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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A Two-Level Model Predictive Control-Based Approach for Building Energy Management including Photovoltaics, Energy Storage, Solar Forecasting and Building Loads

This paper uses a two-level model predictive control-based approach for the coordinated control and energy management of an integrated system that includes photovoltaic (PV) generation, energy storage, and building loads. Novel features of the proposed local controller include (1) the ability to simultaneously manage building loads and energy storage to achieve different operational objectives such as energy efficiency, economic cost efficiency, demand response and grid optimization through the design of specific power trajectory tracking performance functionals, (2) an energy trim function that minimizes the impact of solar forecasting errors on system performance, and (3) the design of a state of charge controller that uses day-ahead forecast of solar power and building loads to intialize energy storage at the start of each day. The local controller is tested in simulation using an exemplary system with PV generation, energy storage and dispatchable building loads. Two sample days with different PV forecasts and multiple case scenarios are considered, and the performance of the algorithm in managing the real and reactive net building load trajectories and the ramp rate of PV injections into the utility network are evaluated. The simulations are based on actual forecasted and measured PV data, and the results show that the local controller meets the tracking requirements for real and reactive power within the operating constraints of the building.

14 SOLAR ENERGY↗
DOE OSTI2019

A New Methodology for Calculating The Energy Performance of Manufacturing Facilities

Total energy comparison (TEC), classic energy intensity (CEI), and linear regression models (LRM) are the three most common approaches used to track the energy performance of manufacturing facilities. TEC simply compares the total energy consumption from utility bills. TEC is rarely used because it does not consider the variation of any factors that may affect energy consumption. One step better, CEI considers the variation of production rates by using the ratio of annual total energy consumption over annual total production. However, CEI fundamentally assumes that energy consumption is zero if the production rate is zero. This is almost never true and can cause significant errors. Using linear regression models, LRM considers the impact of multiple variables and, therefore, most accurately tracks energy performance. Unfortunately, because of the lack of either required data or technical expertise, some facilities cannot create valid linear regression models. For these cases, CEI is the only option. Here, the goal of this article is to develop a new methodology, modified energy intensity (MEI), which is more accurate than CEI, but requires much less data and is easier to implement than LRM. Using the underlying principle of LRM, this article first outlines the mathematical derivation of the equations for MEI, then explains them from an engineering perspective. Finally, the implementation of MEI is discussed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Safety Requirement Management System (SRMS) - Improved Documented Safety Analyses Implementation - 18476

Savannah River Remediation (SRR) developed a new software application, Safety Requirement Management System (SRMS), to improve Documented Safety Analysis (DSA) safety requirement implementation in the Savannah River Site's Liquid Waste facilities. Technical Safety Requirement (TSR) Limited Conditions of Operations (LCOs) and related surveillances were previously tracked using four different applications. Due to their differences and their age, the applications introduced a number of operational challenges and vulnerabilities, including outdated platforms, usage demands beyond original design, and different organizational work processes. SRMS was developed to resolve these issues by using a single web-based approach that provides consistency, wider accessibility, simpler maintenance, and a platform for additional functionality. Other SRS facilities are evaluating the application for its applicability as a standard practice across the site. The new SRMS application decreased the administrative overhead for application maintenance, provided the needed TSR change management functionality, and reduced error precursors with the following advantages: - Consistent process/application across all SRR facilities - More efficient way to track and communicate compliance with DSA time-related requirements (i.e., TSR LCOs and surveillances). - Web-based search capability for LCO entries/exits and a record of surveillance performances. - TSR change management and independent reviews through electronic approvals. For example, the application provides the ability to bundle and stage LCO and surveillance changes associated with a TSR revision. The approval process involves multiple roles from the facility to ensure validity. - Formal configuration management program, fully supported by software life cycle documents. SRMS was implemented at Defense Waste Processing Facility (DWPF) in June 2017, with implementation in all Liquid Waste facilities expected by the end of 2017. Next, SRR plans to expand SRMS functionality to include a linking document database (LDD) to support the DSA requirements. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

First evaluation of the feasibility of MLC tracking using ultrasound motion estimation

