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DOE OSTI2023

A New Proposal Generalized Predictive Control Algorithm With Polynomial Reference Tracking Applied for Sodium Fast Reactors

This paper proposes a generalized predictive control (GPC) with constraints and orthonormal Laguerre functions using the simplified model of the primary system (reactor core and intermediate heat exchanger (IHX)) of a prototypical sodium fast reactor (SFR). This paper develops a multiple-input multiple-output (MIMO) GPC with input constraints able to track polynomial references of any degree applied in coolant temperature difference across the core and fractional power. The manipulated variables of the GPC-SFR are the reactivity and the sodium flow rate of the primary and secondary pipes. Moreover, orthonormal Laguerre functions and step down condition number techniques were also applied to avoid the numerical ill-conditioning issue in quadratic programming of large systems. Thus, a GPC type-2 was designed to control fractional power, coolant temperature difference across the core and sodium tank temperature of the SFR primary system when temperature references change according to a linear ramp after reaching their steady-state operation, sustaining 100% power operation on the reactor. In order to analyze the load tracking capability of the GPC-SFR type-2, the load following from 100% fractional power (FP) to 60% FP at 0.8% FP/min rate is simulated. Constraints on the rate of coolant temperature difference across the core and reactivity were applied for the design safety. For comparison criteria, this paper compares the GPC-SFR type-2 with the GPC-SFR type-1, i.e., standard model predictive control (MPC), to verify the viability and superior performance of the proposal regarding: (a) ramp-tracking capability of temperature and load; (b) the rejections of a reactivity disturbance of -1 cent and a secondary sodium inlet temperature disturbance of +10°F; and (c) a simulation with uncertainty in reactor design. The simulations show that the GPC-SFR type-2 overcome the GPC-SFR type-1 robustness and performance.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2026

Enabling integrated AI control on DIII-D: a control system design with state-of-the-art experiments

We present the design and application of a general algorithm for Prediction And Control using MAchiNe learning (PACMAN) in DIII-D. Machine learning (ML)-based predictors and controllers have shown great promise in achieving regimes in which traditional controllers fail, such as tearing mode (TM) free scenarios, ELM-free scenarios and stable advanced tokamak conditions. The architecture presented here was deployed on DIII-D to facilitate the end-to-end implementation of advanced control experiments, from diagnostic processing to final actuation commands. This paper describes the detailed design of the algorithm and explains the motivation behind each design point. We also describe several successful ML control experiments in DIII-D using this algorithm, including a reinforcement learning controller targeting advanced non-inductive plasmas, a wide-pedestal quiescent H-mode ELM predictor, an Alfvén Eigenmode controller, a Model Predictive Control plasma profile controller and a state-machine TM predictor-controller. There is also discussion on guiding principles for real-time ML controller design and implementation.

machine learning↗

DOE OSTI2023

Machine Learning-Based Model Predictive Control of Two-Time-Scale Systems

In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics of both subsystems. Specifically, a recurrent neural network (RNN) and a feedforward neural network (FNN) are used to predict the slow and fast state vectors, respectively. Moreover, we investigate the generalization error bounds for these machine learning models approximating the dynamics of two-time-scale systems. Next, under the assumption that the fast states are asymptotically stable, our focus shifts toward designing a Lyapunov-based model predictive control (LMPC) scheme that exclusively employs the RNN to predict the dynamics of the slow states. Additionally, we derive sufficient conditions to guarantee the closed-loop stability of the system under the sample-and-hold implementation of the controller. A nonlinear chemical process example is used to demonstrate the theory. In particular, two RNN models are constructed: one to model the full two-time-scale system and the other to predict solely the slow state vector. Both models are integrated within the LMPC scheme, and we compare their closed-loop performance while assessing the computational time required to execute the LMPC optimization problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Transport and confinement physics: Chapter 2 of the special issue: on the path to tokamak burning plasma operation

