Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “feedback control”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Impedance‐matching model‐in‐the‐loop simulation

Abstract Impedance matching is a novel approach to executing model‐in‐the‐loop (MIL) simulations. The concept, key features, and sample applications of this approach have been described in a series of publications. This paper advances theory and implementation for impedance‐matching MIL by: (1) developing a feedback linearization technique for implementing MIL for nonlinear virtual systems, (2) systematically characterizing MIL performance‐stability tradeoffs using three design‐oriented criteria—performance: defined as closeness of the controlled‐actuator impedance to the virtual‐boundary impedance;control effort: low controller response at high frequencies to reduce sensitivity to measurement noise and uncertainties in the actuator model; andstability: pursued using passivity of the controlled actuator system, and (3) assessing, through experimentation, the robustness of two ways to estimate feedback reaction force from the test article. These fundamental advancements to MIL are described using a one‐dimensional configuration consisting of a fluid‐filled cylindrical vessel as the physical test article and a uniaxial hydraulic shake table controlled to imitate different seismic isolation systems at the base of the vessel.

Engineering↗
DOE OSTI2025

Describing Function Analysis of Transformer Magnetizing Inductance for Direct Power Control of Back-to-Back Modular Multilevel Converters with Advanced Grid Support

This paper provides a detailed investigation into the application of describing function-based analysis for assessing transformer magnetizing inductance and its impact on system performance. The focus is on a back-to-back modular multilevel converter architecture, designed to interconnect systems operating at different frequencies. The study explores the implementation of a Direct Power Control strategy, examining its effects on transformer magnetizing inductance saturation and offering effective mitigation techniques. Furthermore, the integration of advanced grid support functionalities is highlighted, demonstrating how these enhancements bolster the converter's ability to improve grid stability and power quality, positioning it as a robust solution for modern power systems. The proposed approach is validated through extensive computer simulations based MAT LAB/Simulink domain, supported by significant case study results, confirming its practical effectiveness.

back-to-back modular multilevel converters (B2B- M↗
DOE OSTI2020

Development of Control System Functional Capabilities within the IES Plug-and-Play Simulation Environment

The concept of an Integrated Energy System (IES) is meant to combine different energy technologies in synergistic ways to achieve a more secure and economical energy supply. The RAVEN-based HYBRID framework is used to find the optimal installed capacity and the optimal economical dispatch of each component of the IES. A new RAVEN (Risk Analysis Virtual ENvironment) plugin for grid and capacity optimization (HERON) has been developed for optimizing the production variables of the IES given the demand profile. Currently, only the limits that affect the production variables and their corresponding time rates of change are considered (explicit constraints). However, other variables are additionally subject to constraints, but the associated limits are not accounted for (implicit constraints). In particular, for the power dispatch problem, the optimization algorithm takes into account the limits on the electrical power output and the corresponding hourly power variations but does not consider other constraints on process variables whose response effects the service life of the IES. This report describes a scheme that allows accounting for implicit constraints without increasing the size of the optimization problem. The Reference Governor (RG) algorithm is traditionally used for enforcing state and control constraints by modifying the set-point trajectories supplied to the feedback regulators. In our application, the RG is coupled within an iterative loop with the HERON-power dispatcher to generate optimal trajectories that ensure the operational constraints are met. A data-driven procedure to derive a representation of the dynamics of the controlled system was developed. First, the variables that represented the state of the system are selected (PCA-based approach), and then state-space representation matrices are derived from the collected measurements (DMDc algorithm). A preliminary version of the developed workflow based on Linear Time Invariant matrices was assessed by adopting a two-unit test case. More sophisticated versions of this workflow foreseeing the on-line derivation of system matrices will be deployed in FY 2021. Finally, a “plug-and-play” library of controllers and state observers was developed in Dymola. Some aspects of the current configuration of the IES unit components, e.g., the encapsulation of the control schemes into dedicated blocks, are consistent with the “plug-and-play” philosophy. Other features, e.g., the system buses collecting the input and the output variables, are not. For this reason, once listed and described the limits of the current configuration, necessary modifications to the plant model interface are presented. As a test-case, the interfaces of the SES model in the RAVEN-based HYBRID framework were reworked accordingly, and two different control schemes were applied to the same plant model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Controls Status for Fermilab’s PIP-II Project