Purpose: To quantify the performance of the Clarity ultrasound (US) imaging system (Elekta AB, Stockholm, Sweden) for real-time dynamic multileaf collimator (MLC) tracking. Methods: The Clarity calibration and quality assurance phantom was mounted on a motion platform moving with a periodic sine wave trajectory. The detected position of a 30 mm hypoechogenic sphere within the phantom was continuously reported via Clarity’s real-time streaming interface to an in-house tracking and delivery software and subsequently used to adapt the MLC aperture. A portal imager measured MV treatment field/MLC apertures and motion platform positions throughout each experiment to independently quantify system latency and geometric error. Based on the measured range of latency values, a prostate stereotactic body radiation therapy (SBRT) delivery was performed with three realistic motion trajectories. The dosimetric impact of system latency on MLC tracking was directly measured using a 3D dosimeter mounted on the motion platform. Results: For 2D US imaging, the overall system latency, including all delay times from the imaging and delivery chain, ranged from 392 to 424 ms depending on the lateral sector size. For 3D US imaging, the latency ranged from 566 to 1031 ms depending on the elevational sweep. The latency-corrected geometric root-mean squared error was below 0.75 mm (2D US) and below 1.75 mm (3D US). For the prostate SBRT delivery, the impact of a range of system latencies (400–1000 ms) on the MLC tracking performance was minimal in terms of gamma failure rate. Conclusions: Real-time MLC tracking based on a noninvasive US input is technologically feasible. Current system latencies are higher than those for x-ray imaging systems, but US can provide full volumetric image data and the impact of system latency was measured to be small for a prostate SBRT case when using a US-like motion input.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Carbon-Ion Pencil Beam Scanning Treatment With Gated Markerless Tumor Tracking: An Analysis of Positional Accuracy

Purpose: Having implemented amplitude-based respiratory gating for scanned carbon-ion beam therapy, we sought to evaluate its effect on positional accuracy and throughput. Methods and Materials: A total of 10 patients with tumors of the lung and liver participated in the first clinical trials at our center. Treatment planning was conducted with 4-dimensional computed tomography (4DCT) under free-breathing conditions. The planning target volume (PTV) was calculated by adding a 2- to 3-mm setup margin outside the clinical target volume (CTV) within the gating window. The treatment beam was on when the CTV was within the PTV. Tumor position was detected in real time with a markerless tumor tracking system using paired x-ray fluoroscopic imaging units. Results: The patient setup error (mean ± SD) was 1.1 ± 1.2 mm/0.6 ± 0.4°. The mean internal gating accuracy (95% confidence interval [CI]) was 0.5 mm. If external gating had been applied to this treatment, the mean gating accuracy (95% CI) would have been 4.1 mm. The fluoroscopic radiation doses (mean ± SD) were 23.7 ± 21.8 mGy per beam and less than 487.5 mGy total throughout the treatment course. The setup, preparation, and irradiation times (mean ± SD) were 8.9 ± 8.2 min, 9.5 ± 4.6 min, and 4.0 ± 2.4 min, respectively. The treatment room occupation time was 36.7 ± 67.5 min. Conclusions: Internal gating had a much higher accuracy than external gating. By the addition of a setup margin of 2 to 3 mm, internal gating positional error was less than 2.2 mm at 95% CI.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2024

Evaluation of GlassNet for physics-informed machine learning of glass stability and glass-forming ability

