Karl A. Stol

Periodic Disturbance Accommodating Control for Blade Load Mitigation in Wind Turbines

Performance of a model-based periodic gain controller for wind turbines is presented using Disturbance Accommodating Control (DAC) techniques to estimate fluctuating wind disturbances. The control objective is to regulate rotor speed at above-rated wind speeds while mitigating cyclic blade root loads. Actuation is via individual blade pitch, and sensors are limited to rotor angle and speed. The modeled turbine is a two-bladed, downwind machine with simple blade and tower flexibility having four degrees of freedom. Comparisons are made to a time-invariant DAC controller and to a proportional-integral-derivative (PID) design. Simulations are performed using a fluctuating wind input and a nonlinear turbine model. Results indicate that the state-space control designs are effective in reducing blade loads without a sacrifice in speed regulation. The periodic controller shows the most potential because it uses a time-varying turbine model to estimate unmeasured states. The use of additional sensors to help reconstruct the blade flap rate can significantly improve the level of load attenuation, as witnessed in full-state feedback results.

Review of modelling and control of two-wheeled robots

Abstract In the past decade, there has been much more research in two-wheeled robots which actively stabilize themselves. Various models and controllers have been applied both to explain and control the dynamics of two-wheeled robots. We explore the methods which have been investigated and the controllers which have been used, first for balancing and movement of two-wheeled robots on flat terrain, then for two-wheeled robots in other situations, where terrain may not be flat, where there may be secondary objectives and where the robots may have additional actuators.

Scheduled Model Predictive Control of a Wind Tur bine

Through high order aeroelastic simulations in turbulent wind, it has been shown that a Scheduled Model Predictive Controller (SMPC) can successfully control a wind turbine in above rated wind conditions. The SMPC shows the ability to control Multi-Input MultiOutput systems with multiple control objectives, allow for system input constraints and also adjust to the aerodynamic nonlinearities of the turbine system. The implementation of the SMPC is also only as complex as implementing a Linear Model Predictive Controller (LMPC) but provides the benefits of being able to control nonlinear systems with higher performance. Furthermore it has been shown that by using a SMPC the user has the ability to finely tune each controller the SMPC is comprised of giving more tailored performance to various operating regions.

Full-State Feedback Control of a Variable-Speed Wind Turbine: A Comparison of Periodic and Constant Gains

An investigation of the performance of a model-based periodic gain controller is presented for a two-bladed, variable-speed, horizontal-axis wind turbine. Performance is based on speed regulation using full-span collective blade pitch. The turbine is modeled with five degrees-of-freedom; tower fore-aft bending, nacelle yaw, rotor position, and flapwise bending of each blade. An attempt is made to quantify what model degrees-of-freedom make the system most periodic, using Floquet modal properties. This justifies the inclusion of yaw motion in the model. Optimal control ideas are adopted in the design of both periodic and constant gain full-state feedback controllers, based on a linearized periodic model. Upon comparison, no significant difference in performance is observed between the two types of control in speed regulation.

Modelling the elastic properties of softwood part 2: The cellular microstructure

Numerical Finite Element models are presented which relate the macroscopic elastic properties of softwood to local cell characteristics such as cell size, wall thickness, moisture content and microfibril angle. Preliminary results show good agreement with reported values. The model is used to assess the effects of S2 microfibril angle and spiral grain on orthotropic wood stiffness, and to predict the stiffening effect of latewood bands.ZusammenfassungDer Beitrag präsentiert numerische FE-Modelle, welche die makroskopischen elastischen Eigenschaften von Nadelholz auf lokale Zellmerkmale wie Größe, Wanddicke, Feuchte und Winkel der Mikronbrillen zurückführen. Erste Ergebnisse zeigen gute Übereinstimmung mit Literturwerten. Mit Hilfe des Modells wird der Einfluß des Winkels der Mikronbrillen in der S2 und der Faserorientierung auf die Biegesteifigkeit des Holzes abgeschätzt sowie ein Versteifungseffekt der Spätholzzonen vorhergesagt.