Testing of Cryomodule first articles at PIP-II's on-site Cryomodule Test Facility (CMTF), where EPICS based controls are already being used, has been invaluable to the project. In addition to validating hardware and controls components, it has provided opportunities to build buy-in and illicit meaningful feedback early-on. A device naming convention has also been significantly refined with an internal working group and the PIP-II integration team. Compressed air and Process Control Water (PCW) systems have been installed, and operations has been engaged in Phoebus display development in preparation for a transition to operations for these systems by 2026. Cryoplant hardware has been put in place, and collaboration between controls and PIP-IIs cryo group for IOC and display development is well underway for commissioning of cryoplant systems to begin early 2026. The project has also received beneficial occupancy of the High-Bay Building in October 2025, keeping us on schedule for Warm Front End commissioning to begin in 2027.

Crisp, Dan [Fermilab]↗
DOE OSTI2025

Reactive Transport Modeling of Hydrogen Production from Serpentinization of Olivine

Hydrogen production from serpentinization of ultramafic rocks represents a promising natural pathway for generating carbon-free energy, yet its kinetics and controlling factors remain incompletely understood. A key challenge in advancing serpentinization research lies in the heterogeneity of porosity and permeability in rocks, which leads to nonuniform fluid velocity fields, as well as uncertainties in estimating reactive surface area and identifying appropriate mineral reaction equilibria. Additional complexities arise from the role of dissolved SiO 2 , Fe 2+ /Fe 3+ partitioning, and the limited effect of pH variations within the strongly alkaline regime on hydrogen yields. These challenges hinder straightforward extrapolation from laboratory tests to practical applications of hydrogen production from natural rocks. Here, in this work, we address these questions using a simulation-based reactive transport modeling framework calibrated against controlled laboratory experiments reported elsewhere. The model couples geochemical kinetics, multiphase flow, and mineralogical feedbacks, enabling systematic evaluation of how surface area, dissolved silica concentration, Fe redox state, temperature, and pressure govern serpentinization and H2 generation. We find that surface area exerts the strongest control on reaction rates and hydrogen yields, while Fe 2+ /Fe 3+ ratios act as secondary modulators. Elevated dissolved silica concentrations suppress hydrogen production but accelerate serpentine precipitation, whereas increasing pH beyond 12 within the strongly alkaline regime produces only marginal gains. Finally, we demonstrate that integrating targeted experiments with calibrated simulations offers a powerful and efficient approach for predicting hydrogen yields and assessing parameter trade-offs in industrial-scale applications. This integration can substantially reduce the experimental burden while improving predictive capability, thereby enhancing both the mechanistic understanding and the practical feasibility of hydrogen production from serpentinization.

08 HYDROGEN↗
DOE OSTI2022

Nonlinear burn control in ITER using adaptive allocation of actuators with uncertain dynamics

Abstract ITER will be the first tokamak to sustain a fusion-producing, or burning, plasma. If the plasma temperature were to inadvertently rise in this burning regime, the positive correlation between temperature and the fusion reaction rate would establish a destabilizing positive feedback loop. Careful regulation of the plasma’s temperature and density, or burn control, is required to prevent these potentially reactor-damaging thermal excursions, neutralize disturbances and improve performance. In this work, a Lyapunov-based burn controller is designed using a full zero-dimensional nonlinear model. An adaptive estimator manages destabilizing uncertainties in the plasma confinement properties and the particle recycling conditions (caused by plasma–wall interactions). The controller regulates the plasma density with requests for deuterium and tritium particle injections. In ITER-like plasmas, the fusion-born alpha particles will primarily heat the plasma electrons, resulting in different electron and ion temperatures in the core. By considering separate response models for the electron and ion energies, the proposed controller can independently regulate the electron and ion temperatures by requesting that different amounts of auxiliary power be delivered to the electrons and ions. These two commands for a specific control effort (electron and ion heating) are sent to an actuator allocation module that optimally maps them to the heating actuators available to ITER: an electron cyclotron heating system (20 MW), an ion cyclotron heating system (20 MW), and two neutral beam injectors (16.5 MW each). Two different actuator allocators are presented in this work. The first actuator allocator finds the optimal mapping by solving a convex quadratic program that includes actuator saturation and rate limits. It is nonadaptive and assumes that the mapping between the commanded control efforts and the allocated actuators (i.e. the effector model) contains no uncertainties. The second actuator allocation module has an adaptive estimator to handle uncertainties in the effector model. This uncertainty includes actuator efficiencies, the fractions of neutral beam heating that are deposited into the plasma electrons and ions, and the tritium concentration of the fueling pellets. Furthermore, the adaptive allocator considers actuator dynamics (actuation lag) that contain uncertainty. This adaptive allocation algorithm is more computationally efficient than the aforementioned nonadaptive allocator because it is computed using dynamic update laws so that finding the solution to a static optimization problem is not required at every time step. A simulation study assesses the performance of the proposed adaptive burn controller augmented with each of the actuator allocation modules.