Glassy materials form the basis of many modern applications, including nuclear waste immobilization, touch-screen displays, and optical fibers, and also hold great potential for future medical and environmental applications. However, their structural complexity and large composition space make design and optimization challenging for certain applications. Of particular importance for glass processing and design is an estimate of a given composition's glass-forming ability (GFA). However, there remain many open questions regarding the underlying physical mechanisms of glass formation, especially in oxide glasses. It is apparent that a proxy for GFA would be highly useful in glass processing and design, but identifying such a surrogate property has proven itself to be difficult. While glass stability (GS) parameters have historically been used as a GFA surrogate, recent research has demonstrated that most of these parameters are not accurate predictors of the GFA of oxide glasses. Here, in this work, we explore the application of an open-source pre-trained neural network model, GlassNet, that can predict the characteristic temperatures necessary to compute GS with reasonable performance and assess the feasibility of using these physics-informed machine learning (PIML)-predicted GS parameters to estimate GFA. In doing so, we track the uncertainties at each step of the computation—from the original ML prediction errors to the compounding of errors during GS estimation, and finally to the final estimation of GFA. While GlassNet exhibits reasonable accuracy on all individual properties, we observe a large compounding of error in the combination of these individual predictions for the PIML prediction of GS, finding that random forest models offer similar accuracy to GlassNet. We also break down the performance of GlassNet on different glass families and find that the error in GS prediction is correlated with the error in crystallization peak temperature prediction. Lastly, we utilize this finding to assess the relationship between top-performing GS parameters and GFA for two ternary glass systems: sodium borosilicate and sodium iron phosphate glasses. We conclude that to obtain true ML predictive capability of GFA, significantly more data needs to be collected.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Comparison of Spatial Discretization Methods for Solving the S N Equations Using a Three-Dimensional Method of Manufactured Solutions Benchmark Suite with Escalating Order of Nonsmoothness

For this study, a comparison of the accuracy and computational efficiency of spatial discretization methods of the three-dimensional S N equations is conducted, including discontinuous Galerkin finite element methods, the arbitrarily high-order transport method of nodal type (AHOTN), the linear-linear method, the linear-nodal (LN) method, and the higher-order diamond difference method. For this purpose, we have developed a suite of method of manufactured solutions benchmarks that provides an exact solution of the S N equations even in the presence of scattering. Most importantly, our benchmark suite permits the user to set an arbitrary level of smoothness of the exact solution across the singular characteristics. Our study focuses on the computational efficiency of the considered spatial discretization methods. Numerical results indicate that the best-performing method depends on the norm used to measure the discretization error. We employ discrete Lp norms and integral error norms in this work. For configurations with continuous exact angular flux, high-order AHOTNs perform best under L p error norms, while the LN method performs best when measured by integral error norms. Lastly, when the angular flux is discontinuous, a new singular-characteristic tracking method for three-dimensional geometries performs best among the considered methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Beam-Based Diagnostics of Electric Guide Fields and Lattice Parameters for Run-1 of the Muon g-2 Storage Ring at Fermilab

A portion of the Muon g-2 Storage Ring electric system, which provides vertical beam focusing, exhibited an unexpected time dependence that produced a characteristic evolution of the stored beam during Run-1 of the Muon g-2 Experiment at Fermilab (E989). A method to reconstruct the Run-1 electric guide fields has been developed, which is based on a numerical model of the muon storage ring and optimization algorithms supported by COSY INFINITY. This method takes beam profile measurements from the Muon g-2 straw tracking detectors as input, and it produces a full reconstruction of the time-dependent fields. The fields can then be used for the reproduction of detailed beam tracking simulations and the calculation of ring lattice parameters for acceptance studies and systematic error evaluations.

43 PARTICLE ACCELERATORS↗
DOE OSTI2020

Vulnerabilities in Artificial Intelligence and Machine Learning Applications and Data

Artificial intelligence (AI) applications driven by machine learning (ML) are transformational technologies within the international nuclear security regime. Advancements realized by AI—faster and improved data insights, more efficient and automated processes, reductions in human error—enable nuclear security applications such as behavior analysis for insider threat mitigation, source tracking of stolen nuclear material, and facial recognition software for physical protection. In addition to the advantages, however, there are also inherent vulnerabilities and threats associated with its use and risk mitigations must be built into any AI/ML-enabled systems. This work provides a background on AI and ML and different data types used in the field, including open-source intelligence information (OSINT) that is discoverable by AI tools and application data that are used by AI tools for decision-making and automation. Current and potential AI applications and vulnerabilities related to their use within the nuclear security regime are also discussed.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2016

Staggered scheduling of sensor estimation and fusion for tracking over long-haul links

Networked sensing can be found in a multitude of real-world applications. Here, we focus on the communication-and computation-constrained long-haul sensor networks, where sensors are remotely deployed over a vast geographical area to perform certain tasks. Of special interest is a class of such networks where sensors take measurements of one or more dynamic targets and send their state estimates to a remote fusion center via long-haul satellite links. The severe loss and delay over such links can easily reduce the amount of sensor data received by the fusion center, thereby limiting the potential information fusion gain and resulting in suboptimal tracking performance. In this paper, starting with the temporal-domain staggered estimation for an individual sensor, we explore the impact of the so-called intra-state prediction and retrodiction on estimation errors. We then investigate the effect of such estimation scheduling across different sensors on the spatial-domain fusion performance, where the sensing time epochs across sensors are scheduled in an asynchronous and staggered manner. In particular, the impact of communication delay and loss as well as sensor bias on such scheduling is explored by means of numerical and simulation studies that demonstrate the validity of our analysis.

