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NREL researcher Andrey Bernstein discusses asynchronous and distributed tracking of time-varying fixed points as part of the Innovative Optimization and Control Methods for Highly Distributed Autonomous Systems workshop. NREL hosted the workshop to exchange ideas on state-of-the-art control and optimization strategies as well as get feedback on work being done at NREL.
In this article, a generic two-vector model predictive control (TV-MPC) strategy is proposed for the hybrid multilevel converters (HMCs). The proposed method selects two optimal voltage vectors among all the vector candidates using a geometric positioning approach to reduce the computational burden, which is a common issue in the existing MPC methods for HMC. Then duty cycles of the two selected vectors are optimized to minimize the current tracking error, such that the current tracking performance can be enhanced compared with the conventional MPC. In addition, the voltages of the floating dc capacitors can be balanced by evaluating all switching sequences that belong to the optimal voltage vectors with optimal duty cycles. Here, the concept of the proposed TV-MPC is generic and applicable for any HMCs. A typical HMC based on active neutral-point-clamped topology is adopted as a case study in this work. Comprehensive simulation and experimental studies are performed on an all silicon-carbide HMC prototype to validate the effectiveness of the proposed control scheme.
Here, this paper proposes a proportional–integral-double–derivative (PID 2 ) optimisation method for the Kaplan hydropower system by building a digital twin. The study first uses one multilayer perceptron (MLP) to model the hydroturbine dynamic and then adopts three connected MLPs to model the generator dynamic, both in an open-loop fashion. Inspired by stochastic distribution control (SDC) theory, we regard the training of the turbine's neural network model as a process control problem, and we propose minimising entropy loss to update the network parameters. The next step is to build the digital twin by connecting the neural network models with a PID 2 controller and a lead-lag exciter and run the whole model in a closed-loop fashion. After that, a binary search approach is applied to optimise the PID 2 parameters based on the obtained digital twin model. The simulation results show that the proposed method can reduce the mean square tracking error by more than 90%. Furthermore, the method is extended to jointly optimise the PID 2 controller and excitation system gains through multiobjective optimisation, leveraging Pareto frontier analysis to balance active power and voltage tracking performance. Simulation results confirm the effectiveness of the proposed method, achieving a 83.46% reduction in relative mean square error of active power, a 47.13% reduction in terminal voltage tracking error, and an 82.78% improvement in the overall scalarized objective.
In this study, the characteristics of simulated tropical cyclones (TCs) over the western North Pacific by a regional model (the WRF Model) are verified. We utilize 12-km horizontal grid spacing, and simulations are integrated for 5 days from model initialization. A total of 125 forecasts are divided into five clusters through the k-means clustering method. The TCs in the cluster 1 and 2 (group 1), which includes many TCs moving northward in the subtropical region, generally have larger track errors than for TCs in cluster 3 and 4 (group 2). The optimal steering vector is used to examine the difference in the track forecast skill between these two groups. The bias in the steering vector between the model and analysis data is found to be more substantial for group 1 TCs than group 2 TCs. The larger steering vector difference for group 1 TCs indicates that environmental fields tend to be poorly simulated in group 1 TC cases. Furthermore, the residual terms, including the storm-scale process, asymmetric convection distribution, or beta-related effect, are also larger for group 1 TCs than group 2 TCs. Therefore, it is probable that the large track forecast error for group 1 TCs is a result of unreasonable simulations of environmental wind fields and residual processes in the midlatitudes.
The first automatic twisting heliostat, with 8 m2 reflector, was completed and tested on-sun in January 2024. It was set up on a target-oriented dual-axis mount, with the target-axis aimed at a target 113 m to the west. The shape-twisting is purely automatic, made by a mechanical cam coupling to the cross-axis, which turns as the angle of incidence of the sun’s rays on the reflector. Three unsaturated images taken at different times of day were recorded of the sun on the target, reflected at angles of incidence of 5°, 49° and 68°. The measured FWHM of three images is very similar, about 1.09 m or 9.5 mrad, only slightly larger than an ideal solar disc, indicating that the different twisted reflector shapes are close to the ideal biconics needed to image the sun. The encircled energy measured for all three images was similar, 87% within approximately 1.30 m diameter. We report here also on a novel, tracking camera that employs a semitransparent beamsplitter fixed perpendicular to the mirror surface and to the plane of incidence. Over 2.5 hours of measurement of closed loop tracking, errors were ≤ 0.36 mrad rms, in both tracking axes.