Physics↗
DOE OSTI2026

Reshaping the Quantum Arrow of Time

While the microscopic laws of physics are often symmetric under time reversal, most natural processes that we observe are not. The emergent asymmetry between typical and time-reversed processes is referred to as the arrow of time. In quantum physics, an arrow of time emerges when a sequence of measurements is performed on a system. We introduce quantum control tools that can yield dynamics more consistent with time flowing backward than forward. The control tools are based on the explicit construction of a Hamiltonian that can replicate the stochastic trajectories of a monitored quantum system. Such a Hamiltonian can reverse the effect of monitoring and, via a feedback process, generate trajectories consistent with a reversed arrow of time. It can also be used to simulate the backward-in-time dynamics of an open quantum system. Finally, we design a feedback-driven continuous measurement engine powered by the energy pumped into the system by the monitoring process. We show that the engine can operate under experimentally realizable conditions with feedback delay and finite-efficiency measurements.

Entropy production↗
DOE OSTI2023

Aligning theoretical and empirical representations of soil carbon-to-nitrogen stoichiometry with process-based terrestrial biogeochemistry models

Soil carbon-nitrogen (C:N) stoichiometry acts as a control over decomposition and soil organic matter formation and loss, making it a key soil property for understanding ecosystem dynamics and projected ecosystems responses to global environmental change. However, the controls of soil C:N and how they respond to increasing pressures from global change agents are not fully understood. The “foundational” controls on soil C:N, namely plant and microbial C:N, have been used to predict soil C:N, but fail to accurately simulate all ecosystems and may be insufficient for predictions under global environmental change. Here we present an “emerging” representation of controls of soil C:N that includes plant-microbe-mineral feedbacks that have been shown to regulate soil C:N. We argue that including representation of these emerging drivers in process-based terrestrial biogeochemistry models, which include biological N fixation, mycorrhizae, priming, root exudation of organic acids, and mineralogy (including soil texture, mineral composition, and aggregation), will improve mechanistic representation of soil C:N and associated processes. Such improvements will produce models that will better simulate a variety of ecological states and predict soil C:N when global changes modify plant-microbe-mineral interactions. Here, we align our empirical understanding of controls of soil C:N with those controls represented in models, identifying contexts where emerging drivers might be particularly important to represent (e.g., priming and root exudation in nutrient-limited conditions) and areas of future work. Additionally, we show that implementing emerging drivers of soil C:N results in different simulated outcomes at steady state and in response to elevated atmospheric CO2. Our review and preliminary simulations support the need to incorporate emerging drivers of soil C:N into process-based terrestrial biogeochemistry models, allowing for both theoretical exploration of mechanisms and potentially more accurate predictions of land biogeochemical responses to global change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Voltage Probability Density Function Shaping Control Strategy Considering Grid Operational Uncertainties

It is well-known that power systems operation always affected by various uncertainties which make the bus voltage a random process that can be characterized by its probability density function (PDF) at any time instant. In this context, this paper presents a novel PDF-based voltage control framework for power systems. By modeling voltage as a stochastic process, we formulate a stochastic differential equationthat captures grid uncertainties. The associated Fokker-Planck-Kolmogorov equation is derived to describe the evolution of the voltage PDF, which enables the formulation of a PDF-shaping control strategy. To simplify the PDF control formulation, a B-spline neural network is introduced for real-time estimation and regulation of the voltage distribution. The proposed PDF control law updates voltage references for energy storage systems and synchronous generators using real-time PDF measurements and feedback signals. The proposed method is validated on a modified Kundur’s two-area system. Simulation results demonstrate that the controller can significantly improve the voltage stability under stochastic conditions, highlighting its effectiveness in modern inverter-rich grids.

