Multi-Degree-of-Freedom Load Reproduction by Electrohydraulic Digital-Servo Loading for Wind Turbine Drivetrain

Abstract

Many drivetrain testing facilities have been built to reproduce multi-degree-of-freedom loads, thus simulating real wind conditions for evaluations of the reliability and durability of turbine subsystems. In this paper, the electrohydraulic schemes for the non-torque loading of a wind turbine’s drivetrain test benches are first analyzed. To deal with the control inaccuracy caused by the drastically increasing loading force, along with the rapid development of large-scale wind turbines, a multi-cylinder electrohydraulic digital-servo loading (MEDSL) technology is proposed. A novel electrohydraulic digital-servo cylinders group is designed. The proposed MEDSL can provide continuous and accurate load recurrence under wider wind conditions by varying the operational area of the cylinders group. Moreover, a sliding mode controller (SMC) is designed to realize the large dynamic loading of the MEDSL system. By comparing the SMC to a traditional PID controller in a servo-valve controlled cylinder, both simulation and experiment results proved the advantage of the proposed SMC. Accordingly, extensive experiments with a 4-cylinder case were carried out on a real full-loading bench using the SMC-based MEDSL device. The excellent tracking performance under complicated signals that represent the real wind loads demonstrated the feasibility and effectiveness of the proposed MEDSL technology and the SMC method.

1. Introduction

The global installed wind power capacity constantly increased during the last decade. The additional installations of 93.6 GW in 2021 have expanded the worldwide cumulative capacity of wind power generation to 837 GW [1]. The largest offshore wind turbine is the MySE16.0-242 with an unprecedented 16 megawatts (MW) nameplate capacity, which was launched by MingYang Smart Energy in 2021 [2]. It is predicted that, by 2025, wind turbines with a single capacity of 20 MW will be available [3,4]. The development of wind turbines is geared towards being large-scale with the increasing demand for renewable energy.

However, concerning this trend, the complexity of construction, operation, maintenance, and inspection has increased because tower heights, rotor radius, and overall weights have amplified in size and capacity [5]. Larger wind turbines tend to have more frequent structural collapses and component failures, and they require higher maintenance costs [6]. Thus, it is necessary to accurately reproduce the specified wind loads on the ground at the pre-production prototype phase to evaluate the reliability and durability of turbine subsystems.

As the growing scale of wind turbines sets corresponding high requirements on the drivetrain testing system, many countries have built national six degree-of-freedom (DOF) ground test facilities for the drivetrain of large wind turbines. The establishment of a 4 MW wind turbine test bench was initiated in 2014 by the Center for Wind Power Drives located at RWTH Aachen University [7,8]. A non-torque loading (NTL) system and a driving motor were utilized as a load application system to replace the rotor of the wind turbine. A hardware-in-the-loop (HiL) system was integrated as a mechanical-level component to simulate the effect of the rotor at the test bench. Through a series of tests involving the model depth and wind field characteristics within the HiL-System, it was concluded that the certification measurements could feasibly be performed on system test benches [9]. Additionally, the control effect was realized by the coordinate transformation of a geometric model. Besides, Germany’s Fraunhofer Dynamic Nacelle Testing Laboratory combined mechanical and grid emulators to test wind turbines up to 10 MW [10].

In America, the 7.5 and 15 MW wind turbine drivetrain test benches have been conducted at Clemson University [11]. The load application units featured in the 15 MW test bench display the capacity to apply thrust forces extending up to ±4000 kN, radial forces up to ±8000 kN, and bending moments reaching ±50,000 kNm all at a frequency of 1 Hz [12]. A sliding mode controller (SMC) was developed on the overactuated system to replicate the full-scale time-varying wind loads of the 7.5 MW test bench. The maximum nominal error is approximately 25 kN forces and 25 kNm moments, or roughly 5% of the requested signals’ amplitude for a specific test profile [13]. Bibo et al. provided a comprehensive assessment of the uncertainty and inaccuracies in applied loads and measured responses, as well as their significance relative to established predefined limits for repetition for a drivetrain exposed to both static and dynamic loads on the 7.5 MW test bench [14]. The experimental results were applied to evaluate the tracking error on the test bench and the cross-coupling occurring between bending moments and forces [15]. The maximum tracking error for the commanded inputs was about 7%, which was the nodding moment [16]. Additionally, by joining the Duke Energy eGRID Center, it was possible to apply realistic loads concurrently to both the mechanical and electrical interfaces of a complete nacelle [17,18].

For the UK, the Offshore Renewable Energy (ORE) Catapult is at the forefront of drivetrain testing, validation, innovation, and research. They have a 15 MW drivetrain testing bench for offshore wind turbine systems with 6 DOF loading. The highly accelerated lifetime testing, power curve, efficiency assessment, and grid compliant tests were carried out to validate and enhance the advanced and complex wind turbine powertrain systems [19]. The National Renewable Energy Center in Spain devised and erected a test bench capable of examining the drivetrain and electrical components of wind turbines reaching up to 8 MW. The powertrain test bench was intended for conducting accelerated durability examinations of mechanical constituents, as well as functional evaluations of high-speed shaft brakes, generator bearings, and high-speed shaft couplings [20].

