A Comparison of Tracking Step Inputs with a Piezo Stage Using Model Predictive Control and Saturated Linear Quadratic Gaussian Control

Compressed Sensing for Atomic Force Microscopy is a newer imaging mode that requires the piezo stage be driven rapidly between measurement locations. In contrast to raster scanning applications, this translates to a setpoint tracking problem. This paper considers the setpoint tracking performance of a piezo nano-positioning stage subject to rate-of-change limitations on the control signal, which is derived from the current limit of the power amplifier. To compensate the vibrational dynamics of the stage, a model predictive control scheme (MPC) and a linear quadratic Gaussian (LQG) controller which saturates the control increment are considered. In both cases, hysteresis and drift are compensated via dynamic inversion. To design the weighting matrices required by the MPC and linear feedback designs, an extension to classic reciprocal root locus ideas is proposed. The robustness of both schemes using classical methods like gain margin, phase margin, and gain of the sensitivity function at low frequencies is analyzed. The overall settle times achieved by both controllers (in both simulation and experiment) across a range of control weights where the reference input is a sequence of step inputs of varying amplitudes are compared. The results show that the best simulation settle time is achieved by MPC using the smallest control weight. However under experimental conditions, the best settle time is achieved by a much larger control weight and the performance of MPC becomes comparable with that of saturated linear feedback. This result is explained by showing that robustness increases with larger control weights. &nbsp;</p

Controllability of Formation Systems on Special Orthogonal Groups over Directed Graphs

Gradient flows provide a means for a networked formation system to reach and stabilize at a target configuration. However, the decentralization&nbsp; constraints and the geometry of the state space makes the appearance of stable but undesired configurations inevitable. The presence of these&nbsp; undesired stable configurations precludes global&nbsp; convergence to the target configuration. In this paper, we address the issue by considering a&nbsp; controlled formation system on special orthogonal&nbsp; groups over a directed graph. Agents of the system are tasked with stabilizing from others at target&nbsp; relative attitudes. The nominal dynamics of the agents are gradient flows of certain potential functions. These functions are parameter dependent, pretuned by the controller. To prevent the formation system from being trapped at an undesired configuration, we formulate and address the problem of whether the controller can steer the system from any configuration to any other configuration by retuning, on the fly, the parameters of the potential functions. We show that the answer is affirmative provided that the underlying graph is rooted with a single root node being fully actuated. We formulate the result as a main theorem and provide a complete proof of the result.</p

System-level design studies for large rotors

We examine the effect of rotor design choices on the power capture and structural loading of each major wind turbine component. A harmonic model for structural loading is derived from simulations using the National Renewable Energy Laboratory (NREL) aeroelastic code FAST to reduce computational expense while evaluating design trade-offs for rotors with radii greater than 100&thinsp;m. Design studies are performed, which focus on blade aerodynamic and structural parameters as well as different hub configurations and nacelle placements atop the tower. The effects of tower design and closed-loop control are also analyzed. Design loads are calculated according to the IEC design standards and used to create a mapping from the harmonic model of the loads and quantify the uncertainty of the transformation. Our design studies highlight both industry trends and innovative designs: we progress from a conventional, upwind, three-bladed rotor to a rotor with longer, more slender blades that is downwind and two-bladed. For a 13&thinsp;MW design, we show that increasing the blade length by 25&thinsp;m, while decreasing the induction factor of the rotor, increases annual energy capture by 11&thinsp;% while constraining peak blade loads. A downwind, two-bladed rotor design is analyzed, with a focus on its ability to reduce peak blade loads by 10&thinsp;% per 5∘ of cone angle and also reduce total blade mass. However, when compared to conventional, three-bladed, upwind designs, the peak main-bearing load of the upscaled, downwind, two-bladed rotor is increased by 280&thinsp;%. Optimized teeter configurations and individual pitch control can reduce non-rotating damage equivalent loads by 45&thinsp;% and 22&thinsp;%, respectively, compared with fixed-hub designs. </div

Comparison of feedforward and model predictive control of wind turbines using LIDAR

LIDAR systems are able to provide preview information of wind disturbances at various distances in front of wind turbines. This technology paves the way for new control concepts such as feedforward control and model predictive control. This paper compares a nonlinear model predictive controller and a feedforward controller to a baseline controller. Realistic wind "measurements" are obtained using a detailed simulation of a LIDAR system. A full lifetime comparison shows the advantages of using the wind predictions to reduce wind turbine fatigue loads on the tower and blades as well as to limit the blade pitch rates. The results illustrate that the feedforward controller can be combined with a tower feedback controller to yield similar load reductions as the model predictive controller

