Robust Control for Floating Wind Turbines Using Adaptive Super-Twisting Algorithm in Region III

Robust Control for Floating Wind Turbines Using Adaptive Super-Twisting Algorithm in Region III Moein Sarbandi, Mohammad Mohammadi Shahir, Mohamed Assaad Hamida and Franck Plestan Abstract—This study presents a robust adaptive control strategy utilising the super-twisting sliding mode algorithm for control of floating offshore wind turbines (FWOTs) operating in above-rated wind speeds. Due to their nonlinear nature and the presence of uncertainties and unmodelled dynamics, FWOTs require advanced control techniques to ensure stable operation. The primary objectives are to regulate power output and reduce fatigue loads on the system through a collective blade pitch controller. The proposed controller effectively addresses the aforementioned challenges without requiring prior knowledge of system uncertainties and their bounds, and thanks to the adaptation law, it does not overestimate the control gain. The performance of the robust adaptive controller is evaluated using the OpenFAST simulator. The simulation results demonstrate the efficiency of the proposed controller by comparing it with the reference open-source controller (ROSCO), which is renowned for its reliable performance. Index Terms—Floating offshore wind turbine, nonlinear control, adaptive gain, super-twisting algorithm. I. INTRODUCTION Offshore wind energy has become a crucial and significant component of the sustainable energy portfolio as the global demand for renewable energy sources has grown to tackle the climate change issue. Most offshore wind turbines have fixedbottom foundations. Despite this, their deployment is restricted to shallow waters. However, since the majority of offshore wind resources are located at depths beyond 60 m, there is growing interest in FOWTs as a viable solution to capture wind energy in deep waters. Positioning turbines in deeper waters allows them to take advantage of stronger and more consistent wind, resulting in increased energy production. Additionally, locating them further offshore minimises their visual impact [1]. However, the floating structure introduces additional degrees of freedom (DOF), e.g., platform rolling, pitching, and yawing, which can cause negative damping and make the power fluctuations worse, and in extreme cases, it could make the system unstable. Consequently, conventional control algorithms designed for onshore wind turbines are not sufficiently effective for floating ones. Therefore, advanced control strategies are required to enhance the stability and efficiency of FOWTs. The FOWT operation is divided into four regions based on the prevailing wind speed [2]. In Region I (below the cut-in wind speed), the turbine sits idle waiting for the wind speed Moein Sarbandi, Mohammad Mohammadi Shahir, Mohamed Assaad Hamida and Franck Plestan are with Nantes Universit´ e, ´ Ecole Centrale Nantes, CNRS, LS2N, UMR 6004, F-44000 Nantes, France (email: [email protected], [email protected], [email protected], [email protected]). to increase, as the available wind energy is insufficient to operate the turbine. In Region IV (above the cut-out wind speed), the turbine also stops operating to prevent potential damage. In contrast, power generation occurs in Region II and Region III, each employing distinct control strategies. In Region II, the objective is to maximise the power coefficient to optimise energy capture. This paper focuses on Region III, where the objective is to keep the power at its nominal value while mitigating fatigue loads. Maintaining power at its rated level is essential to protecting the turbine and ensuring its longevity and operational stability. The control of FOWTs remains an active research area, with significant advancements achieved over the past decade. Many studies have focused on control strategies based on linear mathematical models of FOWTs. In [3], the author investigated the impact of conventional blade pitch control on platform pitch stability in an FOWT, revealing that standard control strategies can induce negative damping effects. To mitigate the issue, the study employed a gain-scheduling proportional-integral (GSPI) controller. Recent studies, such