In Denmark, Lindø Offshore Renewable Center (LORC) Nacelle Testing included three test facilities, the 14 MW, 16 MW, and 25 MW test benches. The 25 MW test facility, installed in January 2021, could supply a torque of 32 MNm, 85 MNm tilt-moment, and 65 MNm yaw moment. The facility offered testing of the drivetrain components up to 16–18 MW, as well as functionality test of nacelles up to about 20 MW [21]. The development of a powertrain and gearbox test bench with a capacity of 30 MW is currently underway by Danish wind turbine testing expert R&D Test Systems. Upon completion, the test bench will host the most potent validation test rig for wind turbines. The machine’s capabilities will allow it to imitate the variety of wind forces that a nacelle powertrain may encounter during its lifespan. Expected to be delivered in 2024, the test bench is hoped to enhance product durability, as well as expedite time to market [22].

Although these aforementioned wind turbine test benches were constructed, and they performed certification activities, the loading design, operating principle, and control strategy were not fully published. Additionally, the dynamics and potential of the loading actuators were not comprehensively addressed. Since the torque simulator of wind turbine has been studied [23], the critical research lies in simulating the other five DOF loads, akin to those encountered during standard operations or severe wind occasions. Yin et al. proposed a loading system and decomposition strategy to accurately simulate five DOF loads. The mean absolute percentage error of five DOF loads could be well kept within 6.6% [24]. However, the advanced control strategy was not involved, and experimental conditions were not fully detailed. Furthermore, when it is applied to the NTL for larger-scale wind turbines, many problems, such as tracking error and response speed, will be exposed. Some co-simulation has been studied for servo valves. A numerical approach was proposed for the multi-domain physical problem of the valve [25]. The particle swarm algorithm was applied to the design optimization of a solenoid actuator [26], and the design of experiments was developed [27]. However, it is difficult to achieve downward compatibility, namely, it can be difficult to realize high-accuracy, as well as quick and continuous loading, for each capacity class.

Aiming to solve the cons mentioned above, the NTL structural schemes were first introduced and analyzed. To deal with the problem of control inaccuracy caused by the drastically increasing loading force along with the rapid development of wind turbines of ten MW-class, a novel multi-cylinder electrohydraulic digital-servo loading (MEDSL) technology was proposed for each loading point. Combined with applying a SMC to the servo-valve controlled (SVC) cylinder, the loading accuracy of the MEDSL was well performed. The results of the simulations and experiments showed the advantages of the MEDSL.

This paper is organized as follows. Three main NTL structural schemes are introduced in Section 2. In Section 3, the structure of the MEDSL technology and the modified loading principle are represented. In Section 4, the effect of the proposed SMC strategy is studied, based on AMESim and SIMULINK co-simulation. In Section 5, experiments of the MEDSL with SMC have been displayed and exhibited encouraging results. Section 6 discusses the conclusion and outlook.

2. Structural Schemes for NTL

Wind turbine loads are primarily derived from a combination of various factors, such as aerodynamic forces, gravitational forces, dynamic interactions, and mechanical controls. Apart from the turbine torque, the majority of loads on the turbine can be categorized into five degrees of freedom components. These components comprise three orthogonal force constituents, as well as two orthogonal moment components [28]. The structure of the wind turbine drivetrain test system is shown in Figure 1, and an electrical motor is developed for the purpose of replicating the actual wind turbine’s rotational speed and shaft torque. Through the reduction gearbox, the other five DOF loads on the rotating surface of the wind turbine are reproduced by the electrohydraulic system in the NTL bench. As the loading target of NTL, the loading disk is fixed on the main drive shaft to involve the mass and inertia effects of the real rotating wind rotor and blades. The remainder of the wind turbine subsystems, including the device under test and the grid emulator are deemed test articles. The NTL application unit built by different countries has various loading forms, as represented in Figure 2.

By analyzing the dynamic structure and loading information, it is concluded that most of the existing NTL technology simulates the five DOF loads of the wind turbine under different operating conditions through the following three layout schemes of electrohydraulic loading actuators.

2.1. Symmetrical Loading Scheme

The symmetrical loading scheme is conducted by twenty-four hydraulic actuators. Sixteen axial electro-hydraulic actuators are symmetrically positioned on the left and right sides of the rotating disk, coupled with the distribution of eight radial actuators across its circumferential surface as illustrated in Figure 3.

The force of axial force F_Li and its symmetrically distributed counterpart F_Ri compose the axial loading force F_Ai = F_Li − F_Ri (i = 1~8). The same pair of radial forces Fdi and Fdi’ along the axis of the rotation disk can be defined as the radial loading force Fri = Fdi − Fdi’ (i = 1~4). Hence, the balance equation between the five DOF (i.e., F_x F_y F_z M_y, and M_z) loads and the twelve force pairs are governed by Equation (1), where r is the loading radius of the rotating disk [28].

$$\left[\begin{array}{l}{F}_x\\ F_y\\ F_z\\ M_y\\ M_z\end{array}\right]=\left[\begin{array}{c}{\displaystyle \sum _{i=1}^8{F}_{Ai}}\\ F_{r3}+\frac{\sqrt{2}}{2}(F_{r2}+F_{r4})\\ F_{r1}+\frac{\sqrt{2}}{2}(F_{r2}-F_{r4})\\ (F_{A5}-F_{A1})\cdot r+\frac{\sqrt{2}}{2}(F_{A4}+F_{A6}-F_{A2}-F_{A8})\cdot r\\ (F_{A3}-F_{A7})\cdot r+\frac{\sqrt{2}}{2}(F_{A2}+F_{A4}-F_{A6}-F_{A8})\cdot r\end{array}\right]$$

(1)

As presented in Figure 2a, the symmetrical loading scheme is applied by Clemson University. Each loading actuator in this scheme is relatively independent, which simplifies the solving procedures. However, because the five DOF loads must be replicated simultaneously with shaft torque loading, the hydrostatic supports should be set to allow the rotating disk to hover over the actuators in order to accurately replicate the cantilevered turbine rotor’s operating conditions [28]. In this case, the thickness of the oil film should be strictly controlled to ensure that the loads are eventually conveyed to the disk and distributed across its annular surface through these supports.

