Yaw Error Research Articles

Effects of mooring line failure on the dynamic responses of a semisubmersible floating offshore wind turbine including gearbox dynamics analysis

Floating offshore wind turbines (FOWTs) are located in complex ocean environments; therefore, they typically exhibit more significant dynamic responses than land-based wind turbines. Examples from the marine and offshore industries have shown that mooring line systems may fail under mild to severe sea conditions during their life cycle, possibly changing the global responses of the FOWTs and affecting their internal drivetrain dynamics. Therefore, this paper considered an OC4 DeepCwind semisubmersible FOWT as a representative model to investigate the influence of one broken mooring line on the steady-state and transient responses of the system, as well as on the internal drivetrain responses when the turbine operated normally. A fully coupled wind turbine model was constructed to analyze the global response, and then a decoupled method was applied to analyze the internal drivetrain responses. Furthermore, a set of load cases were considered to perform the simulations. The results showed that accidental fracture of the upwind line significantly affected platform motions, turbine structural loads, and tensions in the remaining lines. However, the effects of upwind line failure on the electrical power output and the internal gearbox dynamics were relatively small due to the almost unaffected nacelle yaw errors and the actions of pitch-torque control.

Path Tracking of a Four-Wheel Independently Driven Skid Steer Robotic Vehicle Through a Cascaded NTSM-PID Control Method

Four-wheel independently driven skid steer robotic vehicles (IDSSRVs) have been widely applied in many fields. However, limited by small size and low power consumption, many sensors and high-performance processors cannot be equipped into four-wheel IDSSRVs, which makes path tracking more complex. The nonsingular terminal sliding mode (NTSM) is a good choice for small robotic vehicles because of its strong robustness, fast convergence, and low complexity. However, the performance of the NTSM is easily affected by vehicular weight and road friction because a four-wheel IDSSRV has no steering devices and its driving behavior is completed by adjusting the velocity of the four wheels based on the wheel–ground interaction. Furthermore, a minor instability caused by the output difference of the motors can bring extra torque on the vehicle and ultimately lead to a tracking deviation for the NTSM controller. To resolve these problems, a dynamic model of a four-wheel IDSSRV is analyzed first. Subsequently, a cascaded NTSM-proportional–integral–derivative (PID) method is proposed, in which a conversion function based on compensating the sideslip angle is raised to improve the NTSM controller performance of antidisturbance and tracking accuracy with the limitations of the sensors and processors, and a joint PID controller simultaneously optimizing the motor output error and vehicular yaw error is designed to eliminate the imbalance of motor output and to reduce the deviation of the NTSM controller. Finally, comparative experiments are conducted, and the results highlight the benefits of the proposed approach by reducing the tracking error by approximately 80% compared with the dynamic model predictive control (MPC) method and reducing the tracking error by over 30% compared with the pure NTSM method.

Geometric Adaptive Controls of a Quadrotor Unmanned Aerial Vehicle With Decoupled Attitude Dynamics

Abstract This paper presents a geometric adaptive position tracking control system for a quadrotor unmanned aerial vehicle. In particular, the attitude control system is designed on the product of the two-dimensional unit sphere and the one-dimensional circle such that the direction of the thrust that is critical for position tracking is controlled independently from the yawing direction that is irrelevant to the position dynamics. Compared against the prior work with coupled attitude controls on the special orthogonal group, the proposed controller prevents large yaw errors from causing an undesirable performance degradation in tracking a position command. Further, the control input is augmented with adaptive control terms to mitigate the effects of disturbances, and it is formulated globally on the spheres to avoid singularities and complexities of local coordinates. The efficacy of the proposed control system is illustrated by both numerical examples and indoor/outdoor flight experiments.

