Wind energy is essential to meeting the decarbonisation objectives of the European Union (EU) energy system. Consequently, wind energy is expected to heavily contribute to the EU renewable energy targets, with wind energy already covering 19 % of the EU's electricity demand in 2024. This has seen the EU revising the renewable energy directive, which lays down a minimum target of 42.5 % share of renewables by 2030, with the aspiration of reaching 45 %. This is 10.5 % higher than the initial 32 % target. Subsequently, the EU could fulfil its ambition of becoming climate neutral by 2050 .

Offshore wind represents a great asset in this regard, as it benefits from higher, more-consistent speeds than onshore alternatives. Floating offshore wind turbines (FOWTs) further extend this potential by enabling deployment in deep-water basins, such as the Mediterranean and Atlantic, where bottom-fixed turbines are unfeasible. However, FOWTs face harsher environments; unlike onshore systems, they are subjected to coupled wind and wave disturbances. These additional hydrodynamic loads, compounded by wind turbulence, significantly increase structural fatigue .

The main challenge facing the further deployment of FOWTs is their high levelised cost of energy (LCOE). While modifications to their aerodynamic, hydrodynamic and structural design are applied to bring the LCOE down, the control system should not be overlooked . Developing new control architectures can contribute to reducing the LCOE. Another approach is control co-design , which has proven to be highly effective.

From a control perspective, FOWTs present additional complexities compared to onshore turbines. The dynamics introduced by the floating platform make control more challenging. A notable concern is the negative damping effect , as applying a fixed-bottom controller to a floating wind turbine can significantly amplify the system’s dynamic response, leading to large peak-to-peak oscillations and thus compromising both performance and structural safety. The simplest way to avoid closed-loop instability without modifying the conventional baseline controller structure is to detune the control gains such that the closed-loop response of the generator speed mode in isolation has a natural frequency below the platform pitch resonant frequency . However, this leads to a degradation in the reference tracking performance of the blade pitch controller as its ability to effectively respond to disturbances becomes restricted . Maintaining global detuning across all wind speeds sacrifices higher control bandwidths at higher wind speeds that do not suffer from this instability. Accordingly, it is reasonable to schedule the detuning at each wind speed separately .

Other methods explored in the literature involve incorporating extra feedback loops to counteract the instability arising from rotor–platform interactions. By utilising nacelle fore-aft velocity as feedback to adjust the existing baseline controller actuators, blade pitch  and generator torque  control inputs showed that performance improvements could be achieved without the need for additional actuators. Systems with more than one actuating control input and more than one sensor output may be considered as multivariable systems or multi-input, multi-output (MIMO) systems. The control objective for multivariable systems is to obtain a desirable behaviour of several output variables by simultaneously manipulating several input channels. A FOWT is a MIMO system. To evaluate such a system, MIMO transfer function matrix is needed. FOWT control strategies often utilise decoupled feedback loops, where each is tuned independently for a specific output . Although this simplifies the multivariable design into a series of single-loop controllers, it neglects the inherent dynamic coupling of MIMO systems. Consequently, adjustments in one loop can induce undesirable interactions in others, necessitating a control approach that accounts for the coupling simultaneously. It was demonstrated that improved performance could be achieved when optimally tuning all the control loops collectively, accounting for the cross-coupling within the MIMO feedback structure rather than tuning each control loop independently . Modern multivariable control methodologies employing state-feedback architectures, including linear quadratic regulator (LQR)  and H∞ control  demonstrate systematic efficacy in achieving specified stability and performance envelopes for complex dynamical systems .

The majority of control architectures designed to mitigate negative damping instability rely on auxiliary sensors to measure tower-top or platform acceleration in the fore-aft direction. Only recently, demonstrated the feasibility of eliminating these additional sensing requirements, answering a proof-of-concept question: “Could a control structure relying exclusively on generator speed measurement overcome the bandwidth limitation imposed by the RHPZs in FOWTs? If yes, what form would such a structure take?” These questions were answered in a linear, frequency-domain setting only.

