Designing a Predictive Super-Twisting Sliding Mode Control for Floating Offshore Wind Turbines in Region 2

HAL Id: hal-05169436 https://hal.science/hal-05169436v1 Submitted on 18 Jul 2025 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Designing a Predictive Super-Twisting Sliding Mode Control for Floating Offshore Wind Turbines in Region 2 Mohammad Mohammadi Shahir, Moein Sarbandi, Mohammad Rasool Mojallizadeh, Mohamed Assaad Hamida, Franck Plestan To cite this version: Mohammad Mohammadi Shahir, Moein Sarbandi, Mohammad Rasool Mojallizadeh, Mohamed Assaad Hamida, Franck Plestan. Designing a Predictive Super-Twisting Sliding Mode Control for Floating Offshore Wind Turbines in Region 2. Wind Energy Science Conference (WESC 2025), Jun 2025, Nantes, France. �hal-05169436� Wind Energy Science Conference 24-27 June 2025 Nantes, France Designing a Predictive Super-Twisting Sliding Mode Control for Floating Offshore Wind Turbines in Region 2 Mohammad Mohammadi Shahira,Moein Sarbandia,Mohammad Rasool Mojallizadehb, Mohamed Assaad Hamidaa, and Franck Plestana aNantes Universit´ e, ´ Ecole Centrale Nantes, CNRS, LS2N, UMR 6004, F-44000 Nantes, France bArts et M´ etiers Institute of Technology, LAMPA, F-49035 Angers, France E-mail:[email protected] Keywords: Model predictive control, super twisting sliding mode, offshore platform 1 Introduction This study focuses on designing an advanced control strategy for floating offshore wind turbines (FOWTs) to maximize power generation for wind speeds between 3 and 11.25 m/s (region 2) while reducing fatigue loads on the system. One of the main challenges in designing a control law for FOWTs is their nonlinearity and high degree of freedom. To address this issue, various robust nonlinear control methods with reduced knowledge of the model, such as super-twisting controller (STW), and model-based control approaches, such as model predictive control (MPC), are used. However, both of these controllers suffer from disadvantages, such as slow transient time for STW and a lack of robustness against uncertainties for MPC. To address this problem, this paper integrates optimal predictive control and STW to overcome their deficiencies and achieve superior performance. Simulation studies is conducted on the 5MW OC4 FOWT, which is modeled by OpenFAST. The comparison results with the ROSCO method [1], which is the Reference Open Source Controller for Wind Turbines, show that the proposed method improves power generation with a reduction of pitch rate. The primary contribution of this paper can be summarized as: 1) Development of a control law based on optimal predictive control and STW for a FOWT to achieve optimized performance and robustness, 2) Evaluation of the performance of predictive super-twisting sliding mode (PSTW) versus the baseline controller (ROSCO) with quantitative indicators. 2 Dynamic Modeling The mechanical power generated by the wind is calculated as follows: P=1 2ρAv3Cp(λ,β)(1) where ρrepresents the air density, and A=πR2, with Ras the blade radius, vdenotes the wind speed, Cp(λ,β) represents the power coefficient of the wind turbine, which is a function of the blade pitch angle (β) and the tipspeed ratio (λ). The tip-speed ratio is defined as λ=Rωr v, where ωris the rotor speed. The simplified dynamic model of the wind turbine is described as ˙ ωr=1 Jt (Ta−Ktωr)−Ng Jt Tg(2) In this equation, Jtand Ngare the rotor inertia and the gearbox ratio, respectively. Ktrepresents external damping, Tgis the generator torque, and finally, Tais the aerodynamic torque, which is defined as follows: Ta=1 2ρ πR2CP(λ,β) ωr v3(3) Wind Energy Science Conference 24-27 June 2025 Nantes, France 3 Control Design In Region 2, the primary objective is to maximize power output. To achieve this, the TSR control method has been proposed, which is recognized as the maximum power point tracking (MPPT) algorithm. In this method, the generator torque is adjusted so that the turbine operates at its optimal power coefficient. This coefficient is achieved by maintaining a zero blade pitch angle, which maximizes lift and ensures the maximum possible energy is extracted from the wind [2]. The control law is chosen as follows: Tg=1 g(·)(uopt +ustw)(4) where g(·) = −Ng Jt,uopt is the optimal control that stabilizes the nominal model of the system, and ustw is an additional control law which compensates for all uncertainties in the system. Optimal control