2.2. Radial Eccentric Loading Scheme

The radial eccentric loading scheme is carried out by twenty-eight hydraulic actuators. Twelve actuators are arranged on each side of the rotating disk, but only four hydraulic actuators are used in the radial direction, and the loading line is not on the circumferential surface of the rotating disk, as shown in Figure 4.

The loading force vectors on the front and rear sides of the disk make up the axial force F_Ai = F_Li − F_Ri (i = 1~12). Additionally, the four radial loading force vectors are Fri (i = 1~4). Thus, the solution equations can be derived as Equation (2), where r refers to the loading radius and L denotes the eccentricity of radial loading.

$$\left[\begin{array}{l}{F}_x\\ F_y\\ F_z\\ M_y\\ M_z\end{array}\right]=\left[\begin{array}{c}{\displaystyle \sum _{i=1}^{12}{F}_{Ai}}\\ \frac{\sqrt{2}}{2}(F_{r3}+F_{r4}-F_{r1}-F_{r2})\\ \frac{\sqrt{2}}{2}(F_{r2}+F_{r3}-F_{r1}-F_{r4})\\ (F_{A6}-F_{A12})\cdot r+\frac{\sqrt{3}}{2}(F_{A5}+F_{A7}-F_{A1}-F_{A11})\cdot r+\frac{1}{2}(F_{A4}+F_{A8}-F_{A2}-F_{A10})\cdot r+\frac{\sqrt{2}}{2}(F_{r1}+F_{r4}-F_{r2}-F_{r3})\cdot L\\ (F_{A3}-F_{A9})\cdot r+\frac{\sqrt{3}}{2}(F_{A2}+F_{A4}-F_{A8}-F_{A10})\cdot r+\frac{1}{2}(F_{A1}+F_{A5}-F_{A7}-F_{A11})\cdot r+\frac{\sqrt{2}}{2}(F_{r3}+F_{r4}-F_{r1}-F_{r2})\cdot L\end{array}\right]$$

(2)

A typical example is the ORE Catapult in the UK, as shown in Figure 2b. There is also another version of radial eccentric loading, wherein four cylinders are on each axial side, representing twelve cylinders in total, which are employed by the 4 MW test facility at RWTH Aachen University [8]. In this loading scheme, the loading force vector of the radial cylinder has a certain eccentric displacement, so it does not need higher oil pressure while providing a larger bending moment. Nevertheless, the five DOF loads in the solving equation are coupled with each other. Thus, the calculation process is more complex than that of the symmetric loading scheme.

2.3. Parallel Six-Hydraulic-Cylinder Loading Scheme

The parallel six-hydraulic-cylinder loading scheme changes the orientation of the rotating disk by controlling six loading force vectors, as depicted in Figure 5. The five DOF loads’ decomposition calculation of this scheme needs to be carried out in the spatial coordinate system.

The decomposition of five DOF loads can be expressed as Equation (3), where Fi (i = 1~6) denotes loading force vectors; and α, β, and γ are the angles between the vector and the x axis, y axis and z axis, respectively; r refers to the radial distance between the action point of the loading force vectors and the loading disk center. L denotes the eccentricity of radial loading. The loading disk calculation center of the 5 DOF load is marked in a red dot in the left part of Figure 5. L means the distance between the loading force vectors and the loading disk center.

$$\left[\begin{array}{l}{F}_x\\ F_y\\ F_z\\ M_y\\ M_z\end{array}\right]=\left[\begin{array}{c}{\displaystyle \sum _{i=1}^6{F}_i\cdot \cos {\alpha }_i}\\ {\displaystyle \sum _{i=1}^6{F}_i\cdot \cos {\beta }_i}\\ {\displaystyle \sum _{i=1}^6{F}_i\cdot \cos {\gamma }_i}\\ {\displaystyle \sum _{i=5}^6\frac{\sqrt{3}}{2}\cdot F_i\cdot \cos {\alpha }_i\cdot r}-{\displaystyle \sum _{i=2}^3\frac{\sqrt{3}}{2}\cdot F_i\cdot \cos {\alpha }_i\cdot r}-{\displaystyle \sum _{i=1}^6{F}_i\cdot \cos {\gamma }_i\cdot L}\\ {\displaystyle \sum _{i=1}^6{F}_i\cdot \cos {\beta }_i\cdot L+F_4\cdot \cos {\alpha }_4\cdot r-F_1\cdot \cos {\alpha }_1\cdot r+}{\displaystyle \sum _{i=3,5}^{}\frac{1}{2}{F}_i\cdot \cos {\alpha }_i\cdot r-{\displaystyle \sum _{i=2,6}^{}\frac{1}{2}}{F}_i\cdot \cos {\alpha }_i\cdot r}\end{array}\right]$$

(3)

This scheme is applied by the loading bench of LORC in Denmark, as presented in Figure 2c. This loading method can achieve the predetermined loading target through a few hydraulic cylinders, which is easy to control. However, the five DOF loads are highly coupled with each other, thus, the calculation process is more complex than the previous two schemes. Meanwhile, the platform has a large displacement, which needs to be equipped with customized coupling.