Progress in physics understanding and theoretical model development of plasma transport and confinement (TC) in the ITPA TC Topical Group since the publication of the ITER Physics Basis (IPB) document (Doyle et al 2007 Nucl. Fusion 47 S18) was summarized focusing on the contributions to ITER and burning plasma prediction and control. This paper provides a general and streamlined overview on the advances that were mainly led by the ITPA TC joint experiments and joint activities for the last 15 years (see JEX/JA table in appendix). This paper starts with the scientific strategy and scope of the ITPA TC Topical group and overall picture of the major progress, followed by the progress of each research field: particle transport, impurity transport, ion and electron thermal turbulent transport, momentum transport, impact of 3D magnetic fields on transport, confinement mode transitions, global confinement, and reduced transport modeling. Cross references with other Topical Groups are given in order to highlight overlapped topics, such as the 3D effect on the plasma transport in the edge and L-H transition physics. The increasing overlap between the topical groups is a reflection of the progress on integrating the known physics into comprehensive models that are better and better able to reproduce the plasma transport. In recent years, such integration has become increasingly prevalent when considering transport from the SOL, through the edge pedestal, and into the plasma core. In the near future, increased collaboration also with the magneto-hydrodynamic and energetic particles community will be important as we approach burning plasma conditions in next-step fusion devices. A summary of remaining challenges and next steps for each research field is given in the Summary section.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

A Novel Secondary Frequency Regulation with Optimal Priority Selection of AGC Contributions

Automatic generation control (AGC) is used to maintain acceptable frequencies during operation owing to fluctuations in load and variable resources. In conventional industry applications, the AGC signal is allocated to each generator according to the predispatched frequency regulation capacity or the order of economic efficiency. However, with the increasing integration of inverter-based resources (IBRs), the retirement of conventional synchronous generators (SGs) has posed new challenges to frequency control schemes because fewer of them are optional for AGC regulation. In this paper, we propose a novel model predictive control (MPC)-based frequency regulation model to reduce control cost and ensure stability, by considering different critical dynamic factors when optimally selecting the AGC units. The proposed control model – developed in a general form – comprehensively embeds characteristics such as generator ramping rates, reserve capacity, and operation cost. The model predictive control–based two-timescale AGC scheme enhances the capability of immunizing the power disturbance from types of resources by coordinating the control signals between faster IBRs and slower SGs. The case study’s proposed model is verified to be effective in synergistically enforcing different dynamic properties of AGC units into the frequency regulation scheme.

Jiang, Sufan [The University of North Carolina at ↗

DOE OSTI2023

Exceptional enhancement of mechanical properties in high-entropy alloys via thermodynamically guided local chemical ordering

Understanding the local chemical ordering propensity in random solid solutions, and tailoring its strength, can guide the design and discovery of complex, paradigm-shifting multicomponent alloys. First, we present a simple thermodynamic framework, based solely on binary enthalpies of mixing, to select optimal alloying elements to control the nature and extent of chemical ordering in high-entropy alloys (HEAs). Next, we couple high-resolution electron microscopy, atom probe tomography, hybrid Monte-Carlo, special quasirandom structures, and density functional theory calculations to demonstrate how controlled additions of Al and Ti and subsequent annealing drive chemical ordering in nearly random equiatomic face-centered cubic CoFeNi solid solution. We establish that short-range ordered domains, the precursors of long-range ordered precipitates, inform mechanical properties. Specifically, a progressively increasing local order boosts the tensile yield strengths of the parent CoFeNi alloy by a factor of four while also substantially improving ductility, which breaks the so-called strength–ductility paradox. Finally, we validate the generality of our approach by predicting and demonstrating that controlled additions of Al, which has large negative enthalpies of mixing with the constituent elements of another nearly random body-centered cubic refractory NbTaTi HEA, also introduces chemical ordering and enhances mechanical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Virtual Tokamak for Test and Development of Plasma Control Applied to NSTX-U

Safe and efficient operation of tokamak experiments depends on shot preparation prior to the experiment to maximize performance and avoid issues that are predictable consequences of known physics. The General Atomics TokSys toolbox is used to test and develop the plasma control system (PCS) on numerous tokamaks around the world. Tokamaks that use a version of the DIII-D PCS can connect it to a TokSys simulation and control a virtual version of the tokamak with the real PCS. Recent upgrades to the simulation include more detailed profile and transport modeling to support design and implementation of optimized scenarios. The simulation combines a module called “Profiles” that simulates the 1D profiles of density, pressure, and current and a module called “GSevolve'' that evolves the 2D Grad-Shafranov equilibrium. The “Profiles'' module primarily uses simplified models for fueling, heating, and current. The TRANSP code provides precomputed diffusion coefficients and heating/current drive profiles from radio-frequency and neutral beam sources for the scenarios being simulated. The fidelity of a simulation can be enhanced by analyzing it with TRANSP and making corrections to the precomputed values and iterating until convergence. Simulations of the National Spherical Torus Upgrade (NSTX-U) are presented. It is shown that the simulation reproduces the experimental profile evolution. Here, the simulation has also been upgraded to reproduce the experimental outcome at points of bifurcation. This is demonstrated with a simulation of vertical displacement in NSTX-U.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Data-Driven Model Predictive Control for Temperature Management of Heat Pipe Microreactor