Here, a novel framework is proposed for integrating biomimetic-based advanced control and multi-agent optimization approaches for nonlinear chemical process applications. In particular, a Biologically-Inspired Optimal Control Strategy, denoted as BIO-CS, is combined with multi-agent optimization (MAO) techniques to provide optimal solutions for dynamic systems. In this combined framework, the BIO-CS algorithm employs gradient-based optimal control solvers for the intermediate problems associated with the leader-follower agents’ local interactions. Also, the MAO uses the capabilities of heuristic-based optimization techniques by sharing process information to obtain optimal operating setpoints for the controller considering an overall process objective. The applicability of the proposed method is demonstrated using a nonlinear, multivariable, process model of a fermentation system. Specifically, the optimal operating points are computed by the MAO implementation for setpoint tracking, trajectory tracking and plant-model mismatch scenarios for BIO-CS application. Results of the developed framework are compared to a gradient-based Sequential Quadratic Programming (SQP) technique and a classical proportional-integral (PI) controller in terms of optimization and control studies, respectively. As an additional contribution, BIO-CS is also cast as a model predictive controller (MPC) for the first time and compared to the agent-based BIO-CS approach in terms of computational time and tracking error. Closed-loop control results show up to 46% improvement in tracking performance during transient for the multi-agent BIO-CS when compared to BIO-CS as MPC for additional computational expense. The obtained results illustrate the capabilities of this novel integrated framework including BIO-CS as MPC to achieve desired nonlinear system performance for various scenarios.
The goal of this work is to quantify respiratory motion compensation errors for liver tumor patients treated by the CyberKnife system with Synchrony tracking, to identify patients with the smallest tracking errors and to eventually help coach patient’s breathing patterns to minimize dose delivery errors. The accuracy of CyberKnife Synchrony respiratory motion compensation was assessed for 37 patients treated for liver lesions by analyzing data from system logfiles. A predictive model is used to modulate the direction of individual beams during dose delivery based on the positions of internally implanted fiducials determined using an orthogonal x-ray imaging system and the current location of LED external markers. For each x-ray pair acquired, system logfiles report the prediction error, the difference between the measured and predicted fiducial positions, and the delivery error, which is an estimate of the statistical error in the model overcoming the latency between x-ray acquisition and robotic repositioning. The total error was calculated at the time of each x-ray pair, for the number of treatment fractions and the number of patients, giving the average respiratory motion compensation error in three dimensions. The 99{sup th} percentile for the total radial error is 3.85 mm, with the highest contribution of 2.79 mm in superior/inferior (S/I) direction. The absolute mean compensation error is 1.78 mm radially with a 1.27 mm contribution in the S/I direction. Regions of high total error may provide insight into features predicting groups of patients with larger or smaller total errors.
Purpose: To first demonstrate the viability of applying an image processing technique for tracking regions on low-contrast cine-MR images acquired during image-guided radiation therapy, and then outline a scheme that uses tracking data for optimizing gating results in a patient-specific manner. Methods: A first-generation MR-IGRT system—treating patients since January 2014—integrates a 0.35 T MR scanner into an annular gantry consisting of three independent Co-60 sources. Obtaining adequate frame rates for capturing relevant patient motion across large fields-of-view currently requires coarse in-plane spatial resolution. This study initially (1) investigate the feasibility of rapidly tracking dense pixel correspondences across single, sagittal plane images (with both moderate signal-to-noise and spatial resolution) using a matching objective for highly descriptive vectors called scale-invariant feature transform (SIFT) descriptors associated to all pixels that describe intensity gradients in local regions around each pixel. To more accurately track features, (2) harmonic analysis was then applied to all pixel trajectories within a region-of-interest across a short training period. In particular, the procedure adjusts the motion of outlying trajectories whose relative spectral power within a frequency bandwidth consistent with respiration (or another form of periodic motion) does not exceed a threshold value that is manually specified following the training period. To evaluate the tracking reliability after applying this correction, conventional metrics—including Dice similarity coefficients (DSCs), mean tracking errors (MTEs), and Hausdorff distances (HD)—were used to compare target segmentations obtained via tracking to manually delineated segmentations. Upon confirming the viability of this descriptor-based procedure for reliably tracking features, the study (3) outlines a scheme for optimizing gating parameters—including relative target position and a tolerable margin about this position—derived from a probability density function that is constructed using tracking results obtained just prior to treatment. Results: The feasibility of applying the matching objective for SIFT descriptors toward pixel-by-pixel tracking on cine-MR acquisitions was first retrospectively demonstrated for 19 treatments (spanning various sites). Both with and without motion correction based on harmonic analysis, sub-pixel MTEs were obtained. A mean DSC value spanning all patients of 0.916 ± 0.001 was obtained without motion correction, with DSC values exceeding 0.85 for all patients considered. While most patients show accurate tracking without motion correction, harmonic analysis does yield substantial gain in accuracy (defined using HDs) for three particularly challenging subjects. An application of tracking toward a gating optimization procedure was then demonstrated that should allow a physician to balance beam-on time and tissue sparing in a patient-specific manner by tuning several intuitive parameters. Conclusions: Tracking results show high fidelity in assessing intrafractional motion observed on cine-MR acquisitions. Incorporating harmonic analysis during a training period improves the robustness of the tracking for challenging targets. The concomitant gating optimization procedure should allow for physicians to quantitatively assess gating effectiveness quickly just prior to treatment in a patient-specific manner.