47 OTHER INSTRUMENTATION↗
DOE OSTI2019

Optimal dispatch for participation of electric vehicles in frequency regulation based on area control error and area regulation requirement

In this study, optimal strategies are proposed for electric vehicles in charging stations to participate in the secondary frequency regulation, while considering their charging demands. In order to fairly allocate the dispatch from the control center among electric vehicles according to their charging demands, two optimal real-time strategies are proposed, respectively based on area control error and area regulation requirement. With the proposed strategies, the expected charging of electric vehicles is optimally tracked in real time by using the regulation task from the control center. Simulations on a two-area interconnected power grid show that the proposed two strategies can respectively lead to a 12.66% and 16.78% frequency deviation reduction and a 13.76% and 9.86% generator regulation reduction. At the same time, the charging demands of EVs can also be ensured.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

The Good, the Bad, and the Ugly: Pseudopotential Inconsistency Errors in Molecular Applications of Density Functional Theory

The pseudopotential (PP) approximation is one of the most common techniques in computational chemistry. Despite its long history, the development of custom PPs has not tracked with the explosion of different density functional approximations (DFAs). As a result, the use of PPs with exchange/correlation models for which they were not developed is widespread, although this practice is known to be theoretically unsound. The extent of PP inconsistency errors (PPIEs) associated with this practice has not been systematically explored across the types of energy differences commonly evaluated in chemical applications. Here, we evaluate PPIEs for a number of PPs and DFAs across 196 chemically relevant systems of both transition-metal and main-group elements, as represented by the W4-11, TMC34, and S22 data sets. Near the complete basis set limit, these PPs are found to cleanly approach all-electron (AE) results for noncovalent interactions but introduce root-mean-squared errors (RMSEs) upwards of 15 kcal mol –1 into predictions of covalent bond energies for a number of popular DFAs. We achieve significant improvements through the use of empirical atom- and DFA-specific PP corrections, indicating considerable systematicity of the PPIEs. The results of this work have implications for chemical modeling in both molecular contexts and for DFA design, which we discuss.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Development and evaluation of virtual refrigerant mass flow sensors for fault detection and diagnostics

Refrigerant mass flow rate is an important measurement for monitoring equipment performance and enabling fault detection and diagnostics. However, a traditional mass flow meter is expensive to purchase and install. A virtual refrigerant mass flow sensor (VRMF) uses a mathematical model to estimate flow rate using low-cost measurements and can potentially be implemented at low cost. This study evaluates three VRMFs for estimating refrigerant mass flow rate. The first model uses a compressor map that relates refrigerant flow rate to measurements of inlet and outlet pressure, and inlet temperature measurements. The second model uses an energy-balance method on the compressor that uses a compressor map for power consumption, which is relatively independent of compressor faults that influence mass flow rate. The third model is developed using an empirical correlation for an electronic expansion valve (EEV) based on an orifice equation. The three VRMFs are shown to work well in estimating refrigerant mass flow rate for various systems under fault-free conditions with less than 5% RMS error. Each of the three mass flow rate estimates can be utilized to diagnose and track the following faults: 1) loss of compressor performance, 2) fouled condenser or evaporator filter, 3) faulty expansion device, respectively. For example, a compressor refrigerant flow map model only provides an accurate estimation when the compressor operates normally. When a compressor is not delivering the expected flow due to a leaky suction or discharge valve or other internal fault, the energy-balance or EEV model can provide accurate flow estimates. In this paper, the flow differences provide an indication of loss of compressor performance and can be used for fault detection and diagnostics.