as [4] and [5], continue to rely on linearisation across multiple operating conditions. In [5], a linear quadratic controller (LQR) was implemented using gain-scheduling techniques to enhance performance. In addition, a linear quadratic integral (LQI) controller was tested on a 5 MW FOWT in [6]. This controller adds integral action to LQR. The results showed improved regulation of generator speed compared to a conventional PI controller, though at the cost of increased pitch actuator effort. Moreover, model predictive control (MPC) has been explored for its ability to enforce constraints on system inputs and states [7]. However, its practical implementation faces challenges such as high computational costs and the requirement for accurate system models to predict future states. The design of linear control strategies, like the aforementioned studies, is based on the linearisation technique around an operating point. Obviously, numerous operational conditions are essential to defining the complete operating domain; this demands considerable modelling and controller tuning efforts, as tuning the controller parameters is necessary for each operating point. To address these challenges, learning-based and nonlinear control approaches have been proposed. Learning-based methods, such as those explored in [8], [9], eliminate the need for explicit models but require large datasets and a prolonged training phase. Additionally, as the model continuously updates, fluctuations in power 2025 33rd Mediterranean Conference on Control and Automation (MED) June 10 - 13, 2025. Tangier,Morocco 979-8-3315-7719-3/25/$31.00 ©2025 IEEE 1 2025 33rd Mediterranean Conference on Control and Automation (MED) | 979-8-3315-7719-3/25/$31.00 ©2025 IEEE | DOI: 10.1109/MED64031.2025.11073309 Authorized licensed use limited to: University of Nantes. Downloaded on September 28,2025 at 09:56:05 UTC from IEEE Xplore. Restrictions apply. output often occur. Nonlinear control strategies offer an efficient alternative by reducing modelling complexity and tuning efforts, as demonstrated in [10], which presented a comparative study of various nonlinear approaches. Sliding mode control (SMC) has been employed as an effective approach for regulating nonlinear systems affected by uncertainties and disturbances. However, its practical implementation is hindered by chattering and high control activity [11]. Additionally, tuning SMC remains a persistent challenge, as it requires the bounds of perturbations. This challenge serves as the main motivation for using adaptation laws to prevent gain overestimation, which can lead to several issues, including chattering and noise amplification. These methods guarantee the convergence of both the sliding variable and its higher-order derivatives to zero, thereby enhancing control system precision and stability. By incorporating these advanced techniques, FOWT control performance can be significantly improved, leading to more reliable and efficient operation under uncertain environmental conditions. In this paper, an adaptive super-twisting sliding mode controller (ASTW-SMC) is developed for FOWTs. The proposed controller integrates an equivalent control component to enhance system stability and performance while addressing the slow transient response observed in previous studies [12]. This approach ensures that the sliding variable and its first derivative converge to zero despite system uncertainties, thereby improving the accuracy of sliding variable stabilisation. Additionally, the method requires limited modelling effort and tuning complexity, as a single set of tuning parameters is sufficient across all operational domains. The proposed method is validated through simulations using the National Renewable Energy Laboratory (NREL) 5 MW FOWT within the OpenFAST simulation framework [13]. The proposed control is compared with the ROSCO [14]. To the best of the authors’ knowledge, no prior study has conducted a direct comparison between ROSCO and ASTW-SMC for 5 MW FOWTs. The subsequent sections of this paper present a model for the FOWT, followed by the design of an ASTW-SMC. The simulation results are then presented and compared with ROSCO, and the paper concludes with key findings. II. FLOATING