Gui, Yonghao [ORNL] (ORCID:0000000250435534)↗
DOE OSTI2024

Synchronization of the Recent Decline of East African Long Rains and Northwestern Eurasian Warming

Abstract The East African March–April–May (MAM, “long rains”) precipitation decline in recent decades remains a puzzle marked by various proposed large‐scale drivers. Here, the interannual variability of the long rains and their recent drying trend are examined using global model simulations and observations. Comparison of a control simulation and re‐initialized simulations in which land‐surface feedback is suppressed shows that much of the long rains deficit experienced between 1980 and 2014 is synchronized with the warming of the Northwestern Eurasian landmass. In agreement with the modeling results, multiple observational data sets reveal a strong negative correlation between MAM mean East African rainfall amount and the surface temperature over Northwestern Eurasia. Idealized simulations further indicate that warming in Northwestern Eurasia weakens the regional Hadley Cell and diverts the monsoonal transport of moisture away from Eastern Africa toward Europe and southern Africa, highlighting the role of remote land surface warming on the observed precipitation decline.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Design and Performance of a Smartphone-based Cosmic Ray Observatory

This dissertation examines the feasibility of appropriating the global network of smartphones as an observatory for ultra-high-energy cosmic rays. An application and cloud-based data-acquisition system are first proposed for such an observatory, in which heterogenous devices self-calibrate and server feedback optimizes individual device triggers. Methods of monitoring and manually controlling this network are also examined. Detection efficiencies for cosmic muons, MeV-scale gamma rays, and 120 GeV protons are then measured for this trigger, with which a Monte Carlo pixel model is fine-tuned. Extending this model to cosmic ray showers, the effective area of the observatory for super-GZK primaries is shown to equal that of the Pierre Auger Observatory with a global participation rate under 0.1%, far below initial estimates presented in Ref. [83]. A vastly improved sensitivity to photons and more precise modeling of electrons are primarily responsible for this discrepancy, though more refined models of the combinatorial background may yet lead to more stringent requirements.

Swaney, Jeff↗
DOE OSTI2025

Nuclear microreactor transient and load-following control with deep reinforcement learning

The economic feasibility of nuclear microreactors will depend on minimizing operating costs through advancements in autonomous control, especially when these microreactors are operating alongside other types of energy systems (e.g., renewable energy). This study explores the application of deep reinforcement learning (RL) for real-time drum control in microreactors, exploring performance in regard to load-following scenarios. By leveraging a point kinetics model with thermal and xenon feedback, we first establish a baseline using a single-output RL agent, then compare it against a traditional proportional–integral–derivative (PID) controller. This study demonstrates that RL controllers, including both single- and multi-agent RL (MARL) frameworks, can achieve similar or even superior load-following performance as traditional PID control across a range of load-following scenarios. In short transients, the RL agent was able to reduce the tracking error rate in comparison to PID by one half to one third. Over extended 300-minute load-following scenarios in which xenon feedback becomes a dominant factor, PID maintained better accuracy, but RL still remained within a 1% error margin despite being trained only on short-duration scenarios. This highlights RL’s strong ability to generalize and extrapolate to longer, more complex transients, affording substantial reductions in training costs and reduced overfitting. Furthermore, when control was extended to multiple drums, MARL enabled independent drum control as well as maintained reactor symmetry constraints without sacrificing performance---an objective that standard single-agent RL could not learn. We also found that, as increasing levels of Gaussian noise were added to the power measurements, the RL controllers were able to maintain lower error rates than PID, and to do so with at least 10% and upwards of 150% less control effort. These findings illustrate RL's potential for autonomous nuclear reactor control, laying the groundwork for future integration into high-fidelity simulations and experimental validation efforts.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Examining Cloud Feedback Components in the Simple Cloud-Resolving E3SM Atmosphere Model (SCREAM)

