficacy of the robust adaptive super-twisting controller for FOWTs in above-rated wind conditions. By addressing the inherent nonlinearities and uncertainties of FOWTs, the proposed controller achieves slightly better performance compared to the ROSCO, particularly in minimising power error and reducing structural fatigue loads. These findings contribute to the advancement of control strategies for FOWTs, which leads to more reliability and efficiency in renewable energy systems. Acknowledgements This project has received funding from the European Union’s Horizon Europe Framework Programme (HORIZON) under the GA n. 101120278 - DENSE. References [1] N. J. Abbas, D. S. Zalkind, L. Pao, and A. Wright. A reference open-source controller for fixed and floating offshore wind turbines. Wind Energy Science, 7(1):53–73, 2022. [2] J. Jonkman, S. Butterfield, W. Musial, and G. Scott. Definition of a 5-mw reference wind turbine for offshore system development. National Renewable Energy Laboratory, 2009. [3] O. C. Castillo, V. R. Andrade, J. J. R. Rivas, and R. O. Gonz´ alez. Comparison of power coefficients in wind turbines considering the tip speed ratio and blade pitch angle. Energies, 16(6):2774, 2023. [4] M. Taleb and F. Plestan. Adaptive supertwisting controller with reduced set of parameters. In 2021 European Control Conference (ECC), pages 2627–2632, 2021.