Data-driven yaw misalignment correction for utility-scale wind turbines

In recent years, wind turbine yaw misalignment that tends to degrade the turbine power production and impact the blade fatigue loads raises more attention along with the rapid development of large-scale wind turbines. The state-of-the-art correction methods require additional instruments such as laser imaging detection and ranging to provide the ground truths and are not suitable for long-term operation and large-scale implementation due to the high costs. In the present study, we propose a framework that enables the effective and efficient detection and correction of static and dynamic yaw errors by using only turbine supervisory control and data acquisition data, suitable for a low-cost regular inspection for large-scale wind farms in onshore, coastal, and offshore sites. This framework includes a short-period data collection of the turbine operating under multiple static yaw errors, a data mining correction for the static yaw error, and ultra-short-term dynamic yaw error forecasts with machine learning algorithms. Three regression algorithms, i.e., linear, support vector machine, and random forest, and a hybrid model based on the average prediction of the three, have been tested for dynamic yaw error prediction and compared using the field measurement data from a 2.5 MW turbine. For the data collected in the present study, the hybrid method shows the best performance and can reduce the total yaw error by up to 85% (on average of 71%) compared to the cases without static and dynamic yaw error corrections. In addition, we have tested the transferability of the proposed method in the application of detecting other static and dynamic yaw errors.

Sliding mode lateral stand-off tracking control of finless airship

The paper addresses the stand-off tracking control problem for an underactuated finless airship having uncertainties and wind disturbances. The outer loop design sliding surface is based on the line of sight angle rate and its distance from a target, for the inner control loop, generates the reference heading angle commands, the proposed backstepping sliding-mode controller based on the yaw error angle generating commands by actuating the yaw-gyro propulsion. Theoretical results show that the closed loop system is globally asymptotically stable. With the assumption of target movement as disturbances, this framework is also applied to linear and variable direction moving targets. The numerical simulations are conducted for stand-off tracking control for a stationary and a moving target or targets, having servos dynamics and sensor models with measurement noises and external disturbances, and the results verify the effectiveness of the proposed framework for stand-off target tracking. The results obtained by comparing traditional proportional navigation and LQR design demonstrate the capability of the airship to execute a stand-off trajectory tracking with uncertainties and wind disturbances.

Research on Yaw Error Detection of Wind Turbine Based on Particle Swarm Optimization

Yaw system is an important part of the wind turbine, one of its main functions is to automatically face the wind when the wind turbine is in normal operation, to ensure that the engine room is facing the wind direction, so that the wind turbine can make efficient use of wind energy. However, the yaw system can not guarantee the accuracy at all times, which leads to the wind deviation. Too large deviation of wind energy not only reduces the efficiency of wind turbine using wind energy, but also leads to abnormal wear of equipment parts, which is not conducive to the normal operation of the unit. In this paper, a wind turbine deviation detection algorithm based on SCADA data is proposed. The detection algorithm mainly includes wind speed segmentation, data fitting, particle swarm optimization and other key technologies. After wind field verification, the algorithm proposed in this paper can effectively detect the wind deviation of wind turbines, and help to improve the efficiency of wind turbines.

Nonlinear Differential Braking Control for Collision Avoidance During Lane Change

In this paper, a nonlinear differential braking control method is developed to avoid collision during lane change under driver torque. The lateral dynamics consist of lateral offset error and yaw error dynamics and can be interpreted as a semi-strict feedback form. In the differential braking control problem under the driver torque, a matching condition does not satisfy, and the system is not in the form of, the strict feedback form. Thus, a general backstepping control method cannot be applied. To overcome this problem, the proposed method is designed via the combination of the sliding mode control and backstepping. Two sliding surfaces are designed for differential braking control. One of the surfaces is designed considering the lateral offset error, and the other sliding surface is designed using the combination of the yaw and yaw rate errors as the virtual input of the lateral offset error dynamics. A brake steer force input is developed to regulate the two sliding surfaces using a backstepping procedure under the driver torque. Integral action and a super twisting algorithm are used in the lateral controller to ensure the robustness of the system. The proposed method, which is designed via the combination of the sliding mode control and backstepping, can improve the lateral control performance using differential braking. The proposed method is validated through simulations.

Study on Novel Yaw Error Strategy for Wind Turbines Based on a Multi-Body Dynamics Method

At present, using structural dynamics models is the most commonly used and effective method to simulate the dynamic characteristics of large wind turbine. This paper used the multi-body dynamics method to construct the precise multi-flexible body dynamics model of a wind turbine coupled with aerodynamics/structure/control. The model can realize multi-disciplinary co-simulation interactions, and the accuracy was verified by comparing the numerical simulation data with the measured data. The allowable yaw error of a wind turbine is typically simplified to two or three fixed values according to the wind speed range, which cannot often adapt to the high and unsteady change characteristics of wind speed and direction under special conditions. In this paper, an accurate calculation method of allowable yaw error threshold based on measured wind speed and the corresponding optimization strategy of large yaw error are proposed, which not only avoid unnecessary shutdown and improve the availability, but also reduce the load of yaw bearing and improve the safety.