Keeping the proof-of-concept result in mind, the main contribution of this paper is to properly introduce the novel control structure that maintains robust performance without the need for supplementary sensors and to reduce it to an equivalent single-loop structure compatible with standard industrial proportional-integral (PI) tuning practice. We also revisit existing control strategies and equip them with a multi-objective optimisation-based tuning methodology, balancing stability margin, bandwidth, and control effort. The novel controller is further evaluated through non-linear, time-domain simulations under turbulent wind and irregular waves, alongside these alternative control strategies, revealing performance trade-offs. Collectively, these contributions establish a robust framework for mitigating negative damping while simultaneously reducing auxiliary sensing requirements in FOWTs.

This paper is structured as follows: Sect. 2 outlines the fundamental principles of FOWT closed-loop control and the origin of the negative damping phenomenon. Section 3 characterises existing control strategies to establish a baseline for comparison, before detailing our proposed control architecture. In Sect. 4, the controllers are evaluated by simulating the closed-loop system using the non-linear aero-servo-hydro-elastic tool OpenFAST .

In this section, we start by introducing the dynamic model of a conventional fixed-bottom wind turbine. Afterwards, we go on to explain the process of closing the loop with the baseline controller and the tuning methodology of the controller gains. Once this is established, we move on to the FOWTs where we introduce the additional dynamics for the floating platform to form a representative dynamic model of a FOWT to conduct further analysis on the complexities that arise when controlling FOWTs.

Conventional wind turbine dynamics are excited by the imbalance between the aerodynamic torque and the generator torque, which drives the generator speed, and thus a simplified wind turbine model is described as 1JrNgbΩ˙=τa(Ω,β,v)-Ngbτg, where Jr (kg m⁻²) is the rotor drivetrain inertia, Ω (rad s⁻¹) is the generator speed with the dot notation indicating the time derivative, τa (N m⁻¹) is the aerodynamic torque, Ngb (–) is the gearbox ratio, and τg (N m⁻¹) is the generator torque. The aerodynamic torque τa(Ω,β,v) is modelled by a non-linear function: 2τa=12ρπR2Ngbv3ΩCp(λ,β), with ρ (kg m⁻³) as the air density; R (m) being the rotor radius, Cp(λ,β) the power coefficient, which depends on the blade pitch angle β (rad) and the tip-speed ratio λ=ΩR/vNgb; and v (m s⁻¹) the wind speed normal to the rotor plane. At steady state, the non-linear wind turbine dynamics in Eq. () can be linearised using first-order Taylor series expansion around an equilibrium point as 3δΩ˙=NgbJr∂τa∂ΩδΩ+∂τa∂vδv+∂τa∂βδβ-Ngbδτg, where δ denotes state perturbation, and the partial derivatives of τa with respect to its independent variables are known as the aerodynamic sensitivities.

In practice, wind turbines are regulated with a generator speed controller, as at below-rated wind speeds, the controller is seeking to maximise the extracted power by keeping the collective blade pitch angle β constant while varying the generator torque τg as a function of the square of the generator speed Ω as follows : 4τg=kgΩ2, with kg=0.5ρπR2(Cp,max/Ngb3λopt3) being the generator-torque constant. The variable Cp,max is the maximum power coefficient achieved at the optimal tip-speed ratio (TSR) λopt and at a specific constant blade pitch angle known as fine blade pitch angle. It is fair to mention that the controller in Eq. () assumes a constant kg throughout the wind turbine's lifetime. In reality, this is not the case, as it is influenced by modelling inaccuracies and assumption errors. To address this limitation, the TSR tracking controller has proven to be more effective and is widely adopted in the wind energy industry .