Each of the schemes introduced above has different numbers of loading actuators and vectors, which are listed in

Table 1. Character of NTL loading schemes.

Loading Scheme	Loading Actuators	Loading Vectors	Advantage	Disadvantage
Symmetrical scheme	24	12	Simple solving procedure	Difficult hydrostatic support
Radial eccentric scheme	28	16	Can provide large bending moment	Complex calculation process
Parallel six-hydraulic-cylinder scheme	6	6	Few control vectors	Large displacement of the platform and complicated decoupling process

. The advantages and disadvantages of these schemes are also exhibited.

3. MEDSL Technology for Large-Scale Wind Turbine Test Bench

3.1. Structure

The three NTL schemes discussed in Section 2 are loaded with multiple SVC cylinders by different arrangements to reproduce real wind loads. The basic loading unit is an SVC cylinder, consisting of an electrohydraulic servo-valve and an asymmetric cylinder.

However, the reproduced loading force ramps up as the equipped capacity of the wind turbine grows. Since the maximum pressure that the hydraulic system can provide is limited, a larger hydraulic cylinder may be the only option [29]. Nevertheless, this solution requires customized large cylinders and servo-valves. Besides, in the case of light wind, the required loading force is very small, and the response speed of a large SVC cylinder is slower due to the large volume and the huge flow demand compared with a small SVC cylinder. Namely, a single large cylinder has no downward compatibility, and it can hardly realize accurate, quick, and continuous loading for different capacity classes.

Moreover, there exists an inevitable control error for the SVC cylinder because of the nonlinear factors [30]. Additionally, the increment of the cylinder area will enlarge the control error and amplify the loading error of the electrohydraulic system. To improve the basic mechanism of electrohydraulic loading, the MEDSL technology was proposed for each SVC cylinder loading point to deal with the problem of inaccuracy control and to realize precise load recurrence under a wider wind load condition.

The reproduction process of non-torque loads with MEDSL technology can be exhibited in Figure 6. The blue box is the load calculation process. For each loading point, the green box presents the F_A1 example application of MEDSL technology in the case of a four-cylinder combination. The actual five DOF loads are calculated by defining specific working conditions in GH Bladed software. Due to the simple solving procedure of the symmetrical loading scheme, the loads can be decoupled with the case of the symmetrical loading scheme i.e., Equation (1), to obtain the loading force of each point, including eight axial and four radial force points. Because the applied process of every force is identical, the application of MEDSL technology is exhibited with the F_A1 example. The traditional large hydraulic cylinder F_A1 is replaced by several small cylinders (take four-cylinders—F_A10, F_A11, F_A12, and F_A13—as examples). Among them, the F_A10 is exerted by a SVC cylinder, and F_A11, F_A12, and F_A13 are provided by (on-off valve controlled) OVC cylinders I, II, and III, respectively. The force of the SVC cylinder F_A10 can be regulated indefinitely, whereas the three OVC cylinders process solely two loading force states, namely, no loading force or maximum loading force. Thus, the total loading force is continuous by the electrohydraulic and digital combination. The industrial computer can generate loading control signals to determine the spool displacement of the servo valve and the status of the three on-off valves based on the MEDSL structure.

In the case of applying MEDSL technology to the symmetrical loading scheme, the twenty-four hydraulic cylinder groups were designed to substitute the traditional twenty-four SVC hydraulic actuators. Moreover, because of the randomness of the wind load, the reproduced five DOF loads can change over a wide range. Thus, for the small reference loading force, the MEDSL only uses the small SVC cylinder, thus it will greatly improve the response speed in comparison with a single large cylinder. The high precision and downward compatibility are particularly important in the multi-stage MW-class wind turbine drivetrain testing.

3.2. Loading Principle

The basic loading principle of the MEDSL technology is concluded, and the four-cylinder case has been investigated in the section. A traditionally used single cylinder loading is replaced by the novel electrohydraulic digital-servo cylinders group at each basic loading point [31]. In each loading point within the cylinders group, there are N hydraulic cylinders present. One of these cylinders is governed by the electrohydraulic servo valve, whereas the remaining (N − 1) cylinders are controlled through the on-off valve. For each loading point, the total loading force F_Li includes two parts, one is the SVC cylinder, and the other is the sum of the force of the OVC cylinders.

As shown in Figure 7, the force on each loading point consists of the total loading force of a cylinder group. Take the left side of the loading disk as an example, and, thus, the axial force F_Li (i = 1~8) can be defined as:

$$F_{Li}=F_{Li0}+{\displaystyle \sum _{\mathrm{n}=1}^{N-1}{F}_{Li\mathrm{n}}}$$

(4)

where; F_Li0 is the exerted force of the SVC cylinder; F_Lin is the output force of the OVC cylinder; and N is the number of cylinders in a group. In Figure 7, N is set to 4. The forces exerted on the right side (F_Ri) and the radial side (F_di/F_di′) of the disk are defined in the same way. The axial loading forces can be composed as F_Ai = F_Li − F_Ri (i = 1~8). The radial loading forces are Fri = Fdi − Fdi′ (i = 1~4). Due to the areas of the OVC cylinders increasing twice compared to the previous one, the number of the cylinders should be selected as:

$$N=\lceil {\log }_2\left[(F_{\max }/p_{\max })/S_0\right]\rceil +1$$

(5)

where; F_max is the maximum loading force for the loading point; F_a is the control precision; p_max is the pressure of the hydraulic source; the area of the SVC cylinder is S₀ = F_a/p_a; $\lceil \rceil$ represents rounding up. The integer N obtained can calculate S₀* inversely as:

$$S_0*=(F_{\max }/p_{\max })/2^{(N-1)}$$

(6)