A Data-Mining Compensation Approach for Yaw Misalignment on Wind Turbine

As an important subsystem that controls the nacelle direction facing toward the inflow wind, the yaw control subsystem plays an indispensable role in wind turbine generation systems. The yaw performance of wind turbines will directly determine the maximum capture capacity of wind energy. However, owing to the lack of effective calibration on wind vane, yaw misalignments are usually present in practice, which highly impacts the performance of yaw control and power generation efficiency. In this study, a data-mining approach on wind vane for yaw misalignment compensation is presented without involving any additional hardware investment. Briefly, the operation data of wind turbines are first evenly divided in terms of measured yaw error, and a power curve is identified for each yaw partition. Quantified generation performance metrics of all power curves are calculated afterwards for yaw misalignment determination, then the yaw control strategy can be finally corrected for wind turbine generation performance improvement. The feasibility and effectiveness of the proposed scheme are testified with simulation and measured data of a 1.5-MW wind turbine.

High-precision and large-stroke XY micropositioning stage based on serially arranged compliant mechanisms with flexure hinges

Compliant mechanisms are state of the art in micropositioning stages due to their many beneficial features. However, their design usually compromises between motion range, motion accuracy and design space, while mechanisms with distributed compliance are mostly applied. The further use of flexure hinges with common notch shapes strongly limits the stroke in existing high-precision motion systems. Therefore, this paper presents a high-precision compliant XY micropositioning stage with flexure hinges capable of realizing a motion range of ± 10 mm along both axes. The stage is based on a novel plane-guidance mechanism, which is optimized to realize a precise rectilinear motion of the coupler link while keeping the rotation angles of all hinges below 5°. The XY motion is then achieved by coupling two of these mechanisms in a serial arrangement. Next, the synthesis of the monolithic XY stage is realized by replacing all revolute joints of the rigid-body model with flexure hinges using optimized power function notch shapes. Emphasis is also placed on the embodiment design of the stage and the actuator integration to minimize possible error sources. Finally, the quasi-static behavior of the compliant stage is characterized by a simulation with a 3D FEM model and by an experimental investigation of a prototype. According to the results, the developed compliant XY micropositioning stage achieves a maximum positioning deviation of less than 10 μm in both axes and a yaw error of less than 100 μrad over a working range of 20 mm × 20 mm with a comparably compact design of the compliant mechanism of 224 mm × 254 mm.

Optimization of the Yaw Control Error of Wind Turbine

Yaw system is an important part of wind turbine control system, yaw error is an important performance index of wind turbine, which has great influence on power generation. The wind utilization and the output of the power generation have been determined by the yaw error. In order to make the wind turbine better aligned toward the wind direction, reduce the yaw error, and increase the power generated by the unit, the angle errors of yaw control of wind turbine have been analyzed, in this paper, and the method of wind test, the strategy of yaw control have been studied respectively. Based on the results of the study, the method of wind test, the restart control strategy of yaw system and the performance of control strategy of yaw system have been optimized in this paper. In this way, the three important links are optimized, it will effectively reduce the yaw error as well as significantly improve the wind turbine generating electricity.

Aeroelastic performance analysis of horizontal axis wind turbine (HAWT) swept blades