Cloud feedback remains the main source of uncertainty in climate sensitivity estimated by global climate models (GCMs), largely because subgrid cloud responses are parameterized in GCMs due to their coarse resolution. Here, this study examines cloud feedback in the global 3.25-km Simple Cloud-Resolving Energy Exascale Earth System Model (E3SM) Atmosphere Model (SCREAM 3 km) through a pair of 1-yr atmosphere-only simulations with control and +4-K sea surface temperature perturbations. SCREAM 3 km produces a positive cloud feedback that falls within but at the upper end of the range of Coupled Model Intercomparison Project phase 5 (CMIP5) and CMIP phase 6 (CMIP6) models and expert judgment. The positive cloud feedback arises from positive contributions from both high- and low-level clouds, with increases in high-cloud altitude and decreases in low-cloud amount and optical depth playing key roles. The stronger-than-CMIP-average feedback is mainly attributable to the high-cloud altitude feedback, owing to cloud tops rising nearly isothermally in SCREAM 3 km. The positive low-cloud amount feedback is weaker in SCREAM than in GCMs because estimated inversion strength (EIS) increases more dramatically with warming. A coarser 12-km resolution version of SCREAM exhibits a weaker positive cloud feedback than SCREAM 3 km, mainly because its low-cloud-radiative flux is more sensitive to EIS, leading to a stronger negative low-cloud amount feedback. With this process-level assessment of cloud feedback, this study reveals where SCREAM aligns with and diverges from conventional GCMs and expert assessment, providing insights to inform further model improvement and future expert assessment.

Cloud radiative effects↗
DOE OSTI2025

Multi-scale, Multi-disciplinary, and Multi-agent Explainable AI with Koopman-Undergirded Learning, Prediction, and Analysis (M3EA KULPA) (Project Closeout Report)

The goal of this project was to develop and use domain-aware machine learning formulations, based on the Koopman Operator (KO), for modelling multi-scale, multi-disciplinary (e.g., multi-physics), and/or multi-agent systems. The project developed these formulations for the following cases: • Systems with dynamics at two separate time scales, • Systems with a bi-level hierarchical control structure, • Systems with bi-level hierarchical control and dynamics at two separate time scales (the lower level controls operating at the faster time scale), and • Systems with n separate but interacting agents/disciplines (with/without control, respectively); the controls for each agent could include bi-level hierarchical control and dynamics at two separate time scales as described above. The project then defined a set of dynamical systems consisting of different nonlinear oscillators that could be used to test these different formulations and then subsequently learned the KO models for those systems. With the KO models, we were able to do the following: • Quantify system stability, including both long-term and transient behavior, • Quantify the effects of feedbacks between the different time scales and agents/disciplines in terms of those feedbacks’ effects on system stability, • Replace a standard Proportional-Integral (PI) control in the hierarchical control structure with a KO-based Linear-Quadratic Regular (LQR), a form of optimal control, • Calculate optimal supervisory control policies a) with and without time scale separated dynamics at the lower level control levels and b) with both PI and KO-based LQR lower level control policies, and • Calculate dynamic Nash equilibria for multi-agent systems where each agent makes its own control decisions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Predicting Deposition Rate and Closing the Loop on Aerosol Jet Printing with In‐Line Light Scattering Measurements