OFFSHORE WIND TURBINE MODELLING The present study focuses on the NREL 5 MW FOWT, which is supported by a semi-submersible floating platform with the characteristics listed in Table I, and modelled using OpenFAST. The aerodynamic power Paand torque τagenerated by the rotor are expressed as Pa=1 2ρπR2Cp(λ, β)v3,(1) τa=Pa ω,(2) where ρrepresents the air density, Rdenotes the rotor radius, Cpis the power coefficient, vis the wind speed, and ω corresponds to the rotor speed. The power coefficient is a function of the blade pitch angle, β, and the tip-speed ratio (TSR), λ, as depicted in Fig. 1. The TSR is given by λ=ω vR. (3) Fig. 1. Relationship between power coefficient, blade pitch, and TSR. The simplified nonlinear control-oriented model of the FOWT’s drive-train is defined as [15] ˙ω=1 J(τa−Ngτg) + ∆(·),(4) with Jthe total inertia of the turbine, τaand τgthe aerodynamic and generator torques, respectively, Ngis the gearbox ratio, and ∆(·)represents all the uncertainties and perturbations. Note that this model is straightforward and simple, as it disregards platform motions and mooring lines. In the present study, the idea is to develop the controller on a very simplified model and then apply it to the complete system with all DOF. Consequently, the design of a robust controller is essential. TABLE I KEY PARAMETERS FOR THE 5-MW FOWT [13]. Parameter Value Rated power 5 MW Platform type OC4 semi-submersible Rotor orientation, configuration Upwind, 3 blades Rotor diameter, hub height 126, 90 (m) Cut-in, rated, cut-out wind speed 3, 11.4, 25 (m/s) Rated rotor and generator speed 12.1, 1173.7 (rpm) Blade pitch angle range and rate limit 0◦-90◦,±8◦/s III. CONTROL DESIGN The FOWT model (4) is a highly nonlinear system with uncertainties influenced by external forces such as wind and waves. By considering (4), the relative degree of the system can be identified as the one that makes the system welldefined. This paper introduces a nonlinear control method utilising an adaptive super-twisting (ASTW) approach with limited information of the model in order to fulfil the control objectives. This development enhances robustness and accuracy while reducing tuning and modelling efforts. 2 Authorized licensed use limited to: University of Nantes. Downloaded on September 28,2025 at 09:56:05 UTC from IEEE Xplore. Restrictions apply. A. Adaptive super-twisting sliding mode Consider the following nonlinear system as [16], [17]: ˙σ=ψ(·) + γ(·)u, (5) where the functions ψ(·)and γ(·)satisfy conditions ψ∈ [−ψm, ψM]and γ∈[γm, γM],with ψm,ψM,γm, and γM are positive constants that exist but are unknown. The variable σis the sliding variable; when both σand its derivative ˙σ converge to zero, the control objective is achieved. Therefore, the aim of the control input uis to ensure that σ= ˙σ= 0 within a finite time, even when the system model is not fully known. This is achieved using ASTW. Assumption 1. The functions ψ(·)and γ(·)can be presented as [16] ψ(·) = ψn(·)+δψ(·)and γ(·) = γn(·)+δγ(·), where ψn(·)and γn(·)>0represent the nominal parts and δψ(·) and δγ(·)denote the corresponding uncertain components, such that |δγ(·)| ≪ γn(·). ˙σ= (ψn+δψ)+(γn+δγ)u. (6) The control law is defined in two parts based on sliding mode theory: one part, known as the equivalent control, is derived by setting ˙σ= 0, and the other part is based on the super-twisting algorithm ξ, which is defined subsequently. u=1 γn (−ψn+ξ),(7) by substituting the control law (7) into (6), the closed-loop system is obtained as ˙σ=ψn+δψ+1 γn (γn+δγ) (−ψn+ξ), =δψ−δγ γn ψn |{z } δ +1 + δγ γnξ, (8) given Assumption 1, |δγ(·)| ≪ γn(·), the closed-loop system can be written as ˙σ=ξ+δ. (9) Assumption 2. δis Lipschitz continuous, meaning that its time derivative ˙ δ(t)exists and is bounded. |˙ δ(t)| ≤ δM,for all t≥0.(10) The super-twisting control law, based on [18], is now derived to achieve ˙σ=σ= 0 or to remain near zero within a finite time despite the presence of uncertainty. The supertwisting control law is given by ξ=−k1|σ|1 2sgn(σ) + κ, ˙κ=−k2sgn(σ).