Over the past decades, the capacity of commercial wind turbines has risen from 50 kW with 10 to 15 m rotor diameter to 5 MW with more than 120 m rotor diameter. Conversely, increase in the rotor blade length causes substantial blade deflection in torsional, lead-lag and flap-wise directions which leads to unsteady aerodynamic load distributions. The structural safety and stability of the wind turbine will also be affected by the undesirable aerodynamic performance. It is important to analyze the aeroelastic performance of wind turbines under yaw conditions for large scale wind turbine design. Swept blade is a recent innovation to increase the power production of wind turbines while reducing the blade loads. There are insufficient studies in which the effect of yaw error on aeroelastic performance of Horizontal Axis Wind Turbine (HAWT) swept blade has been analysed yet. In this study, aeroelastic performance analysis was performed to investigate the effect of yaw angle on the aeroelastic performance of HAWT with swept blades. The same analysis was performed on HAWT unswept blade, so as to compare the results with that of HAWT swept blade. CFD analysis in ANSYS Fluent was chosen for aerodynamic analysis whereas FEA in ANSYS Static Structural was chosen for structural dynamic analysis. The aeroelastic performance analysis of wind-swept blades under yaw angles of 0°, 10°, 30° and 60° at wind speed of 10 m/s was performed. The results show that yaw error has negative effect on the aeroelastic performance of swept blade as well as unswept blade. It can be proven that swept blades have a better aeroelastic performance in terms of higher rotor power and lower deformation than unswept blades, i.e. higher stability of swept blades under yaw condition compared to unswept blades.

XE112-2000 Wind Turbine Yaw Strategy With Adaptive Yaw Speed Using DEL Look-Up Table

With the increasing capacity of wind turbines, the importance of the yaw system has gradually become more prominent. The supervisory control and data acquisition (SCADA) system of XEMC Windpower Co., Ltd. is used in this paper to analyze the yaw data of the No. 5 wind turbine of Baozhong Mountain Wind Farm in Hunan Province. In order to evaluate the power generation and the damage equivalent load (DEL) of the yaw bearing during the yaw process, an economic model predictive control (EMPC) yaw strategy based on light detection and ranging (LIDAR) was proposed. EMPC takes the yaw error and wind speed as the disturbance of the cost function (CF) at the same time by establishing the yaw bearing DEL look-up table in advance. Discrete adaptive yaw speed control set is proposed to adapt to different wind conditions sets. Finally, the effectiveness of EMPC is verified using the model of XE112-2000 wind turbine in simulation software Bladed.

A 2.5MW Wind Turbine TL-EMPC Yaw Strategy Based on Ideal Wind Measurement By LiDAR

This paper analyzes the yaw data of the 2.5MW wind turbine of XEMC Windpower Company, and the real wind information collected by the wind farm, and proposes a two-level economic model predictive control (TL-EMPC) yaw strategy based on ideal wind measurement by light detection and ranging (LiDAR). This strategy comprehensively considers the power loss caused by yaw misalignment and the structural loads of the yaw bearing during the yaw process, making the yaw system more efficient and economical: In the high wind speed range, the yaw system has a higher sensitivity by setting the threshold of the yaw error angle, so as to fully capture wind energy; in the low wind speed range, fully consider the fatigue load of the critical parts of the wind turbine during the yaw process, thus Improve the economy of the wind turbine yaw system. The fatigue load and limit load of the yaw actuator at different yaw speeds are analyzed, and the best yaw speed is obtained. The finite control set of the yaw speed is established, which is used as the constraint set of the second-level minimum objective function. Finally, an external controller was used to simulate the 2.5MW wind turbine model in Bladed, and the effectiveness of the control strategy was verified.

Numerical Investigation of Three-Dimensional and Vortical Flow Phenomena to Enhance the Power Performance of a Wind Turbine Blade

The performance of a wind turbine generator (WTG) is highly dependent on the interaction of a rotor blade with complex fluid behaviors, especially the induced vortex structure. In this paper, vortical flows around a blade were first investigated by the unsteady Reynolds averaged Navier–Stokes (RANS) simulation with shear stress transport (SST) turbulence model. It showed that the vortical flows were strongly formed at the blade tip due to the 3D behavior of the boundary layers dominated by pressure gradient. The strong secondary flow was also formed at the near hub due to the Coriolis force and the centrifugal force. At the interacting region of the rotating blade with the tower, the power production was reduced by 22.1% due to the high-pressure fluctuation of the 3P frequency. Based on the close investigation, methods for enhancing the power performance of a WTG were explored, which included the optimization of winglet and ogee design for the blade tip and optimal layout of the nacelle anemometer. The optimized winglet achieved the increase of aerodynamic performance with 0.54%, and the optimal location of the nacelle anemometer was found with a low-turbulence intensity level of 0.003 normalized by the rotor tip speed. The results showed that the traditional anemometer needs to consider the intrinsic flow angle of 11.43° to avoid the loss of aerodynamic performance caused from yaw error.