At above-rated wind speeds (referred to as Region 3), a conventional wind turbine controller relies on the blade pitch to regulate the generator speed to its rated value Ωrat, while keeping the generator torque constant at its rated value . As a result, generator power fluctuations are directly proportional to the oscillations occurring in the generator speed δΩ=Ω-Ω¯. The collective blade pitch controller regulates the generator speed about its steady-state value Ω¯=Ωrat according to the following feedback control law : 5δβ=kpδΩ+ki∫δΩdt, where kp and ki are the proportional and integral controller gains, respectively. To reach a description of the gains, the azimuth angle ψ is introduced as Ω=ψ˙ in Eqs. () and (). By combining both equations and focusing on the generator speed terms, we derive a closed-loop system. When rewritten in the standard form of a second-order mass-spring-damper system, it becomes  6δψ¨+-NgbJr∂τa∂Ω+∂τa∂βkp︸2ζcωcδψ˙+-NgbJr∂τa∂βki︸ωc2δψ=0. Equation () represents the closed-loop system of the wind turbine in the above-rated region. Therefore, only the terms containing ψ and its derivatives are considered . The remaining terms are irrelevant to the control problem and therefore do not appear in Eq. (). Accordingly, we can parameterise the PI blade pitch controller gains : 7ki=-ωc2JrNgb∂τa∂β-18kp=-2ζcωcJrNgb-∂τa∂Ω∂τa∂β-1. Given a desired natural frequency ωc and damping ratio ζc, the PI controller gains can be computed . By defining the ωc and ζc of the generator speed response, the dynamic response of the rotor to wind speed variations can be altered. The value of ωc defines the bandwidth of the feedback controller. Typically, the controller bandwidth is chosen below the lowest structural natural frequency of the system to avoid interaction with lightly damped modes, leading to instability. The bandwidth should not include the right-half-plane zeros (RHPZs) existing in the wind turbine system as  reported. As shown in Eqs. () and (), their controller gains depend on the aerodynamic sensitivities, which significantly vary across operating points. As a result, the controller gains are scheduled at each operating point and modified during operation as the wind speed changes to maintain consistent closed-loop transient behaviour using a linear controller.

The main challenge associated with the control of FOWTs within Region 3 concerns their fore-aft motion . Therefore, it is critical to include floating platform dynamics in the control design model.

This section reviews various control strategies proposed for mitigating the negative damping instability in FOWTs, beginning with the most straightforward approaches and progressing towards more complex solutions involving additional sensors and actuators. Each method is evaluated in terms of its ability to address the negative damping effect and its effectiveness in overcoming the bandwidth limitation imposed by the RHPZs. Ultimately, the analysis concludes that only the incorporation of an additional actuator can effectively alleviate the constraint on closed-loop bandwidth.

Figure  shows the block diagram of the closed-loop FOWT system with the simple feedback PI controller. Each block represents a linear TF, with G(s) mapping β, the collective blade pitch angle, to Ω, the generator speed, while KPI(s) is the collective blade pitch controller.

Neglecting the floating platform dynamics during the FOWT control design often yields instability at the operating points containing RHPZs, since the high control bandwidth, associated with the high feedback control gains, causes platform pitch excitation . At first, one might expect exponential growth in the response due to negative damping, but this is not the case because of the non-linear dynamic coupling between the different FOWT modes. Yet the FOWT keeps oscillating back and forth without reaching a steady state, which is still undesirable. There are several ways to mitigate this challenging problem. Thus, in the remainder of this section, the conventional solutions are presented, followed by our proposed solution in the next section.

The FOWT system (NREL 5 MW RWT; , atop OC3 floater; ) was simulated in OpenFAST  with the five controllers discussed in Sect.  in environmental conditions of turbulent wind and irregular waves. The simulations were conducted in the above-rated Region 3 (vrated=11.4 m s⁻¹) at average wind speeds ranging from 12 to 24 m s⁻¹, with TurbSim  to simulate the turbulent wind field, where the International Electrotechnical Commission (IEC) Kaimal spectral model was used as a turbulence model with a turbulence intensity of 14 % and a wind shear exponent of 0.14. The irregular waves were generated using JONSWAP spectrum at a significant wave height Hs=3 m and peak period Tp=12 s. All the simulations were performed for a simulation time of 1200 s, with the first 600 s neglected for transients.

An example time-domain simulation at a reference wind speed of 18 m s⁻¹ is illustrated in Figs.  and . The time traces are complemented with the power spectra for a detailed view of the controllers' performance. Looking at the rotor speed signal in Fig. , we can see the significant impact the robust tuning of the SISO PI controller can make in comparison to the Detuned SISO PI controller. The rotor speed's peak-to-peak amplitude of the Robust SISO is significantly reduced compared to the Detuned SISO. This is also evident in the spectral content of its power spectrum, as the rotor speed oscillations are suppressed until 0.1 Hz.