Solid oxide electrolysis cell (SOEC) hydrogen production technology can range in size from small, appliance-size equipment to large-scale, central production facilities that can be tied directly to renewable or non-greenhouse-gas-emitting forms of electricity production, making it an ideal resource for demand response (DR). The SOEC hydrogen production system is a complex integrated system that encompasses fluid dynamics, electrical dynamics, and electrochemical and thermal dynamics, all of which involve non-linearity and non-convexity. Proper control of the SOEC hydrogen production system is crucial to enable its participation in the DR program. Here, to overcome the difficulty of designing an explicit control law for such nonlinear systems with nonconvex optimization features in DR applications, deep reinforcement learning (DRL) is explored to achieve the optimal control of the SOEC system for DR participation. Specifically, a twin delayed deterministic policy gradient (TD3) control framework is applied to achieve optimal response performance during DR events by considering power tracking error and hydrogen production efficiency with a suitable reward function. Two case studies with grid connections for tracking different DR commands were investigated. The first case study involved operating conditions reaching the boundaries, while the second involved operating conditions within the boundaries. The results showed that the proposed DRL-based control for SOEC can track the DR signal in a timely manner while maintaining high energy efficiency.
Here in this article, a novel approach is proposed for integrating a Biologically-Inspired Optimal Control Strategy (BIOsingle bondCS) with an Artificial Neural Network (ANN)-based adaptive component for advanced energy systems applications. Specifically, BIOsingle bondCS employs gradient-based optimal control solvers in a biologically-inspired manner, following the rule of pursuit for ants, to simultaneously control multiple process outputs at their desired setpoints. Also, the ANN component captures the mismatch between the controller and the plant models by using a single-hidden-layer technique with online learning capabilities to augment the baseline BIOsingle bondCS control laws. The resulting approach is a unique combination of biomimetic control and data-driven methods that provides optimal solutions for dynamic systems. The applicability of the proposed framework is illustrated via an Integrated Gasification Combined Cycle (IGCC) process with carbon capture as an advanced energy system example. In particular, a multivariable control structure associated with a subsystem of the IGCC plant simulation in DYNSIM® is addressed. The proposed control laws are derived in MATLAB®, while the plant models are built in DYNSIM®, and a previously developed MATLAB®-DYNSIM® link is employed for implementation purposes. The proposed integrated approach improves the overall performance of the process up to 85% in terms of reducing the output tracking error when compared to stand-alone BIOsingle bondCS and Proportional-Integral (PI) controller implementations, resulting in faster setpoint tracking. The proposed framework thus provides a promising alternative for advanced control of energy systems of the future.
Power towers, a type of concentrating power tower technology, use a large number of heliostats to concentrate sunlight and produce renewable energy. Optical errors of heliostats can cause drastic losses in the efficiency of power-tower plants. Accurately measuring optical errors is crucial to assessing and improving plant performance. This analysis discusses an innovate non-intrusive optical (NIO) approach to measure slope, canting, and tracking errors by detecting distortions in the reflected tower structure in heliostat images. Further in this work a sensitivity study is carefully conducted to determine the uncertainty requirements to allow the method to calculate slope errors with an accuracy of 0.25 mrad. Measurement uncertainty sources include camera resolution and position uncertainty, tower position uncertainty, and number of collected images. Each uncertainty source is investigated to determine its impact on the accuracy of the slope-error calculation. A combination of theoretical results and experimental results obtained from data collected on a heliostat at Sandia National Laboratories is used to determine and validate uncertainty requirements. The analysis shows that a measurement uncertainty of 0.25 mrad can be realized by realistically controlling uncertainty sources when implementing the NIO method. It demonstrates the superior performance of NIO in performing in-situ optical characterization.