(11) Adjusting the gains k1and k2requires knowledge of the perturbation bound, as discussed in [16]. However, in realworld problems, this information is often unavailable. A common approach to addressing this limitation is to conservatively estimate the perturbation bound. While effective in ensuring stability, this often leads to an overestimation of the gains, which can significantly amplify chattering [17]. Alternatively, adaptive gain strategies offer a more flexible solution by dynamically adjusting the gains based on the system’s behaviour. In some cases, such as systems with slow dynamics like FOWTs, incorporating a bias into these adaptive gains can further enhance convergence and robustness, as demonstrated in the results. The gains are dynamically updated based on the adaptation law defined in [19] as ˙ ki=   α fi(σ),|σ|> ε −ki,|σ| ≤ ε ,for i= 1,2,(12) given f1(σ) = | − ˙ ˆσ|+εand f2(σ)=2|σ|1 2, where, α, and εare positive design parameters, and ˙ ˆσrepresents an estimate of the first derivative of σover time (for further details, refer to [19]). The parameter εdetermines the target accuracy. Therefore, based on (12), when |σ|> ε, which means the sliding variable is outside the interval of target accuracy, the adaptation law ensures that kiincreases to drive the sliding variable toward the origin. Once |σ| ≤ ε, the gains ˙ kibecome negative, causing both gains to decrease. Considering the system described by (5), under Assumptions 1 and 2, the super-twisting controller (11) is implemented with the adaptive law (12). As demonstrated in [19], the sliding variable and its time derivative achieve finite-time convergence to a neighbourhood of the origin. B. Application to the floating offshore wind turbine In Region III, the objective is to maintain the power at its rated value P∗while simultaneously mitigating floating platform oscillations. These objectives are achieve by imposing a constant generator torque in rated value τ∗ gwhile the blade pitch angle varies to maintain the power at the nominal value. ω∗=P∗ Ngτ∗ g ,(13) with ω∗the rated rotor speed. It is important to note that the above problem is called underactuated when there are more control objectives than available control inputs (this is the case in this scenario). This results in a trade-off between rotor speed and platform pitch oscillation. To address this, the scaled platform pitch rate κ˙φ[20] is incorporated into the sliding variable σ, which is defined as σ=ω−ωd,(14) where ωd=ω∗−κ˙φrepresents the desired rotor speed and κ > 0is a constant. There are various approximations of Cpusing polynomial, sinusoidal, and exponential equations proposed in the literature [21]. In this study, a polynomial-based approximation that is linear in βis expressed as Cp(λ, β) = f(λ)β+g(λ),(15) 3 Authorized licensed use limited to: University of Nantes. Downloaded on September 28,2025 at 09:56:05 UTC from IEEE Xplore. Restrictions apply. where f(λ)and g(λ)are polynomial functions of λ, defined as1 f(λ) = 4 X i=0 aiλi, g(λ) = 4 X j=0 bjλj,(16) the coefficients aiand bjare determined through polynomial regression in the operating domain (Table II). TABLE II VALUES OF COEFFICIENTS FOR f(λ)AND g(λ). Function Coefficients value (aiand bj, with i, j = 0,...,4) f(λ)−1.8960,1.1560,−0.2454,0.0293,−0.0020 g(λ)−0.1046,0.0808,−0.0221,0.0023,−8.17 ×10−5 Thus, substituing Cpby its polynomial expression (15), the reduced order model (4) by considering (2)–(3), one has ˙ω=1 J1 2ρπR2Cp(λ, β)v3 ω−Ngτg+ ∆(·), =1 J1 2ρπR3(f(λ)β+g(λ)) v2 λ−Ngτg+ ∆(·). (17) Therefore, the dynamics of the sliding variable can be expressed, based on the discussion in [22], [23], in the form of (5), where ψn= (ρπR3g(λ)v2)/(2Jλ)−(Ngτg)/J −˙ωd and γn= (ρπR3f(λ)v2)/(2Jλ)are derived from (17). Now, based on the previous section, the control law u=β, which incorporates both the equivalent control βeq and the ASTW βastw, is capable of operating effectively in the presence of uncertainties while achieving the desired objective. For the equivalent control part, by setting the derivative of the sliding variable (14) to zero, and considering from (7) that βeq =−(1/γn)ψnit is calculated as βeq =−g(λ) f(λ)+2λ ρπR3f(λ)v2(Ngτg+J˙ωd),(18) after implementation βeq the closed-loop system is simplified to ASTW terms (11) and uncertainty. Hence, the supertwisting part now handles the uncertainties and perturbations of the system, as discussed in the previous section. In Fig. 2, a general overview of the