For the SISO controller, the generator torque is kept constant and the generator power in Region 3 is directly related to the generator speed. The reduction in the rotor speed oscillations reflects on the generator power, leading to an improved power quality with less fluctuations. However, such an improved performance comes at the cost of actuation. This is to be expected since the increased bandwidth of the Robust SISO means higher control activity, which can be seen in the blade pitch signal with higher spectral content across the frequency range, leading to an increase in the blade pitch variation.

Regarding the MISO controller in Fig. , its main objective is to add damping to the closed-loop system, through extra blade pitch action, to compensate for the severe reduction in the overall system damping caused by the negative aerodynamic damping, as explained by Eqs. () and (). In this work, the MISO controller is composed of the Robust SISO controller, and added to it is the inner feedback loop from the platform pitch rate θ˙ to blade pitch, as shown in Fig. . The MISO controller in Fig.  appears to be doing slightly better than the Robust SISO in a small frequency segment within the low-frequency region before 0.05 Hz, while no significant difference is observed between both controllers at other frequencies. Similar to the detuned and Robust SISO cases, the generator power follows the same trend as the rotor speed since the generator torque is constant in the case of the MISO controller. This explains the absence of the generator torque curves relevant to the three cases in the power spectrum. The MISO controller blade pitch actuation does not change much from the Robust SISO controller. It simply is a little more active and thus more oscillatory because of the extra blade pitch input added.

As for the MIMO controller in Fig. , the generator torque is employed as an extra actuator to provide parallel compensation  to the FOWT system to deal with the RHPZs. Implementing the MIMO controller results in a modest enhancement of rotor speed, as the substantial improvement achieved by the Robust SISO controller over the detuned version significantly limits the potential for further error reduction. With the generator torque not constant anymore, the power variation includes contributions from both generator speed and generator torque, showing a clear drawback of the MIMO controller.

Transitioning to the newly proposed control structure, the SIMO controller demonstrates superior performance in generator speed regulation – the primary objective of this controller – particularly when compared to the Detuned SISO controller. While one might expect increased blade pitch activity to achieve better generator speed regulation, this is not the case. Instead, the blade pitch action remains nearly identical to that of the Robust SISO, MISO, and MIMO controllers. This is because, beyond a certain point, generator torque takes over, as previously shown in Fig. . Consequently, the generator torque response becomes highly aggressive, exhibiting significant variations to maintain a more stable generator speed signal, even reaching saturation. However, this comes at the expense of power quality, similar to the MIMO controller. Notably, the SIMO controller exhibits an even more aggressive generator torque action than the MIMO controller. A less aggressive tuning of the SIMO controller would reduce the actuator usage and improve the power quality. Nevertheless, if the power quality is the main control objective, a controller aimed at that objective could be synthesised but at the cost of increased drivetrain loads .

Across the above-rated wind speed spectrum, the SIMO controller achieves the lowest rotor speed oscillations, as indicated by the standard deviation, without any notable difference in blade pitch action compared to other controllers (see Fig. ). However, the generator torque experiences a large increase with the SIMO controller, even at wind speeds where the RHPZs are expected to disappear (above 16 m s⁻¹). This is because, unlike other controllers, the SIMO controller continuously engages the generator torque actuator across all wind speeds, including those without RHPZs. As a result, variations in generator speed have a considerable impact on generator power. In the simulations conducted at reference wind speeds of 12–14 m s⁻¹, the system occasionally operates below the rated wind speed, leading to fluctuations in generator torque. This occurs despite the Detuned SISO, Robust SISO, and MIMO controllers being designed to maintain a constant generator torque with zero standard deviation in Region 3 – a condition that is fully realised at wind speeds above 14 m s⁻¹.

Examining Figs.  and simultaneously, it is evident that all controllers reduce platform pitch oscillations compared to the fluctuations observed with the Detuned SISO. Among them, the MISO controller achieves the greatest reduction, as it is specifically designed to enhance platform pitch damping – an effect clearly visible in the power spectrum around the platform pitch eigenfrequency (≈0.033 Hz).

Although the SIMO controller is primarily designed to mitigate generator speed fluctuations, it also succeeds in reducing platform pitch oscillations below the Detuned SISO level. While its effectiveness in this regard is lower than that of the MISO and MIMO controllers, this reduction remains beneficial.