A Novel Alignment Method for SINS with Large Misalignment Angles Based on EKF2 and AFIS.

In order to achieve the fine alignment of strapdown inertial navigation (SINS) under large misalignment angles, a novel filtering alignment method is proposed based on the second-order extended Kalman filter (EKF2) and adaptive fuzzy inference system (AFIS). Firstly, the quaternion is employed to represent the attitude errors of SINS. A second-order nonlinear state equation is made based on the nonlinear velocity error model and attitude error model, and the linear measurement equation is based on the velocity outputs from SINS. Then, the filtering scheme is designed based on EKF2 and AFIS. The error estimation and fine alignment can be achieved by using the proposed filtering scheme. The results of Monte Carlo Simulation show that the errors of pitch, roll and yaw misalignment angles quickly decrease to about 14″, 15″ and 7.62′ respectively in 350 s under the condition of any misalignment angles with pitch error from −40° to 40°, roll error from −40° to 40°, and yaw error from −50° to 50°. Even when the initial misalignment angles are all very large such as (80°, 120°, 170°), the proposed nonlinear alignment method still can converge normally by utilizing the adaptive fuzzy inference system (AFIS) to adjust the covariance matrix Pk/k−1. Finally, the turntable experiment was performed, and the effectiveness and superiority of the proposed method were further verified by compared with other nonlinear methods.

Adaptive fuzzy sliding mode formation controller for autonomous underwater vehicles with variable payload

PurposeIn this paper, an adaptive fuzzy sliding mode controller (AFSMC) is developed for the formation control of a team of autonomous underwater vehicles (AUVs) subjected to unknown payload mass variations during their mission.Design/methodology/approachA sliding mode controller (SMC) is designed to drive the state trajectories of the AUVs to a switching surface in the state space. The payload mass variation results in parameter variation in AUV dynamics leading to actuator failure. This further leads to loss of communication among the members of the team. Hence, an adaptive SMC based on fuzzy logic is developed to maintain the coordinated motion of AUVs with payload mass variation.FindingsThe results are obtained by employing adaptive SMC for AUVs with and without payload variations and are compared. It is observed that the proposed adaptive SMC exhibits improved performance and tracks the desired trajectory in less time even with variation in the payload. The adaptive fuzzy control algorithm is developed to handle variation in payload mass variation. Lyapunov theory is used to establish stability of AFSMC controller.Research limitations/implicationsPerfect alignment is assumed between centres of gravity (OG) and buoyancy (OB), thus AUVs maintaining horizontal stability during motion. The AUVs’ body centres are aligned with centres of gravity (OG), thus the distance vector being rg = [0,0,0]T. As it is a tracking problem, sway motion cannot be neglected as the AUVs are travelling in a curved locus, hence susceptible to Coriolis and centripetal forces. The AUV is underactuated as only two thrusters at the stern plate that are employed for the surge and yaw controls and error in Y- direction are controlled by adjusting control input in surge and heave direction. Control inputs to the thruster are constants, and depth control is achieved by adjusting the rudder angle.Practical implicationsAUVs are employed in military mission or surveys, and they carry heavy weapons or instrument to be deployed at or picked from specific locations. Such tasks lead to variation in payload, causing overall mass variation during an AUV’s motion. A sudden change in the mass after an AUV release or pick load results in variation in depth and average velocity.Social implicationsThe proposed controller can be useful for military missions for carrying warfare and hydrographic surveys for deploying instruments.Originality/valueA proposed non-linear SMC has been designed, and its performances have been verified in terms of tracking error in X, Y and Z directions. An adaptive fuzzy SMC has been modelled using quantized state information to compensate payload variation. The stability of AFSMC controller is established by using Lyapunov theorem, and reachability of the sliding surface is ensured.