Purpose: Prostate SABR is emerging as a clinically viable, potentially cost effective alternative to prostate IMRT but its adoption is contingent on providing solutions for accurate tracking during beam delivery. Our goal is to evaluate the performance of the Clarity Autoscan ultrasound monitoring system for inter-fractional prostate motion tracking in both phantoms and in-vivo. Methods: In-vivo evaluation was performed under IRB protocol to allow data collection in prostate patients treated with VMAT whereby prostate was imaged through the acoustic window of the perineum. The probe was placed before KV imaging and real-time tracking was started and continued until the end of treatment. Initial absolute 3D positions of fiducials were estimated from KV images. Fiducial positions in MV images subsequently acquired during beam delivery were compared with predicted positions based on Clarity estimated motion. Results: Phantom studies with motion amplitudes of ±1.5, ±3, ±6 mm in lateral direction and ±2 mm in longitudinal direction resulted in tracking errors of −0.03 ± 0.3, −0.04 ± 0.6, −0.2 ± 0.9 mm, respectively, in lateral direction and −0.05 ± 0.30 mm in longitudinal direction. In phantom, measured and predicted fiducial positions in MV images were within 0.1 ± 0.6 mm. Four patients consented to participate in the study and data was acquired over a total of 140 fractions. MV imaging tracking was possible in about 75% of the time (due to occlusion of fiducials) compared to 100% with Clarity. Overall range of estimated motion by Clarity was 0 to 4.0 mm. In-vivo fiducial localization error was 1.2 ± 1.0 mm compared to 1.8 ± 1.9 mm if not taking Clarity estimated motion into account. Conclusion: Real-time transperineal ultrasound tracking reduces uncertainty in prostate position due to intrafractional motion. Research was supported by Elekta.
Hybrid modeling—combining physical testing and numerical simulation in real time$-$opens new opportunities in floating wind turbine research. Wave basin testing is an important validation step for floating support structure design, but the conventional approaches that use physical wind above the basin are limited by scaling problems in the aerodynamics. Applying wind turbine loads with an actuation system that is controlled by a simulation responding to the basin test in real time offers a way to avoid scaling problems and reduce cost barriers for floating wind turbine design validation in realistic coupled wind and wave conditions. This paper demonstrates the development of performance specifications for a system that couples a wave basin experiment with a wind turbine simulation. Two different points for the hybrid coupling are considered: the tower-base interface and the aero-rotor interface (the boundary between aerodynamics and the rotor structure). Analyzing simulations of three floating wind turbine designs across seven load cases reveals the motion and force requirements of the coupling system. By simulating errors in the hybrid coupling system, the sensitivity of the floating wind turbine response to coupling quality can be quantified. The sensitivity results can then be used to determine tolerances for motion tracking errors, force actuation errors, bandwidth limitations, and latency in the hybrid coupling system. These tolerances can guide the design of hybrid coupling systems to achieve desired levels of accuracy. An example demonstrates how the developed methods can be used to generate performance specifications for a system at 1:50 scale. Results show that sensitivities vary significantly between support structure designs and that coupling at the aero-rotor interface has less stringent requirements than those for coupling at the tower base. As a result, the methods and results presented here can inform design of future hybrid coupling systems and enhance understanding of how test results are affected by hybrid coupling quality.