However, there exists a minor eccentric moment due to the installation distance between cylinders in each cylinder group. As can be seen from the blue box in Figure 7, the actual loading point at each point will change with the magnitude of the loading force. This loading point will move from the center of each cylinder or some specific force equivalent points to S₀. Thus, the distance between the actual loading point of each cylinder group and the center of the loading disk (r(F_Ai)), and the angle with the coordinate axis, become nonlinear functions, varying with the loading force. Therefore, the five DOF loads loading formula also needs to be modified as:

$$\left[\begin{array}{l}Fx\\ Fy\\ Fz\\ My\\ Mz\end{array}\right]=\left[\begin{array}{c}{\displaystyle \sum _{i=1}^8{F}_{Ai}}\\ {\displaystyle \sum _{i=1}^4{F}_{ri}}\cos \phi \left(F_{ri}\right)\\ {\displaystyle \sum _{i=1}^4{F}_{ri}}\sin \phi \left(F_{ri}\right)\\ {\displaystyle \sum _{i=4,5,6}}{F}_{Ai}\cdot r\left(F_{Ai}\right)\sin \theta \left(F_{Ai}\right)-{\displaystyle \sum _{i=1,2,8}}{F}_{Ai}i\cdot r\left(F_{Ai}\right)\sin \theta \left(F_{Ai}\right)+{\displaystyle \sum _{i=3,7}}{F}_{Ai}\cdot r\left(F_{Ai}\right)\sin \theta \left(F_{Ai}\right)+{\displaystyle \sum _{i=1}^4{M}_{\mathit{yi}}}\\ {\displaystyle \sum _{i=2,3,4}}{F}_{Ai}\cdot r\left(F_{Ai}\right)\cos \theta \left(F_{Ai}\right)-{\displaystyle \sum _{i=6,7,8}}{F}_{Ai}\cdot r\left(F_{Ai}\right)\cos \theta \left(F_{Ai}\right)+{\displaystyle \sum _{i=1,5}}{F}_{Ai}\cdot r\left(F_{Ai}\right)\cos \theta \left(F_{Ai}\right)+{\displaystyle \sum _{i=1}^4{M}_{\mathit{zi}}}\end{array}\right]$$

(7)

where; $\theta (F_{Ai})$ is the angle between the actual loading point of each axial cylinders group and the y-axis; $\phi (F_{Ai})$ is the angle between the actual loading point of each radial cylinders group and the z-axis; $M_{yi}$ is the additional bending moment produced by the i-th cylinders group in the y-direction; $M_{zi}$ is the additional bending moment produced by the i-th cylinders group in the z-direction.

Generally, the MEDSL technology improves the structure of each basic unit of the wind turbine NTL electrohydraulic system. It provides a new scheme for the drivetrain testing system of large-scale wind turbines. Furthermore, the accuracy of the novel loading scheme using MEDSL mainly depends on two aspects. Firstly, the loading formula could be modified and recalculated in real-time to ensure the implementation of accurate reproduction of five DOF loads under the coordination and integration of multiple hydraulic cylinder groups. Secondly, the accuracy of each hydraulic cylinder group is quite important. The advanced controller should be adopted to enhance the loading performance of each loading point.

4. Controller Development

The control performance of the proposed MEDSL technology lies in the precise control of the SVC cylinder pressure system. Since there exists an inevitable control error caused by typical nonlinear factors for electrohydraulic servo systems, while the OVC cylinder does not have this error. Therefore, it is essential to design an advanced control algorithm to deal with parameter uncertainty and system nonlinearity. Sliding mode variable structure control has the benefits of high control accuracy and simple structure with strong robustness, which has been widely used in electromechanical and electrohydraulic servo control [32,33].

4.1. Model of the SVC Cylinder Pressure System

Assuming constant supply pressure, the flow equation of a SVC cylinder can be expressed as [34]:

$$q_L=K_q{x}_v-K_c{p}_L$$

(8)

where; q_L is the load flow rate; K_q and K_c are flow gain and the flow-pressure coefficient, respectively; x_v is defined as the spool displacement of the servo-valve; p_L is called the load pressure. The load flow continuity equation includes the flow that pushes the piston, the leakage flow, and the compression flow, which can be given as:

$$q_L=Ap\frac{d{x}_p}{dt}+C_{tp}{p}_L+\frac{V_t}{4{\beta }_e}\frac{d{p}_L}{dt}$$

(9)

where; A_p is the effective area of the piston; x_p is the displacement of the piston rod; C_tp is the total leakage coefficient of the hydraulic cylinder; V_t is the total volume of compressed fluid in the circuit; β_e is the oil effective bulk modulus. The force balance equation can be derived as:

$$A_p{p}_L=m_t\frac{d^2{x}_p}{d{t}^2}+B_p\frac{d{x}_p}{dt}+K{x}_p+F_L$$

(10)

where; m_t is the equivalent mass; B_p and K are the equivalent viscous damping coefficient and the load stiffness; F_L denotes the external force. The pressure–flow characteristic equation of the servo-valve can be written as:

$$q_L=C_{d}W{x}_v\sqrt{\frac{1}{\rho }\left(p_s-\frac{x_v}{\left|x_v\right|}{p}_L\right)}$$