law is designed based on predictive control theory [3]. In this method, the sliding value is predicted and optimized within a finite time horizon to track the desired rotor speed. The sliding variable is defined as σ=e=ωr−λ∗ Rv,where λ∗ represents the optimal value of the tip-speed ratio. Using the Taylor series, the sliding value can be expanded for the next time step as follows: σ(t+h) = σ(t)+h(f(·)+uopt )−λ∗ R˙v(5) where where f(·) = 1 Jt(Ta−Ktωr)and his prediction time. For the reaching control law, the performance index is defined as follows: j=1 2w1[σ(t+h)]2+1 2w2[u2 opt ](6) where w1>0 and w2≥0 are the weighting factors. By solving the optimization problem ∂j ∂uopt and setting it equal to zero, the control law can be defined as uopt =−h h2+λe+hf(.)−λ∗ R˙v.(7) where λ=w2 w1is control weight ratio. The control law is extracted from the simplified model, which incorporates several sources of uncertainty. As a result, the model is unreliable in accurately describing the behavior of offshore wind turbines under various conditions. For that reason, STW is incorporated into the control law to compensate for all of the uncertainties in the system. The STW approach can be described as follows [4]: ustw =−K1p|σ|sgn(σ)+υ,(8) ˙ υ=−K2sgn(σ).(9) where K1>0 and K2>0 are design parameters. 4 Results and analysis To evaluate the performance of the proposed controller, stochastic wind conditions with irregular waves, as shown in Figs 1(a) and 1(b), are considered. Figs 1(c), 1(d), 1(e), and 1(f) illustrate the comparison result of the proposed controller with the ROSCO method. According to this figures, it can be seen that the proposed control method has the ability to produce more power with less generator torque consumption. Moreover, the variation in power production is reduced by 9.18%. To analyze the effectiveness of the proposed approach, the RMS results of the proposed controller, which are normalized based on the Rosco results, are shown in Fig 2. According to these results, platform roll and platform pitch rates are decreased. Moreover, this control method applies fewer forces on all mooring lines except for ANCHTEN 2 and FAIRTEN 3. 5 Conclusion This article presents a robust control method to enhance the performance of FOWT in Region 2. The results showed that combining two control methods, optimal predicitve control and STW improves the performance and reliability of the system in the presence of uncertainties, offering a promising solution for the wind energy system. Wind Energy Science Conference 24-27 June 2025 Nantes, France 0 200 400 600 800 1000 Time (sec) 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 Wind Speed [m/s] (a) 0 200 400 600 800 1000 Time (sec) -3 -2 -1 0 1 2 3 Wave Height [m] (b) 0 200 400 600 800 1000 Time (sec) 0 500 1000 1500 Power [kw] Rosco Proposed (c) 0 200 400 600 800 1000 Time (sec) 0 2 4 6 8 10 12 14 16 18 Generator Torque (kN-m) Rosco Proposed (d) 0 200 400 600 800 1000 Time (sec) 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Power Coefficient Rosco Proposed 385 390 395 400 405 0.42 0.44 0.46 0.48 0.5 0.52 Rosco Proposed (e) 0 200 400 600 800 1000 Time (sec) -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Platform pitch rate [deg/s] Rosco Proposed 600 620 640 660 680 700 720 -0.1 -0.05 0 0.05 (f) Figure 1: The simulation results of the predictive super twisting sliding mode for the stochastic wind: (c) Power, (d) Generator Torque, (e) Power Coefficient, (f) Platform pitch rate. GenSpeed GenTor Power 0 0.2 0.4 0.6 0.8 1 1.2 Normalized Values (a) PtfmRoll PtfmPitch PtfmYaw Pitch Rate 0 0.2 0.4 0.6 0.8 1 1.2 Normalized Values (b) ANCHTEN1 ANCHTEN2 ANCHTEN3 FAIRTEN1 FAIRTEN2 FAIRTEN3 0.994 0.996 0.998 1 1.002 1.004 1.006 (c) Figure 2: Normalized RMS values of the system: (a) RMS of Gen-Speed, Gen-Tor and Power, (b) RMS of platform motions, (c) RMS of the mooring lines. 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] D. Kumar and K. Chatterjee. A review of conventional and advanced mppt algorithms for wind energy systems. Renewable and Sustainable Energy Reviews, 55:957–970, 2016. [3] M. Mirzaei, G. Alizadeh, M. Eslamian, and Sh. Azadi. An optimal approach to non-linear control of vehicle yaw dynamics. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 222(4):217–229, 2008. [4] A. Levant. Sliding order and sliding accuracy in sliding mode control. International journal of control, 58(6):1247–1263, 1993.