Purpose: To develop an advanced testbed that combines a 3D motion stage and ultrasound phantom to optimize and validate 2D and 3D tracking algorithms for real-time motion management during radiation therapy. Methods: A Siemens S2000 Ultrasound scanner utilizing a 9L4 transducer was coupled with the Washington University 4D Phantom to simulate patient motion. The transducer was securely fastened to the 3D stage and positioned to image three cylinders of varying contrast in a Gammex 404GS LE phantom. The transducer was placed within a water bath above the phantom in order to maintain sufficient coupling for the entire range of simulated motion. A programmed motion sequence was used to move the transducer during image acquisition and a cine video was acquired for one minute to allow for long sequence tracking. Images were analyzed using a normalized cross-correlation block matching tracking algorithm and compared to the known motion of the transducer relative to the phantom. Results: The setup produced stable ultrasound motion traces consistent with those programmed into the 3D motion stage. The acquired ultrasound images showed minimal artifacts and an image quality that was more than suitable for tracking algorithm verification. Comparisons of a block matching tracking algorithm with the known motion trace for the three features resulted in an average tracking error of 0.59 mm. Conclusion: The high accuracy and programmability of the 4D phantom allows for the acquisition of ultrasound motion sequences that are highly customizable; allowing for focused analysis of some common pitfalls of tracking algorithms such as partial feature occlusion or feature disappearance, among others. The design can easily be modified to adapt to any probe such that the process can be extended to 3D acquisition. Further development of an anatomy specific phantom better resembling true anatomical landmarks could lead to an even more robust validation. This work is partially funded by NIH grant R01CA190298.
This paper investigates the ability of a collection of deferrable heating, ventilation and air conditioning (HVAC) loads to directly emulate energy storage devices (ESD), that is, to absorb any low frequency fluctuations in solar generation. We find the optimal number of aggregated HVAC loads to absorb solar fluctuation in the same frequency band based on frequency analysis. To guarantee quality of service in afleet of residential buildings, an optimization problem is formed to compute optimal schedule of the HVAC loads considering temperature comfort band and available solar generation. By minimizing the tracking error between solar generation and total consumption, the proposed method also quantifies the minimum capacity of ESD (battery or fly-wheel) . The simulation results show that the proposed techniques are able to achieve good solar tracking performance as well as obtain a minimal ESD capacity. Therefore, we show that most of the renewable generation can be consumed locally through an intelligent coordination of HVAC loads, their impacts on the grid would be minimal and the required ESD capacity can be minimized.
This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time-invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the algorithm is based on continuous-time primal-dual dynamics, properly modified to incorporate feedback from the LTI dynamical system, applied to a proximal augmented Lagrangian function. The resultant closed-loop algorithm tracks the solution of the time-varying optimization problem without requiring knowledge of (time-varying) disturbances in the dynamical system. The analysis leverages integral quadratic constraints to provide linear matrix inequality (LMI) conditions that guarantee global exponential stability and bounded tracking error. Analytical results show that, under a sufficient time-scale separation between the dynamics of the LTI dynamical system and the algorithm, the LMI conditions can be always satisfied. The paper further proposes a modified algorithm that can track an approximate solution trajectory of the constrained optimization problem under less restrictive assumptions. As an illustrative example, the proposed algorithms are showcased for power transmission systems, to compress the time scales between secondary and tertiary control, and allow to simultaneously power re-balancing and tracking of DC optimal power flow points.
This paper presents an integrated path planning and tracking control framework for a marine current turbine (MCT), where the MCT is treated as an energy-harvesting autonomous underwater vehicle (AUV). Considering the ocean (space of action) is continuous, the proposed framework employs two modules to address path planning and path tracking enabled by the proximal policy optimization (PPO) algorithm, which is a policy gradient deep reinforcement learning (RL) method. Further, to enable fully autonomous operation in a stochastic oceanic environment, the proposed path planning seeks a primary objective of maximizing the harvested energy; then, the path tracking module is designed to minimize the tracking error and avoid collisions with static and dynamic obstacles. Using field-collected acoustic Doppler current profiler (ADCP) data, the performance of the proposed framework is evaluated. Comparative studies with baseline algorithms in three different scenarios of path planning, path tracking without an obstacle, and path tracking with collision avoidance verify the effectiveness of our proposed approach.
This paper presents a methodology for optimizing pre-calculated collision-free paths of differential-drive wheeled robots. The main advantage of this methodology is that optimization is done by considering the kinematics and mechanical constraints of the mobile robot. In accordance to this proposal, the optimized path is achieved by applying recursively a local smoothing on an initial path which is originally modeled as a one-dimensional piecewise linear function. By this recursive smoothing, it can be ensured that the original piecewise linear function can be transformed into a smooth one that fulfill the constraints established by the kinematic equations of the wheeled mobile in terms of a minimum radius of curvature. As a result of this, a trajectory which guarantees lower power consumption and lower mechanical wear, is obtained. To show the better performance of the proposed approach, numerical simulation results are contrasted to those obtained from other reported methods with regards to path length, minimum radius of curvature, cross track error, continuity and resulting acceleration.