To enable the self-regulating capability of heat pipe (HP) microreactors, an anticipatory control strategy through model predictive control (MPC) could proactively respond to potential disturbances and deviations in operating setpoints. However, a key factor prohibiting the widespread adoption of MPCs in nuclear applications is the effort and computational costs associated with learning and calibrating first-principles-based process models when the target system is complex and when there are gaps between modeled and target reactor systems. In this paper, we demonstrate data-driven MPC using three approaches for modeling the system dynamics, including a linear state-space model, feedforward neural network, and recurrent neural networks long short-term memory. We present the development and validation process of each model and compare the performance of data-driven MPCs in controlling the temperatures of selected HPs at the evaporator and condenser regions in a 37-HP-monolith system. Our results show that, qualitatively, all data-driven MPCs are producing similar control actions, while quantitatively, with artificial neural nets (especially feedforward neural nets), MPC can better follow drastic changes in setpoints with smallest errors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

DESI 2024 VII: cosmological constraints from the full-shape modeling of clustering measurements

We present cosmological results from the measurement of clustering of galaxy, quasar and Lyman-α forest tracers from the first year of observations with the Dark Energy Spectroscopic Instrument (DESI Data Release 1). We adopt the full-shape (FS) modeling of the power spectrum, including the effects of redshift-space distortions, in an analysis which has been thoroughly validated in a series of supporting papers as summarised in [1]. We combine the full-shape information with DESI's DR1 constraints from the baryon acoustic oscillations (BAO) of these tracers. In the flat ΛCDM cosmological model, DESI (FS+BAO), combined with a baryon density prior from Big Bang Nucleosynthesis and a weak prior on the scalar spectral index, determines matter density to Ω m = 0.2962 ± 0.0095, and the amplitude of mass fluctuations to σ 8 = 0.842 ± 0.034. The addition of the cosmic microwave background (CMB) data tightens these constraints to Ω m = 0.3056 ± 0.0049 and σ 8 = 0.8121 ± 0.0053, while further addition of the joint clustering and lensing analysis from the Dark Energy Survey Year-3 (DESY3) data further improves these measurements, and leads to a 0.4% determination of the Hubble constant, H 0 = (68.40 ± 0.27) km s -1 Mpc -1 . In models with a time-varying dark energy equation of state parametrised by w 0 and w a , combinations of DESI (FS+BAO) with CMB and type Ia supernovae continue to show the preference, previously found in the DESI DR1 BAO analysis, for w 0 > -1 and w a < 0 with similar levels of significance. DESI data, in combination with the CMB, improve the upper limits on the sum of the neutrino masses relative to the case when only the DR1 BAO was available, giving ∑m ν < 0.071 eV at 95% confidence. We finally constrain deviations from general relativity represented by two modified gravity parameters. DESI (FS+BAO) data alone measure the parameter that controls the clustering of massive particles, μ 0 = 0.11 +0.45 -0.54 , in agreement with the zero value predicted by general relativity. The combination of DESI with the CMB and the clustering and lensing analysis from DESY3 constrains both modified-gravity parameters, giving μ 0 = 0.04 ± 0.22 and Σ 0 = 0.044 ± 0.047, again in agreement with general relativity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

HHL algorithm with mapping function and enhanced sampling for model predictive control in microgrids