Furthermore, this improvement extends to the tower base fore-aft moment (MTwrBs,y), as there is a strong correlation between platform pitch motion and tower base loading. Consequently, controllers that effectively suppress platform oscillations also contribute to significant tower fatigue reduction.

Regarding the blade-root flapwise moment (MFlp,y), all controllers outperform the Detuned SISO across all wind speeds, as shown in Fig. . This improvement is evident at low frequencies up to 0.1 Hz, after which there is a slight drop in performance, temporarily exceeding the level of the Detuned SISO. Beyond this point, all controllers converge, exhibiting no significant differences, as depicted in Fig. .

Rotor-shaft torsional loading (τshaft) is a well-known drawback of torque feedback in wind turbine control systems. While both the Robust SISO and MISO controllers exhibit smaller shaft loading excursions compared to the Detuned SISO, the MIMO and SIMO controllers, which rely on torque feedback, introduce greater fluctuations in shaft torsional loading. As shown in Fig. , this effect is particularly pronounced in the SIMO controller, which exhibits elevated shaft loading variations across all wind speeds, as further illustrated in Fig. .

Based on these findings, the authors recommend an adaptive approach, where different proposed controllers are alternated depending on environmental conditions and control objectives. For example, at certain times, the turbine operator may prioritise minimising generator speed oscillations and activate the corresponding controller. At other times, the focus may shift to reducing structural loading, necessitating a different control strategy. Since no single controller can simultaneously optimise all objectives – some of which may be conflicting – dynamic selection based on operational priorities is advised.

Another recommendation is to incorporate a feedforward control strategy to reduce dependence on reactive feedback control. If an accurate preview of disturbances affecting the FOWT is available, a LiDAR feedforward controller  targeting the wind turbulence and a wave feedforward controller  targeting the wave forces can be implemented to mitigate the effects of wind and wave disturbances on the FOWT, respectively. This approach alleviates the need for a high-bandwidth feedback controller, as the feedforward controllers would handle most of the disturbance rejection.

A new fixed-structure controller has been developed for FOWTs to effectively mitigate the well-known “negative damping” instability and address the non-minimum phase behaviour introduced by the persistent RHPZs in GΩβ. Designed specifically for generator speed regulation, the proposed controller was evaluated through non-linear simulations in OpenFAST, where it outperformed the existing FOWT controllers from the literature. Furthermore, it demonstrated robustness in a high-fidelity simulation environment, effectively handling additional system dynamics.

The primary advantage of the proposed FOWT controller is that it operates without requiring any additional sensors, preserving the conventional SISO configuration by relying exclusively on generator speed measurement. This approach enhances robustness, as incorporating extra signals can increase sensitivity to unmodelled dynamics. Additionally, the controller can be regarded as an artificial SISO controller, as shown in Figs.  and , where the plant transfer function is pre-filtered to achieve the desired control performance.

While the MIMO controller features a simpler control structure compared to the SIMO controller, the SIMO configuration provides built-in redundancy within the FOWT system, ensuring continued operation in the event of floating platform sensor failure. If the wind turbine is equipped with platform pitch sensors and the MIMO controller is in use, a sensor malfunction could compromise performance. In such a scenario, the SIMO controller acts as a backup solution, allowing the system to operate despite the loss of platform pitch measurements.

Incorporating inner loops into the standard control loop GΩ,β – whether using MISO, SIMO, or MIMO structures – expands the design space for the SISO PI feedback controller, enabling the achievement of higher bandwidth. However, a well-known drawback of employing generator torque actuation for parallel compensation is the resulting increase in shaft and drivetrain loads , along with deteriorated power quality. To mitigate power quality concerns, alternative MIMO feedback architectures, such as a constant-power controller , can be integrated.

Furthermore, the cost function in the robust control tuning approach from  has been modified to prevent actuator saturation. Without this adjustment, actuator activity could become unbounded, leading to simulation instability. This refinement has enhanced performance in the primary objectives of generator speed regulation and tower load reduction, even in the presence of modelling inaccuracies resulting from dynamic simplifications and omitted degrees of freedom.