(11)

where; C_d is the flow discharge coefficient; W is the valve orifice area gradient; ρ is the fluid density; p_s is the supply pressure; x_v = τu, τ is the proportional coefficient between the spool displacement and control signal u. The flow nonlinear part of the servo-valve is induced into a separate expression as follows to simplify the modeling process.

$$g(u)=\sqrt{p_s-\mathrm{sgn}(u)p_L}$$

(12)

Due to the proximity of the natural frequency of the servo-valve and the hydraulic cylinder’s frequency, it is reasonable to represent the load flow transfer function of the servo-valve as a second-order oscillation component whilst still retaining the flow’s nonlinear properties [35].

$${\ddot{q}}_L=-k_B{\dot{q}}_L-k_k{q}_L+k_{s}ug(u)$$

(13)

where; k_B, k_k, and k_s are the servo coefficients. The Laplace transform of Equation (11) can be written as:

$$q_L=\frac{k_s}{S^2+k_{B}S+k_k}ug(u)$$

(14)

Taking the Laplace transform Equation (12) into (14), the third derivative of load pressure p_L can be obtained. Define a set of state variables as $x={\left[x_1,x_2,x_3,x_4,x_5\right]}^T={\left[x_p,{\dot{x}}_p,p_L,{\dot{p}}_L,{\ddot{p}}_L\right]}^T$. The external disturbance is much smaller than the static loading force. When the loading disk is attached without a hydrostatic support system, the external force F_L is 0. Therefore, by ignoring the influence of external force, the pressure control system of the SVC cylinder can be described by combining Equations (8)–(14) in state–space form as:

$$\{\begin{array}{l}{\dot{x}}_1=x_2\\ {\dot{x}}_2=\frac{1}{m_t}\left(-K{x}_1-B_p{x}_2+A_p{x}_3\right)\\ {\dot{x}}_3=\frac{4{\beta }_e}{V_t}\left(-A_p{x}_2-C_{tp}{x}_3+q_L\right)\\ {\dot{x}}_4=x_5\\ {\dot{x}}_5=a_1{x}_1-a_2{x}_2-a_3{x}_3-a_4{x}_4-a_5{x}_5+\frac{4{\beta }_e{k}_s}{V_t}ug(u)\end{array}$$

(15)

where $a_1=\frac{4K{A}_p{\beta }_e}{m_t{V}_t}{k}_B-\frac{4B_{p}K{A}_p{\beta }_e}{{m_t}^2{V}_t}$, $a_2=\frac{4A_p{\beta }_e}{V_t}{k}_k-\frac{4K{A}_p{\beta }_e}{m_t{V}_t}-\frac{4B_p{A}_p{\beta }_e}{m_t{V}_t}{k}_B+\frac{4{B_p}^2{A}_p{\beta }_e}{{m_t}^2{V}_t}$, $a_3=\frac{4Ctp{\beta }_e}{V_t}{k}_k-\frac{4B_p{A_p}^2{\beta }_e}{{m_t}^2{V}_t}$ $+\frac{4{A_p}^2{\beta }_e}{m_t{V}_t}{k}_B$, $a_4=k_k+\frac{4C_{tp}{\beta }_e}{V_t}{k}_B+\frac{4{A_p}^2{\beta }_e}{m_t{V}_t}$, $a_5=k_B+\frac{4C_{tp}{\beta }_e}{V_t}$.

4.2. SMC Design

Set p_r as the expected output pressure of the SVC cylinder, and the tracking error and its derivatives are given by:

$$\{\begin{array}{l}{e}_1=p_r-p_L\\ e_2={\dot{p}}_r-{\dot{p}}_L\\ e_3={\ddot{p}}_r-{\ddot{p}}_L\end{array}$$

(16)

Design the sliding mode switching function of the hydraulic cylinder output pressure system as:

$$s=c_1{e}_1+c_2{e}_2+e_3$$

(17)

where; c₁ and c₂ are the switching function coefficients, positive real numbers. The derivative of the switching function is given by:

$$\dot{s}=c_1{e}_2+c_2{e}_3+{\stackrel{⃛}{p}}_r-(a_1{x}_1-a_2{x}_2-a_3{x}_3-a_4{x}_4-a_5{x}_5+\frac{4{\beta }_e{k}_s}{V_t}ug(u))$$

(18)

In order to force the states to arrive at a state of equilibrium on a sliding surface and remain on it thereafter, the reaching law is used to obtain SMC:

$$\dot{s}=-\epsilon sat(\frac{s}{\varphi })-ks$$

(19)

where; $\epsilon >0,k>0$ are reaching law designable parameters, and ϕ is the thickness of the boundary layer. Additionally, the saturation function is defined as follows to eliminate the chattering problem [36]:

$$sat(\frac{s}{\varphi })=\{\begin{array}{l}\frac{s}{\varphi }\\ \mathrm{sgn}(\frac{s}{\varphi })\end{array}\begin{array}{l}\mathrm{if}\left|\frac{\mathrm{s}}{\varphi }\right|<1,\\ \mathrm{if}\left|\frac{\mathrm{s}}{\varphi }\right|\ge 1,\end{array}$$

(20)

The expression of the SMC for the SVC cylinder output pressure system can be obtained as:

$$u=\frac{1}{\frac{4{\beta }_e{k}_s}{V_t}g(u)}(-(a_1{x}_1-a_2{x}_2-a_3{x}_3-a_4{x}_4-a_5{x}_5)+c_1{e}_2+c_2{e}_3+{\stackrel{⃛}{p}}_r+\epsilon sat(\frac{s}{\varphi })+ks)$$

(21)

4.3. Simulation Verification

A hydraulic system model of the SVC cylinder under SMC was built through AMESim and SIMULINK co-simulation to verify the accuracy performance of pressure control. The details of the parameter settings are listed in

Table 2. Parameters of the SVC cylinder pressure system.