control concept is shown. It illustrates how the controller works together to manage blade pitch in Region III, where the generator torque is fixed at its rated value. IV. SIMULATION RESULTS In this section, the performance of the proposed control method is compared with ROSCO [14]. The analysis is based on the NREL 5 MW FOWT, supported by a semisubmersible floating platform. The proposed control strategy is implemented using MATLAB/SIMULINK 2023a, interfaced with OpenFAST for co-simulation. In contrast, ROSCO is executed through a co-simulation setup involving OpenFAST 1Fourth-order polynomials were selected as a trade-off between model accuracy and computational complexity. + − ω∗ − + ˙ ki=   α fi(σ),|σ|> ε −ki,|σ| ≤ ε for i= 1,2 f1(σ) = |˙ ˆσ|+ε,f2(σ)=2|σ|1 2 Adaptive law ξ=−k1|σ|1 2sgn(σ) + κ ˙κ=−k2sgn(σ) Super-twisting algorithm Equivalent controller −g(λ) f(λ)+2λ ρπR3f(λ)v2(Ngτg+J˙ωd) Low-pass filter τg,rated + +β Rotor speed Scaled platform pitch rate ωd d /dt v k1k2 σ βastw βeq Fig. 2. Block diagram of the proposed control system, illustrating the integration of the super-twisting algorithm with the adaptive law and the equivalent controller for regulating the blade pitch angle in an FOWT. and Ubuntu Linux. Simulations are conducted under identical conditions over a 500 s period, with turbulent wind speed profiles generated using TurbSim with a mean velocity of 18 m s−1, following the Kaimal turbulence model, which is widely used for simulating realistic wind conditions, as shown in Fig. 3. Additionally, the HydroDyn module in OpenFAST is employed to generate an irregular wave with a significant wave height of 2.25 m, based on the Pierson– Moskowitz spectrum (Fig. 3) [24]. Although the proposed control strategy is developed using a reduced model (4), all 24 DOF are activated in the simulation. The Euler algorithm Fig. 3. Turbulent wind speed profiles (left axis) generated by TurbSim and an irregular wave profile (right axis) generated by the HydroDyn module. is also used, and the time step is set to 0.0125 s. The blade pitch angle is limited by a saturation limit and a rate limiter. This constrains the angle within [0◦,90◦]with a maximum rate of change of 8◦/s enhancing simulation accuracy relative to the real system. The simulation results, depicted in Fig. 4, provide a comparative analysis of the proposed controller and the ROSCO. It is evident that both controllers effectively accomplish satisfactory results in all aspects, including power generation and tracking. However, the proposed controller exhibits a superior transient response with reduced oscillations and operates closer to the rated value. 4 Authorized licensed use limited to: University of Nantes. Downloaded on September 28,2025 at 09:56:05 UTC from IEEE Xplore. Restrictions apply. 4.8 4.9 5 5.1 5.2 Power [MW] 11.5 12 12.5 Rotor speed [rpm] 10 12 14 16 18 Blade pitch angle [°] 0 50 100 150 200 250 300 350 400 450 500 Time [s] -0.5 -0.25 0 0.25 0.5 Platform pitch rate [°/s] Fig. 4. Comparison of the proposed controller and ROSCO in terms of key operational parameters. The generated power (top) with a rated value of 5 MW, rotor speed (second) with a rated value of 12.1 rpm, blade pitch angle (third), and platform pitch rate (bottom) are shown over time. The evaluation of the adaptive gains of the controller is shown in Fig. 5. The gains have bias values of 0.05 and 2.5×10−3for k1and k2, respectively. This approach further improves convergence speed and robustness, as the faster adaptation of the gains enables the controller to respond more effectively to model uncertainties. Fig. 5. Time evolution of adaptive gains k1(left axis) and k2(right axis) in the super-twisting control scheme. For a more precise comparison, the controller’s performance is evaluated using key performance metrics, including RMS, RMSE, and variations (VAR) to evaluate critical FOWT parameters. The choice between RMSE or RMS depends on the availability of a reference value: (i) RMSE is applied when a rated or reference value exists, such as for power and rotor speed, to quantify deviations from the expected performance; (ii) RMS is used when no specific reference value is available, serving as a measure of overall variability in the parameter; and (iii) VAR is calculated as the sum of absolute differences between consecutive values of Y, expressed as P|Ynext −Ycurrent|, which effectively captures fluctuations in key parameters such as platform pitch rate and blade pitch angle. RMSE Power RMSE Rotor speed Platform roll Platform yaw Platform pitch Tower base fore-aft Tower base side-to-side Tower base torsional Blade root flap-wise Blade root edge-wise VAR Blade pitch VAR Platform pitch rate Fairlead force 1 Fairlead force 2 Fairlead force 3 Anchor force 1 Anchor force 2 Anchor force 3 0.8151 0.9944 0.9636 0.9900 0.9586 0.9524 0.9551 1.0000 0.9484 0.9973 1.0525 1.0106 1.0039 0.9909 1.0040 1.0049 0.9895 1.0049 0.5 0.6 0.7 0.8 0.9 1 1.1 Normalised values Mooring lines Root mean square Fig. 6. Normalised RMS and VAR values comparing the proposed method with ROSCO. Values are normalised with respect to ROSCO, where green bars indicate more than 1% improved performance, orange bars represent comparable performance (within ±1%), and red bars indicate more than 1% worse performance relative to ROSCO. 5 Authorized licensed use limited to: University of Nantes. Downloaded on September 28,2025 at 09:56:05 UTC from IEEE Xplore. Restrictions apply. To ensure comparability, all performance measures are normalised relative to ROSCO, where a lower value indicates superior performance. Additionally, a colour scheme is employed, with green, orange, and red bars representing different performance levels: green bars indicate an improvement of more than 1%, orange bars denote comparable performance (within ±1%), and red bars signify a performance reduction exceeding 1% relative to ROSCO, as illustrated in Fig. 6. In terms of power tracking, which is the most critical objective for FOWTs, the proposed control method outperforms ROSCO by 18.4% in RMSE with the most significant difference observed in the transient phase, while the remaining performance aspects are generally comparable. Furthermore, for the examination of platform fatigue loads, the RMS values of the following are conducted: tower base movements (fore-aft, side-to-side, and torsional); blade root moments (flap-wise and edge-wise); as well as forces from the fairlead and anchor of the three mooring lines. The results from Fig. 6 indicate the proposed controller demonstrates superior performance in terms of the RMS values of platform roll, yaw, pitch, and tower base fore-aft and side-to-side motions. However, it exhibits a little higher VAR in the blade pitch and the platform pitch. V. CONCLUSION This study presents an ASTW-SMC for FOWTs operating in above-rated wind conditions. The proposed control strategy is evaluated against ROSCO, with results demonstrating that both controllers achieve satisfactory power regulation and system stability. However, the proposed controller exhibits a faster convergence to the desired value at transient response in power tracking, reducing RMSE by 18.4% compared to ROSCO. Additionally, platform fatigue loads and mooring line forces remain comparable, with specific improvements in certain parameters. Furthermore, the proposed controller achieves this performance with reduced computational complexity, as it does not rely on extensive gain scheduling and linearisation across multiple operating points. This reduction in complexity enhances its adaptability and implementation efficiency. ACKNOWLEDGMENT This project has received funding from the European Union’s Horizon Europe Framework Programme (HORIZON) under the GA n. 101120278 - DENSE. REFERENCES [1] D. Stockhouse, M. Phadnis, A. Henry, N. J. Abbas, M. Sinner, M. Pusch, and L. Y. Pao, “A tutorial on the control of floating offshore wind turbines: Stability challenges and opportunities for power capture,” IEEE Control Systems, vol. 44, no. 5, pp. 28–57, 2024. [2] M. Sarbandi and H. Khaloozadeh, “Quantifying the impact of sensor precision on power output of a wind turbine: A sensitivity analysis via monte carlo simulation study,” Wind Engineering, vol. 48, no. 4, pp. 497–517, 2024. [3] J. Jonkman, “Influence of control on the pitch damping of a floating wind turbine,” in 46th AIAA aerospace sciences meeting and exhibit, 2008, p. 1306. [4] Q. Hawari, T. Kim, C. Ward, and J. Fleming, “A robust gain scheduling method