Aerosol jet printing is a compelling noncontact, digital manufacturing technology for flexible, hybrid, and conformal electronics, but batch‐to‐batch variability and process drift inhibit systematic study and translation to production environments. Emerging measurement techniques for the aerosol volume fraction, a key parameter governing deposition rate, have shown promise for real‐time response, including a recent demonstration of human‐in‐the‐loop control. By integrating improved light scattering measurements with custom software, a robust environment for real‐time monitoring is established and fully automated closed‐loop control over the deposition rate during printing is enabled. The physical basis for scattering measurements as a feedback source is examined and the quantitative insight this provides for ink development and fundamental process studies is highlighted. Three candidate process variables for closed‐loop control, namely the atomizer voltage, carrier gas flow rate, and print speed, are then evaluated. The atomizer voltage demonstrates the best extended duration validity because it addresses atomization variability directly, but carrier gas flow rate and print speed provide faster and more deterministic responses. This methodology is then demonstrated for electrical properties using a silver nanoparticle ink, maintaining 98% of printed patterns within 10% of the mean resistance value over 3 h of printing.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Deciphering the sensitivity of urban canopy air temperature to anthropogenic heat flux with a forcing-feedback framework

Abstract The sensitivity of urban canopy air temperature ( T a ) to anthropogenic heat flux ( Q A H ) is known to vary with space and time, but the key factors controlling such spatiotemporal variabilities remain elusive. To quantify the contributions of different physical processes to the magnitude and variability of Δ T a / Δ Q A H (where Δ represents a change), we develop a forcing-feedback framework based on the energy budget of air within the urban canopy layer and apply it to diagnosing Δ T a / Δ Q A H simulated by the Community Land Model Urban over the contiguous United States (CONUS). In summer, the median Δ T a / Δ Q A H is around 0.01 K W m − 2 − 1 over the CONUS. Besides the direct effect of Q A H on T a , there are important feedbacks through changes in the surface temperature, the atmosphere–canopy air heat conductance ( c a ), and the surface–canopy air heat conductance. The positive and negative feedbacks nearly cancel each other out and Δ T a / Δ Q A H is mostly controlled by the direct effect in summer. In winter, Δ T a / Δ Q A H becomes stronger, with the median value increased by about 20% due to weakened negative feedback associated with c a . The spatial and temporal (both seasonal and diurnal) variability of Δ T a / Δ Q A H as well as the nonlinear response of Δ T a to Δ Q A H are strongly related to the variability of c a , highlighting the importance of correctly parameterizing convective heat transfer in urban canopy models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Coherency-Aware Learning Control of Inverter-Dominated Grids: A Distributed Risk-Constrained Approach

Here, this letter investigates the importance of integrating the coherency knowledge for designing controllers to dampen sustained oscillations in wide-area power networks with significant penetration of inverter-interfaced resources. Coherency is a fundamental property of power systems, where time-scale separation in frequency dynamics leads to clustered behavior among generators of different groups. Large-scale penetration of inverter-driven low inertia resources replacing conventional synchronous generators (SGs) can lead to perturbation in the coherent partitioning; hence, integrating such information is of utmost importance for oscillation control designs. We present the coherency-aware design of a distributed output feedback-based reinforcement learning method that additionally incorporates risk constraints to capture the uncertainties related to net-load fluctuations. The use of domain-aware coherency information has produced improved training and oscillation performance than the coherency-agnostic control design, hence proving to be effective in controller design. Finally, we validated the proposed method with numerical experiments on the benchmark IEEE 68-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

A Modular Accelerator Robotics Framework for AD Robotics

Accelerator tunnels, such as the ones at Fermilab, remain highly radioactive after beam shutoff due to induced radiation from the beam. This residual radiation creates a hazardous environment for manual inspection and repair of beamline components. To minimize worker radiation dose and reduce beam downtime, the AD Robotics Initiative previously built a fleet of low-cost custom mobile robots. However, the custom Python sockets server-client architecture lacked standardization, causing development delays and complicating the integration of new sensors and actuators. Here, we developed a modular system using ROS2 and Docker to standardize the teleoperation and control interfaces. This system was validated by implementing a teleoperation controller with real-time, low-latency, and high-definition video feedback. The aim of this framework is for a new feature or even a robot to be integrated into the system simply by documenting the hardware configuration. Current integration of LiDAR, Odometry, and Depth Cameras provides the foundation for Simultaneous Localization and Mapping (SLAM) tasks. Finally, future work involves integration into the accelerator control system and the attachment of a 6 degree-of-freedom robotic arm for telemanipulation.

Rayyan Khan, M. [Fermilab; Rensselaer Poly.; Unlis↗