1. Introduction
Wind energy has achieved significant growth due to its renewable and clean characteristics [
1]. Traditional control strategies focus on the maximum power tracking [
2,
3]. However, the uncertain disturbances pose new challenges for operation and maintenance. For instance, the wind shear and tower shadow effects increase extra load fluctuation on the rotor, leading to fatigue through the drivetrain [
4]. Tower load suppression is also crucial for individual wind turbines. Hence, control systems should take reliability into account seriously to reduce structural loads on wind turbines [
5]. Numerous studies have been conducted to optimize fatigue loads.
In the pursuit of enhanced operational stability, rotor speed control (RSC) has emerged as a key strategy for virtual inertia reduction [
6]. However, studies have revealed that RSC can induce unintended drivetrain torsional oscillations and secondary frequency deviations, compromising the system’s dynamic response [
7]. To address the limitation of traditional Proportional Integral (PI) controllers in achieving simultaneous power tracking and load reduction, pitch angle control (PAC) strategies, including collective and individual pitch control, have been developed [
8,
9]. In practice, RSC utilizes turbine inertia as an energy buffer, reducing pitch activity and capturing more wind energy [
10]. Nevertheless, a significant challenge arises when the rotor speed reaches its upper limit at high wind speeds or under a low power reference, necessitating a switch from RSC to PAC for power reference tracking [
11]. This leads to frequent pitch actuation, which is detrimental to the pitch system. This challenge underscores the need for predictive control strategies that can seamlessly integrate RSC and PAC operations.
MPC has been proposed to address these cooperative control challenges. Researchers have implemented MPC for regulating both PAC and RSC [
12,
13], with validation even extending to physical tests on scaled wind turbine benches [
14]. To resolve conflicting control objectives, generalized MPC frameworks with distributed communication protocols have been developed to mitigate instability induced by grid-connected devices [
15]. The superiority of MPC in multi-objective optimization for Multiple Input Multiple Output (MIMO) systems, including simultaneous power tracking and fatigue load suppression, has been emphasized [
16]. However, a critical limitation persists: conventional MPC relies on linearized models from fixed operational points, which inadequately represent the nonlinear dynamics of wind turbines across their wide operating range [
17].
Significant progress has been made to reduce the dependency on a single linear model. Adaptive MPC frameworks integrate real-time parameter estimation to mitigate linearization errors [
3], while data-driven approaches using deep reinforcement learning adapt aerodynamic sensitivities online, bypassing fixed linearization points [
18]. These methods contrast with traditional multiple model predictive control (MMPC), which employs gap metric theory to construct a bank of models covering different operating points [
19]. A fundamental drawback of conventional MMPC is its tendency to generate destabilizing control ripples during abrupt switches between models [
20]. When the model gap is sufficiently small, MMPC can achieve approximate soft switching [
21]. However, this leads to a substantial expansion of the model library size and an increased switching frequency. Collectively, while the field is shifting towards dynamic model adaptation, computational complexity and ensuring transient stability during controller transitions remain critical barriers, especially in turbulent wind conditions requiring multi-strategy coordination.
From the reviewed literature, three primary challenges for advanced wind turbine control can be identified. First, the model linearization required for nonlinear MPC often results in a reduction in global control accuracy. While nonlinear or adaptive MPC offers a solution, the associated non-convex optimization problems increase computational cost and reduce the feasibility of solutions. Most existing research relies on segmented or local linearization, a simplification that causes accuracy loss and undermines robustness across the entire operating range. Second, frequent controller switching in MMPC can lead to system instability. Existing MMPC and SSMMPC approaches often use a small gap metric threshold to approximate nonlinear behavior, which necessitates a large model bank and, consequently, more frequent switching. This frequent switching introduces instability and fluctuations into the closed-loop system, highlighting an urgent need for a genuine soft-switching rule. Third, control signal oscillation and linearization error collectively weaken the controller’s multi-objective optimization capability. Output signal oscillations directly impact the actuator, detrimentally affecting both load reduction and reference tracking. The errors from operating point linearization further challenge RSC and PAC. Therefore, it is necessary to propose a multi-objective cooperative load reduction control algorithm that incorporates suppression of control signal oscillation.
Inspired by these challenges, this paper proposes an SSMMPC strategy for wind turbines that considers fatigue load suppression. The main contributions of this work are threefold. First, a hybrid membership function is designed to smooth signal oscillations during MMPC transitions. The proposed SSMMPC, based on a triangular–trapezoidal hybrid membership function, simultaneously adjusts rotor speed and pitch angle for two-degree-of-freedom control. This soft-switching mechanism suppresses control signal oscillations during model transitions, achieving lower mechanical fluctuation and smoother power output. The stability of the proposed SSMMPC is rigorously proven using Lyapunov’s second method. Second, the proposed soft-switching method enables the construction of small-size model libraries based on large-gap thresholds. Different from previous work, this approach eliminates excessive switching actions by allowing a larger gap metric threshold. The introduced hybrid membership function mitigates signal oscillation and achieves genuine soft switching. It not only ensures switching smoothness but also reduces reliance on prior knowledge, thereby improving the flexibility and fault tolerance of threshold selection. Third, the multi-objective optimization capability of the SSMMPC is comprehensively validated for both power tracking and fatigue load reduction. The proposed controller demonstrates excellent performance in mitigating fatigue loads, particularly the main shaft torque and tower bending moment, while maintaining precise power reference tracking. Several experiments in the partial-load region and full-load region are conducted to verify the effectiveness of SSMMPC across a wide range of operating points.
The rest of the paper is organized as follows.
Section 2 gives a presentation of the nonlinear wind turbine model with small-signal linearization.
Section 3 introduces the controller design of the SSMMPC. The case studies are discussed in
Section 4. Limitations are analyzed in
Section 5. Finally, the conclusion is given in
Section 6.