Aeroelastic load validation in wake conditions using nacelle-mounted lidar measurements

Abstract. We propose a method for carrying out wind turbine load validation in wake conditions using measurements from forward-looking nacelle lidars. Two lidars, a pulsed- and a continuous-wave system, were installed on the nacelle of a 2.3 MW wind turbine operating in free-, partial-, and full-wake conditions. The turbine is placed within a straight row of turbines with a spacing of 5.2 rotor diameters, and wake disturbances are present for two opposite wind direction sectors. The wake flow fields are described by lidar-estimated wind field characteristics, which are commonly used as inputs for load simulations, without employing wake deficit models. These include mean wind speed, turbulence intensity, vertical and horizontal shear, yaw error, and turbulence-spectra parameters. We assess the uncertainty of lidar-based load predictions against wind turbine on-board sensors in wake conditions and compare it with the uncertainty of lidar-based load predictions against sensor data in free wind. Compared to the free-wind case, the simulations in wake conditions lead to increased relative errors (4 %–11 %). It is demonstrated that the mean wind speed, turbulence intensity, and turbulence length scale have a significant impact on the predictions. Finally, the experiences from this study indicate that characterizing turbulence inside the wake as well as defining a wind deficit model are the most challenging aspects of lidar-based load validation in wake conditions.

GNSS/IMU/ODO/LiDAR-SLAM Integrated Navigation System Using IMU/ODO Pre-Integration.

In this paper, we proposed a multi-sensor integrated navigation system composed of GNSS (global navigation satellite system), IMU (inertial measurement unit), odometer (ODO), and LiDAR (light detection and ranging)-SLAM (simultaneous localization and mapping). The dead reckoning results were obtained using IMU/ODO in the front-end. The graph optimization was used to fuse the GNSS position, IMU/ODO pre-integration results, and the relative position and relative attitude from LiDAR-SLAM to obtain the final navigation results in the back-end. The odometer information is introduced in the pre-integration algorithm to mitigate the large drift rate of the IMU. The sliding window method was also adopted to avoid the increasing parameter numbers of the graph optimization. Land vehicle tests were conducted in both open-sky areas and tunnel cases. The tests showed that the proposed navigation system can effectually improve accuracy and robustness of navigation. During the navigation drift evaluation of the mimic two-minute GNSS outages, compared to the conventional GNSS/INS (inertial navigation system)/ODO integration, the root mean square (RMS) of the maximum position drift errors during outages in the proposed navigation system were reduced by 62.8%, 72.3%, and 52.1%, along the north, east, and height, respectively. Moreover, the yaw error was reduced by 62.1%. Furthermore, compared to the GNSS/IMU/LiDAR-SLAM integration navigation system, the assistance of the odometer and non-holonomic constraint reduced vertical error by 72.3%. The test in the real tunnel case shows that in weak environmental feature areas where the LiDAR-SLAM can barely work, the assistance of the odometer in the pre-integration is critical and can effectually reduce the positioning drift along the forward direction and maintain the SLAM in the short-term. Therefore, the proposed GNSS/IMU/ODO/LiDAR-SLAM integrated navigation system can effectually fuse the information from multiple sources to maintain the SLAM process and significantly mitigate navigation error, especially in harsh areas where the GNSS signal is severely degraded and environmental features are insufficient for LiDAR-SLAM.

Effect of detector installation error on the measurement accuracy of multi-degree-of-freedom geometric errors of a linear axis

A linear axis is the key component of several mechanical machines, especially of computer numerical control machine tools. The simultaneous measurement of the geometric motion errors of a linear axis is indispensable to compensate the machine errors, which improves the accuracy of machine tools. The principle of laser collimation is widely used for measuring the multi-degree-of-freedom (MDOF) geometric motion errors of a linear axis. However, installation errors of the detectors affect the measurement accuracy. In this study, we have proposed, for the first time, a measurement model for investigating the influence of all detector installation errors on the accuracy of the simultaneous measurement of MDOF geometric motion errors in a linear axis. The effect of detector installation errors on the horizontal straightness, vertical straightness, pitch, and yaw are analyzed using the homogeneous transformation method, which indicates that angular installation errors of detectors along the X0-axis direction can cause a crosstalk between the two straightness errors and between pitch and yaw errors. In addition, translational installation errors of position-sensitive detectors in the X0-axis direction, which is often called the defocusing amount, has a significant effect on the pitch and yaw measurements. To elucidiate the effect of defocusing, a measurement model was verified by both Zemax simulation and experiments. The experimental results indicate that the maximum deviation of the measured results obtained using the proposed model from that obtained using a Renishaw XL-80 interferometer can be greatly reduced by compensating the measurement errors induced by defocusing.