Component	Parameter	Value	Component	Parameter	Value
Hydraulic oil	Density/kg·m−3	850	Hydraulic source	Pressure source/MPa	5
	Bulk modulus/MPa	800		Pump displacement cc/rev	100
SVC cylinder	Piston diameter/mm	50		Typical speed of pump rev/min	1500
	Rod diameter/mm	32
	Cylinder stroke/mm	50	Load	Mass/kg	20,000
	a1	1646	SMC	c1	50,000
	a2	3.156 × 1014		c2	10
	a3	363,100		$\epsilon$	10,000
	a4	11,460		k	20
	a5	147.4		$\varphi$	0.001

.

The comparison results of tracking performance under the target value $p_r=15(1-\cos (0.4\pi t))$ bar between SMC and proportional-integral-derivative (PID) have been illustrated in Figure 8a. Additionally, Figure 8b gives the corresponding tracking errors of SMC and PID. In contrast, the tracking error of SMC is kept within 0.005 bar, and that of PID is kept within 0.015 bar, the accuracy is increased by 67%, which proves the strength of the proposed SMC strategy for the SVC system.

For the tracking characteristics of the derivatives of p_r as shown in Figure 9a, it can be found that SMC can generally track ${\dot{p}}_r$ well, and the tracking pressure has an error of ±0.9 bar, as seen in Figure 9b. The advantages of applying the proposed SMC to the SVC cylinder have been validated in the co-simulation.

5. Experimental Study and Discussion

5.1. Experimental Setup

As illustrated in the left photo of Figure 10, experiments were first conducted in an NTL test bench to verify the analysis of the symmetrical loading scheme in the reproduction of the five DOF loads for a 100 kW wind turbine under normal operating conditions [24]. The reference force of each cylinder was derived by the GH Bladed software and therein calculated by Equation (1). The reproduced actual forces precisely tracked the five DOF reference loads. Thus, the loading scheme was capable of reproducing the five DOF wind loads with high tracking accuracy. Furthermore, to verify the effectiveness and the capability of the MEDSL technology and the SMC strategy, an experimental bench of a loading point was manufactured based on the study of four-cylinder loading, as shown in the right part of Figure 10. The single-point single cylinder was replaced by single-point four cylinders by using MEDSL technology as the white circle and black arrow indicated. The next four parts were the main components of the MEDSL device. The hydraulic station provided a hydraulic oil power source for the experiment, which was controlled by the electric cabinet. The control hardware included 5 V and 24 V DC power supply, acquisition card terminal board, and relay. The control system adopted an Advantech 610H industrial personal computer and a PCLD-8710 wiring terminal board. Then, the interface of the industrial computer through the LabVIEW program was presented.

The procedures behind the LabVIEW interface could be divided into the following steps. Firstly, according to Equation (6), the control signal u was determined by dividing the reference force to be replicated by a value p_max·S₀. The load distribution consisted of eight cases, which were categorized according to the value of u. Secondly, in each signal case, the decimal portion was provided by the SVC cylinder, while the integer portion was determined by the OVC cylinders. Through the adjustment of both the spool displacement of the servo valve and the on-off valve states, the cylinders could activate in a case-dependent manner. Finally, the force error was generated by the comparison between the reference force and the actual total force of four cylinders. This error was subsequently employed in the SMC to formulate the loading control command, which was ultimately dispatched to the SVC cylinder.

To measure the loading force signals exerted by each hydraulic actuator piston, the strain gauges were affixed to their respective end points of pistons. The error between the actual force and the reference force can be calculated by the industrial computer. Feedback force signals were processed by the computer, which applied the SMC method in LabVIEW software to generate loading control commands. Subsequent to their generation, the valves could receive the loading control commands through data acquisition cards to regulate how much force the SVC cylinder outputs and decide the states of the remaining OVC cylinders. Therefore, the closed-loop control of four-cylinder loading was completed and eventually drove the actuators to accurately produce the given loading forces.

5.2. Experimental Results

The verification method of the controller was to use some basic signals, such as step, square wave, triangle wave, and sinusoidal wave, to validate the performance of the controller in the aspect of response time, overshoot, tracking error, and other characteristics. This paper evaluated the performance of the response time and overshoot by the step and square tests. Meanwhile, the tracking error and the time delay were assessed by the sinusoidal signal. To validate the improvement of accuracy for the proposed SMC method experimentally, the traditional used PID controller was applied in the experiment for comparison. A test of 5 kN step load for the SVC cylinder was first carried out, as illustrated in Figure 11a. The performance of the SMC was better compared with the PID controller. The response time of PID was twice as much as that of SMC. Additionally, the overshoot was about four times as that of SMC. Moreover, the loading error under SMC was much smaller than that of the PID, as shown in

Table 3. Experiment results.