Automatic controller tuning using a zeroth-order optimization algorithm

We develop an automated controller tuning procedure for wind turbines that uses the results of nonlinear, aeroelastic simulations to arrive at an optimal solution. Using a zeroth-order optimization algorithm, simulations using controllers with randomly generated parameters are used to estimate the gradient and converge to an optimal set of those parameters. We use kriging to visualize the design space and estimate the uncertainty, providing a level of confidence in the result. The procedure is applied to three problems in wind turbine control. First, the below-rated torque control is optimized for power capture. Next, the parameters of a proportional-integral blade pitch controller are optimized to minimize structuralloads with a constraint on the maximum generator speed; the procedure is tested on rotors from 40 to 400 m in diameter and compared with the results of a grid search optimization. Finally, we present an algorithm that uses a series of parameter optimizations to tune the lookup table for the minimum pitch setting of the above-rated pitch controller, considering peak loads and power capture. Using experience gained from the applications, we present a generalized design procedure and guidelines for implementing similar automated controller tuning tasks.</p

Constrained power reference control for wind turbines

The cost of wind energy can be reduced by controlling the power reference of a turbine to increase energy capture, while maintaining load and generator speed constraints. We apply standard torque and pitch controllers to the direct inputs of the turbine and use their set points to change the power output and reduce generator speed and blade load transients. A power reference controller increases the power output when conditions are safe and decreases it when problematic transient events are expected. Transient generator speeds and blade loads are estimated using a gust measure derived from a wind speed estimate. A hybrid controller decreases the power rating from a maximum allowable power. Compared to a baseline controller, with a constant power reference, the proposed controller results in generator speeds and blade loads that do not exceed the original limits, increases tower fore-aft damage equivalent loads by 1%, and increases the annual energy production by 5%. &nbsp;</p

Model Predictive Active Power Control for Optimal Structural Load Equalization in Waked Wind Farms

In this paper, we propose a model predictive active power control (APC) enhanced by the optimal coordination of the structural loadings of wind turbines operating with fully developed wind farm flows that have extensive interactions with the atmospheric boundary layer. In general, the APC problem, that is, distributing a wind farm power reference among the operating wind turbines, does not have a unique solution; this fact can be exploited for structural load alleviation of the individual wind turbines. Therefore, we formulated a constrained optimization problem to simultaneously minimize the wind farm power reference tracking errors and the structural load deviations of the wind turbines from their mean value. Thewind power plant is represented by a dynamic 3D large&ndash;eddy simulation model, whereas the predictive controller employs a simplified, computationally inexpensive model to predict the dynamic power and load responses of the turbines that experience turbulent wind farm flows and wakes. An adjoint approach is an efficient tool used to iteratively compute the gradient of the formulated parameter-varying optimal control problem over a finite prediction horizon. We have discussed the applicability, key features, and computational complexity of the controller by using a wind farm example consisting of 3�4 turbines with different wake interactions for each row. The performance of the proposed adjoint&ndash;based model predictive control for APC was evaluated by measuring power reference tracking errors and the corresponding damage equivalent fatigue loads of the wind turbine towers; we compared our proposed control design with recently published proportional&ndash;integral&ndash;based APC approaches.</p

Grand challenges in the science of wind energy

Modern wind turbines already represent a tightly optimized confluence of materials science and aerodynamic engineering. Veers et al. review the challenges and opportunities for further expanding this technology, with an emphasis on the need for interdisciplinary collaboration. They highlight the need to better understand atmospheric physics in the regions where taller turbines will operate as well as the materials constraints associated with the scale-up. The mutual interaction of turbine sites with one another and with the evolving features of the overall electricity grid will furthermore necessitate a systems approach to future development.</p

Uncertainties identification of blade-mounted lidar-based inflow wind speed measurements for robust feedback-feedforward control synthesis

The current trend toward larger wind turbine rotors leads to high periodic loads across the components due to the non-uniformity of inflow across the rotor. To address this, we introduce a blade-mounted lidar on each blade to provide a preview of inflow wind speed that can be used as a feedforward control input for the mitigation of such periodic blade loads. We present a method to easily determine blade-mounted lidar parameters, such as focus distance, telescope position, and orientation on the blade. However, such a method is accompanied by uncertainties in the inflow wind speed measurement, which may also be due to the induction zone, wind evolution, &ldquo;cyclops dilemma&rdquo;, unidentified misalignment in the telescope orientation, and the blade segment orientation sensor. Identification of these uncertainties allows their inclusion in the feedback&ndash;feedforward controller development for load mitigation. We perform large-eddy simulations, in which we simulate the blade-mounted lidar including the dynamic behaviour and the induction zone of one reference wind turbine for one above-rated inflow wind speed. Our calculation approach provides a good trade-off between a fast and simple determination of the telescope parameters and an accurate inflow wind speed measurement. We identify and model the uncertainties, which can then be directly included in the feedback&ndash;feedforward controller design and analysis. The rotor induction effect increases the preview time, which needs to be considered in the controller development and implementation.</p