Disturbance Tracking Control and Blade Load Mitigation for Variable-Speed Wind Turbines

A composite linear state-space controller was developed for a multi-objective problem in the variable-speed operation of wind turbines. Disturbance Tracking Control theory was applied to the design of a torque controller to optimize energy capture under the influence of persistent wind disturbances. A limitation in the theory for common multi-state models is described; this led to the design of a complementary pitch controller The goal of the independent blade pitch design was to minimize blade root fatigue loads. A SymDyn model of a two-bladed, 600-kW machine was used for the simulation studies. Results indicate a 24% reduction in blade fatigue damage using the proposed controllers, compared to a conventional torque-only design. However, energy capture was not improved as much as expected, partly due to nonlinearity effects degrading the performance of the state-space estimator design. Tower base fatigue damage was shown to decrease significantly using active pitch.

Disturbance Tracking and Blade Load Control of Wind Turbines in Variable-Speed Operation

A composite state-space controller was developed for a multi-objective problem in the variable-speed operation of wind turbines. Disturbance Tracking Control theory was applied to the design of a torque controller to optimize energy capture under the influence of persistent wind disturbances. A limitation in the theory for common multi-state models is described, which led to the design of a complementary pitch controller. The goal of the independent blade pitch design was to minimize blade root fatigue loads. Simulation results indicate an 11% reduction in fatigue damage using the proposed controllers, compared to a conventional torque-only design. Meanwhile, energy capture is almost identical, partly because of nonlinear effects.

A Comparison of Multi-Blade Coordinate Transformation and Direct Periodic Techniques for Wind Turbine Control Design

The inherent periodic behavior of an operating wind turbine is not well accommodated by common time-invariant analysis and control techniques. A multi-blade coordinate transformation (MBC) helps to overcome this issue for rotors with three or more blades by mapping the dynamic state variables into a non-rotating reference frame. A number of researchers have applied MBC for modal analyses and individual blade pitch controller designs. They do so by assuming the transformed system model from MBC is time-invariant, which is not often the case. The paper explores the validity of the time-invariant assumption by comparison to direct periodic techniques, which retain all periodic system information. In a modal analysis study, eigenvalues of a system after MBC are compared to direct Floquet modes. In an individual blade pitch control design study, a linear quadratic regulation (LQR) design after MBC is compared to direct periodic LQR. A 5-MW three-bladed wind turbine model is used to quantify performance differences. Normal operating conditions are considered as well as conditions selected to increase the harmonics that are unfiltered by MBC. It is found that the direct periodic methods produce almost identical results to timeinvariant methods after MBC under all conditions studied. MBC is recommended for threebladed turbines, which can be followed by Floquet analysis or periodic control design methods if necessary.

Dynamics and control of horizontal axis wind turbines

This tutorial paper describes the field of wind turbine control. It begins with the simplest turbine dynamic models and progresses to more advanced models which incorporate structural resonances in the blades and supporting tower. Disturbance accommodating control techniques are used to provide power control in fluctuating wind fields.

Floquet Modal Analysis of a Teetered-Rotor Wind Turbine

This paper examines the operating modes of a two-bladed wind turbine structural model. Because of the gyroscopic asymmetry of its rotor, this turbines dynamics can be quite distinct from that of a turbine with three or more blades. This asymmetry leads to system equations with periodic coefficients that must be solved by the Floquet approach to extract the correct modal parameters. A discussion of results is presented for a series of simple models with increasing complexity. We begin with a single-degree-of-freedom system and progress to a model with seven degrees-of-freedom: tower fore-aft bending, tower lateral bending, tower twist, nacelle yaw, hub teeter, and flapwise bending of each blade. Results illustrate how the turbine modes become more dominated by the centrifugal and gyroscopic effects as the rotor speed increases. Parametric studies are performed by varying precone angle, teeter stiffness, yaw stiffness, teeter damping, and yaw damping properties. Under certain levels of yaw stiffness or damping, the gyroscopic coupling may cause yaw and teeter mode coalescence, resulting in self-excited dynamic instabilities. Teeter damping is the only parameter found to strictly stabilize the turbine model.