Kim, Woohyun↗
DOE OSTI2016

SU-G-JeP1-02: A New Intra-Fractional Prostate Motion Tracking Method in Volumetric Modulated Arc Therapy (VMAT) Via 2D/3D Registration

Purpose: Intra-fractional prostate motion leads uncertainty on delivered dose in radiotherapy and may cause significant dose deviation from the planned dose distribution. This is especially a concern in scenarios with a high dose per fraction and hence a long delivery time, e.g. stereotactic body radiotherapy. Knowledge about intra-fractional prostate motion is valuable to address this problem, e.g. by reconstructing delivered dose and performing adaptation. This study proposes a new approach to determine intra-fractional prostate motion in VMAT via 2D/3D maker registration. Methods: At our institution, each patient has three markers implanted in the prostate. During treatment delivery, kV triggered images were taken every three seconds to acquire 2D projection of 3D anatomy at the direction orthogonal to the therapeutic beam. Projected marker locations were identified on each projection image using template matching with geometric constraints. 3D prostate translation and rotation for each triggered image were obtained by solving an optimization problem, such that the calculated marker locations match the measured ones. Inter-image motion smoothness was employed as a constraint. We tested this method in simulation studies with five realistic prostate motion trajectories acquired via Calypso and in real phantom experiments. Results: For the simulation case, the motion range for these patients was 0.5∼6.0 mm. Root mean square (RMS) error of calculated motion along left-right (LR), anterior-posterior (AP) and cranial-caudal (CC) directions were 0.26mm, 0.36mm, and 0.016mm, respectively. The motion range in the phantom study along LR, AP, and CC directions were 15mm, 20mm and 10mm. The mean RMS errors along these directions were 1.99mm, 1.37mm and 0.22mm. Conclusion: A new prostate motion tracking algorithm based on kV triggered images has been developed and validated. Clinically acceptable accuracy has been achieved.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

An integrated model-driven method for in-treatment upper airway motion tracking using cine MRI in head and neck radiation therapy

Purpose: For the first time, MRI-guided radiation therapy systems can acquire cine images to dynamically monitor in-treatment internal organ motion. However, the complex head and neck (H&N) structures and low-contrast/resolution of on-board cine MRI images make automatic motion tracking a very challenging task. In this study, the authors proposed an integrated model-driven method to automatically track the in-treatment motion of the H&N upper airway, a complex and highly deformable region wherein internal motion often occurs in an either voluntary or involuntary manner, from cine MRI images for the analysis of H&N motion patterns. Methods: Considering the complex H&N structures and ensuring automatic and robust upper airway motion tracking, the authors firstly built a set of linked statistical shapes (including face, face-jaw, and face-jaw-palate) using principal component analysis from clinically approved contours delineated on a set of training data. The linked statistical shapes integrate explicit landmarks and implicit shape representation. Then, a hierarchical model-fitting algorithm was developed to align the linked shapes on the first image frame of a to-be-tracked cine sequence and to localize the upper airway region. Finally, a multifeature level set contour propagation scheme was performed to identify the upper airway shape change, frame-by-frame, on the entire image sequence. The multifeature fitting energy, including the information of intensity variations, edge saliency, curve geometry, and temporal shape continuity, was minimized to capture the details of moving airway boundaries. Sagittal cine MR image sequences acquired from three H&N cancer patients were utilized to demonstrate the performance of the proposed motion tracking method. Results: The tracking accuracy was validated by comparing the results to the average of two manual delineations in 50 randomly selected cine image frames from each patient. The resulting average dice similarity coefficient (93.28% ± 1.46%) and margin error (0.49 ± 0.12 mm) showed good agreement between the automatic and manual results. The comparison with three other deformable model-based segmentation methods illustrated the superior shape tracking performance of the proposed method. Large interpatient variations of swallowing frequency, swallowing duration, and upper airway cross-sectional area were observed from the testing cine image sequences. Conclusions: The proposed motion tracking method can provide accurate upper airway motion tracking results, and enable automatic and quantitative identification and analysis of in-treatment H&N upper airway motion. By integrating explicit and implicit linked-shape representations within a hierarchical model-fitting process, the proposed tracking method can process complex H&N structures and low-contrast/resolution cine MRI images. Future research will focus on the improvement of method reliability, patient motion pattern analysis for providing more information on patient-specific prediction of structure displacements, and motion effects on dosimetry for better H&N motion management in radiation therapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Technical Note: A novel leaf sequencing optimization algorithm which considers previous underdose and overdose events for MLC tracking radiotherapy