Type	Single SVC Cylinder						MEDSL
Index	5 kN steady-state load		Square load		Sinusoidal load		40 kN steady-state load	Square load	Sinusoidal load	Random load
	PID	SMC	PID	SMC	PID	SMC				I	II	III
Figure	Figure 11a		Figure 11b		Figure 11c		Figure 12a	Figure 12b	Figure 12c	Figure 13a	Figure 13b	Figure 13c
Response time (s)	0.30	0.15	0.163	0.10			0.30	0.425
Overshoot	9.31%	2.24%	13.21%	6.68%			3.36%	1.03%
Error range (kN)	1.328	0.314	3.129	1.492	2.413	0.924	1.185	4.932	6.870	56.644	23.115	8.147
Error average (kN)	0.103	0.039	0.075	0.052	0.376	0.126	0.103	0.189	0.728	1.352	1.979	0.963

.

Meanwhile, other types of loads checked for the SVC cylinder are square and sine inputs, as presented in Figure 11b,c. It was observed that the tracking performance of the PID controller had a larger overshoot and more steady-state error for the square wave. Besides, the lag was obvious for the sinusoidal input of the PID controller. The loading average accuracy was improved by 66.4%, approximately, calculated in Table 3. This verified that the feasibility and the effectiveness of the proposed SMC, and the tracking performance could meet the demands of accurate control of loading force for MEDSL technology.

Extensive experiments have been conducted on the MEDSL bench under the SMC method. The MEDSL tracking for a 40 kN steady load was displayed in Figure 12a. The response time of four-cylinder loading was about 0.3 s. This was mainly because the response speed of the servo-valve was faster than that of the three on-off valves. As for control accuracy, due to the linear relationship between force and area, the loading error of a single large SVC cylinder was considered as eight times of the error values under SMC in Figure 11a, which is about 0.312 kN error average and 2.512 kN error range. Hence, the loading average accuracy was improved by 67%.

The tracking for square signal exhibited excellent results in Figure 12b. Although the response time was longer, there was almost no overshoot since the proportion of the SVC cylinder was greatly reduced. Besides, compared with eight times error values of the large SVC cylinder which was an 11.936 kN error range and 0.416 kN error average, the steady-state error immensely decreased. The results implicated that the loading range and average accuracy were increased by 58.7% and 54.6%, respectively.

The tracking behavior for the sine load was shown in Figure 12c. There were some small load sudden changes caused by the asynchronization of valve opening and closing. However, the whole tracking performance showed that the MEDSL precisely follows the reference force. For comparison, the error of a single large SVC cylinder was considered as eight times of the error values in Figure 11c, which is about 1.008 kN error average and 7.392 kN error range. The error average was reduced by 28%. Besides, compared with the results under the same 0.1 Hz sinusoidal loading condition without SMC [31], which was 9.182 kN error range and 1.445 kN error average, the loading accuracy was raised by 25.2% and 49.6%. The improvement demonstrated that the SMC is more effective than the previous full closed-loop PID controller.

Furthermore, based on the research on the variation frequency of actual wind load [37], 1 Hz dynamic loading frequency can meet the requirements of the wind turbine drivetrain test bench. Therefore, three types of random signals representing real wind loads have been conducted on the MEDSL test bench. Firstly, random loads were tested in step form, as shown in Figure 13a. There were peak values at each switching point due to the existence of the load response time. However, the steady-state error was relatively small, and the total error average value was only 1.352 kN. Random loads II and III were shown in Figure 13b,c, and both results revealed good tracking performance, and the error average of random load III was less than 1 kN.

The above results show that the loading error of the four-cylinder was less than the single SVC cylinder, and the SMC has a better effect compared with traditional PID. The experimental results have good agreement with the aforementioned discussion and simulation, and again validate the effectiveness and the feasibility of the presented MEDSL technology. In addition, the excellent loading performance of a single point builds a theoretical and experimental foundation for global loading.

6. Conclusions

In this paper, three main NTL structural schemes are introduced, based on dynamic structural analysis and loading information. To deal with the control inaccuracy in hydraulic loading systems due to the growing scale of the wind turbine, aiming at each loading point, this paper proposed a MEDSL technology for the precise reproduction of multi-DOF large loads representing real continuously turbulent wind loads. The successive accurate large loading can be realized by varying the loading area of the proposed cylinder group. Additionally, its downward compatibility is essential to the multi-stage drivetrain testing of MW-class wind turbines.

An SMC is proposed to further improve the loading accuracy of the SVC cylinder. The accuracy was increased by 67% in the 0.2 Hz sinusoidal loading simulation, as well as about 62% in the 5 kN steady-state load experiment compared with the PID controller. Both results under static and dynamic signals proved the excellent dynamic performance of the electrohydraulic system and the effectiveness of the proposed SMC. Based on the good reproducing performance of the five DOF wind loads on the NTL test bench, extensive experiments with an N = 4 case were conducted on a real full-loading bench using the designed SMC, which validated the feasibility and effectiveness of the proposed MEDSL technology. The results implicated the loading average accuracy was improved by 54.6% compared with a single SVC cylinder for the 0.1 Hz square loads. Additionally, the MEDSL exhibited excellent tracking performance for three random signals representing real wind loads. It builds a theoretical and technical foundation for the drivetrain testing system of MW-class wind turbines.