for a pi collective pitch controller of multi-mw onshore wind turbines,” Renewable Energy, vol. 192, pp. 443–455, 2022. [5] O. Bagherieh and R. Nagamune, “Gain-scheduling control of a floating offshore wind turbine above rated wind speed,” Control Theory and Technology, vol. 13, no. 2, pp. 160–172, 2015. [6] S. Sarkar, B. Fitzgerald, and B. Basu, “Individual blade pitch control of floating offshore wind turbines for load mitigation and power regulation,” IEEE Transactions on Control Systems Technology, vol. 29, no. 1, pp. 305–315, 2021. [7] M. A. Evans, M. Cannon, and B. Kouvaritakis, “Robust mpc tower damping for variable speed wind turbines,” IEEE Transactions on Control Systems Technology, vol. 23, no. 1, pp. 290–296, 2015. [8] F. Didier, S. Laghrouche, and D. Depernet, “Deep reinforcement learning-based pitch control for floating offshore wind turbines,” in 2023 9th International Conference on Control, Decision and Information Technologies (CoDIT), 2023, pp. 1–6. [9] J. Xie, H. Dong, and X. Zhao, “Power regulation and load mitigation of floating wind turbines via reinforcement learning,” IEEE Transactions on Automation Science and Engineering, 2023. [10] E. Aslmostafa, M. A. Hamida, and F. Plestan, “Nonlinear control strategies for a floating wind turbine with pmsg in region 2: A comparative study based on the openfast platform,” Ocean Engineering, vol. 300, p. 117507, 2024. [11] V. I. Utkin and A. S. Poznyak, “Adaptive sliding mode control with application to super-twist algorithm: Equivalent control method,” Automatica, vol. 49, no. 1, pp. 39–47, 2013. [12] M. Taleb, A. Marie, C. Zhang, M. A. Hamida, P.-E. Testelin, and F. Plestan, “Adaptive nonlinear control of floating wind turbines: new adaptation law and comparison,” in IECON 2021–47th Annual Conference of the IEEE Industrial Electronics Society. IEEE, 2021, pp. 1–6. [13] J. Jonkman, S. Butterfield, W. Musial, and G. Scott, “Definition of a 5mw reference wind turbine for offshore system development,” National Renewable Energy Laboratory, 2009. [14] N. J. Abbas, D. S. Zalkind, L. Pao, and A. Wright, “A reference opensource controller for fixed and floating offshore wind turbines,” Wind Energy Science, vol. 7, no. 1, pp. 53–73, 2022. [15] M. Capaldo and P. Mella, “Damping analysis of floating offshore wind turbine (fowt): a new control strategy reducing the platform vibrations,” Wind Energy Science Discussions, vol. 2022, pp. 1–29, 2022. [16] Y. Shtessel, M. Taleb, and F. Plestan, “A novel adaptive-gain supertwisting sliding mode controller: Methodology and application,” Automatica, vol. 48, no. 5, pp. 759–769, 2012. [17] F. Plestan, Y. Shtessel, V. Br´ egeault, and A. Poznyak, “New methodologies for adaptive sliding mode control,” International Journal of Control, vol. 83, no. 9, pp. 1907–1919, 2010. [18] A. Levant, “Sliding order and sliding accuracy in sliding mode control,” International Journal of Control, vol. 58, no. 6, pp. 1247– 1263, 1993. [19] M. Taleb and F. Plestan, “Adaptive supertwisting controller with reduced set of parameters,” in 2021 European Control Conference (ECC), 2021, pp. 2627–2632. [20] R. Chaaban and C.-P. Fritzen, “Reducing blade fatigue and damping platform motions of floating wind turbines using model predictive control,” in International Conference on Structural Dynamics, 2014. [21] 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, vol. 16, no. 6, p. 2774, 2023. [22] C. Zhang, S. Gutierrez, F. Plestan, and J. de Le´ on-Morales, “Adaptive super-twisting control of floating wind turbines with collective blade pitch control,” IFAC-PapersOnLine, vol. 52, no. 4, pp. 117–122, 2019. [23] E. Aslmostafa, M. Mirzaei, M. Mojallizadeh, M. Hamida, and F. Plestan, “Robust control strategies for floating wind turbines: preliminary experimental results,” in 2024 17th International Workshop on Variable Structure Systems (VSS). IEEE, 2024, pp. 298–303. [24] W. J. Pierson Jr and L. Moskowitz, “A proposed spectral form for fully developed wind seas based on the similarity theory of sa kitaigorodskii,” Journal of geophysical research, vol. 69, no. 24, pp. 5181–5190, 1964. 6 Authorized licensed use limited to: University of Nantes. Downloaded on September 28,2025 at 09:56:05 UTC from IEEE Xplore. Restrictions apply.