Purpose: Multileaf collimator (MLC) tracking radiotherapy is complex as the beam pattern needs to be modified due to the planned intensity modulation as well as the real-time target motion. The target motion cannot be planned; therefore, the modified beam pattern differs from the original plan and the MLC sequence needs to be recomputed online. Current MLC tracking algorithms use a greedy heuristic in that they optimize for a given time, but ignore past errors. To overcome this problem, the authors have developed and improved an algorithm that minimizes large underdose and overdose regions. Additionally, previous underdose and overdose events are taken into account to avoid regions with high quantity of dose events. Methods: The authors improved the existing MLC motion control algorithm by introducing a cumulative underdose/overdose map. This map represents the actual projection of the planned tumor shape and logs occurring dose events at each specific regions. These events have an impact on the dose cost calculation and reduce recurrence of dose events at each region. The authors studied the improvement of the new temporal optimization algorithm in terms of the L1-norm minimization of the sum of overdose and underdose compared to not accounting for previous dose events. For evaluation, the authors simulated the delivery of 5 conformal and 14 intensity-modulated radiotherapy (IMRT)-plans with 7 3D patient measured tumor motion traces. Results: Simulations with conformal shapes showed an improvement of L1-norm up to 8.5% after 100 MLC modification steps. Experiments showed comparable improvements with the same type of treatment plans. Conclusions: A novel leaf sequencing optimization algorithm which considers previous dose events for MLC tracking radiotherapy has been developed and investigated. Reductions in underdose/overdose are observed for conformal and IMRT delivery.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2021

Gimballed Tracking Mount Pointing Angle Qualification

Tonopah Test Range (TTR), in support of its testing mission and modernization effort acquired a fleet of new gimballed tracking mounts (GTMs) manufactured by BAE Systems. The new GTMs can be operated remotely during flight tests and provide near real-time target tracking data. Furthermore, test vehicle Time-Space-Position-Information (TSPI) is evaluated using post-test synchronized imagery and pointing angle measurements acquired from each tracking mount. To comply with the Nuclear Enterprise Assurance Program (NEAP), all measurements devices must be certified. In keeping with the NEAP program, qualification of the new GTMs have been assessed to confirm that their pointing angle measurements produce acceptable TSPI results. This study only evaluated the four GTMs as a stand-alone solution and found that the GTMs meet their performance requirement of 0.006 degrees RMS error (or less) for post-processed pointing angles and produced TSPI solution with error volumes on the order of one meter or less. The new GTMs will be utilized in combination with existing optical tracking mounts, which will only improve the accuracy of the resulting TSPI data product. Details regarding the approach, analysis, summary results, and conclusions are presented.

42 ENGINEERING↗
DOE OSTI2026

Multilevel Conditional Disturbance Rejection Control for Satellite Attitude Tracking

Recently, the conditional disturbance rejection controller (CDRC) was proposed to improve control performance by leveraging disturbances that have beneficial effects on the system. However, it only considers disturbances acting on the state variable directly influenced by them. Although fast convergence of this state can be achieved with the CDRC, it may unintentionally affect the convergence of the output (i.e., the primary state). Here, in this article, a multilevel CDRC is proposed to enhance satellite attitude control performance by accounting for the effect of disturbances on both attitude (output) and angular velocity. The extended state observer is employed to estimate the lumped disturbance, including the modeling errors and external disturbances. Then, a backstepping-based controller with the multilevel disturbance rejection law (ML-DRL) is designed for attitude tracking. The ML-DRL is developed to improve the control performance by using a disturbance with a damping effect on both attitude and velocity. Faster convergence of attitude and velocity can be achieved by conditionally compensating for the disturbance. The stability of the proposed control method is analyzed by demonstrating that the errors are bounded as time tends to infinity. The attitude control performance of the proposed method is evaluated through numerical examples conducted using the MATLAB/Simulink Multibody tool.

Active disturbance rejection control (ADRC)↗