Here, this paper presents a refined quantum Harrow Hassidim Lloyd (HHL) algorithm for microgrid control. The first novelty of the developed method is that a mapping shift function enables the original HHL algorithm to handle general linear equations with non-singular and indefinite matrix. Second, a method of Matrix Extension for Amplifying Sampling Probabilities of Intended Solution (ME-ASPI) is proposed to design the reformulated linear algebraic equations, allowing for improved sampling efficiency of the quantum tomography in the refined HHL algorithm. Then, we applied the method to solve the model predictive control (MPC) problem in nonlinear dynamical microgrids. Specifically, with the ME-ASPI method, the refined HHL algorithm can effectively obtain the intended partial optimal control inputs for MPC. The optimization of quadratic programming problem in each time step of MPC is transformed into a linear system problem, which is addressed by the proposed quantum solver through using only partial information, with the time complexity improved from $\mathscr{O}(\mathscr{N}^{2.37286})$ classically to $\mathscr{O}(\mathscr{N}^{2} log \mathscr{N}$ x $p$ log $p)$ in quantum. Numerical examples have validated the effectiveness of the refined HHL algorithm with the proposed mapping function and the ME-ASPI method. By leveraging quantum properties, the proposed method provides a hybrid quantum–classical framework for microgrid control. This generic method can also potentially tackle many other challenges in analyzing and controlling general complex engineered systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

DOE OSTI2024

Autonomous control for Heat-Pipe microreactor using Data-Driven model predictive control

To enable a self-regulating capability for heat pipe (HP) microreactors, an anticipatory control strategy achieved via model predictive control (MPC) could proactively respond to potential disturbances and deviations in operating setpoints. This paper demonstrates data-driven methods for predicting the distribution and transient of temperatures and heat fluxes at selected components and regions in a 37-HP system, based on which the optimal control actions in response to changes in user-defined setpoints can be found. We present the development and validation of linear state-space model, feedfoward, and recurrent neural networks. Here, we compare the performance of MPCs with different modeling approaches in terms of following setpoints for temperatures and averaged output heat fluxes. The accuracies of the three data-driven models are similar, but the control actions initiated by neural-network-based MPC can better adapt to drastic changes in setpoints yet generate the smallest errors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Understanding plasma turbulence through exact coherent structures

Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a generalized framework to analyze plasma turbulence that utilizes periodic orbit theory. In periodic orbit theory, doubly periodic solutions (coherent structures) of the governing equation(s) serve as building blocks of the considered turbulent dynamics. To illustrate the concept and method, the particularly simple Kuramoto–Sivashinsky (referred to here as LMRT for the original authors: LaQuey, Mahajan, Rutherford, and Tang) trapped-ion mode toy model is used. By applying numerical optimization techniques to the LMRT equation, we extract coherent spacetime patterns that represent the library of allowable fundamental structures of the equation. These structures provide a framework to systematically describe turbulence as a composition of recurrent solutions, revealing an underlying order within chaotic plasma motion. Although illustrated here using the simplified LMRT model for clarity, this framework provides a general strategy that can be extended to more complex and realistic models of plasma turbulence, including gyrokinetic systems. This offers a new method for predicting and potentially controlling transport processes in fusion plasmas by providing a bridge between nonlinear dynamical systems theory and plasma physics in the form of a generalized framework with which to analyze and understand spatially extended nonlinear partial differential equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Accurate Machine Learning for Predicting the Viscosities of Deep Eutectic Solvents

Deep eutectic solvents (DESs) are emerging as environmentally friendly designer solvents for mass transport and heat transfer processes in industrial applications; however, the lack of accurate tools to predict and thus control their viscosities under both a range of environmental factors and formulations hinders their general application. While DESs may serve as designer solvents, with nearly unlimited combinations, this unfortunately makes it experimentally infeasible to comprehensively measure the viscosities of all DESs of potential industrial interest. To assist in the design of DESs, we have developed several new machine learning (ML) models that accurately and rapidly predict the viscosities of a diverse group of DESs at different temperatures and molar ratios using, to date, one of the most comprehensive data sets containing the properties of over 670 DESs over a wide range of temperatures (278.15–385.25 K). Three ML models, including support vector regression (SVR), feed forward neural networks (FFNNs), and categorical boosting (CatBoost), were developed to predict DES viscosity as a function of temperature and molar ratio and contrasted with multilinear and two-factor polynomial regression baselines. Further, quantum chemistry-based, COSMO-RS-derived sigma profile (σ-profile) features were used as inputs for the ML models. The CatBoost model is excellent at externally predicting DES viscosity, as indicated by high R 2 (0.99) and low root-mean-square-error (RMSE) and average absolute relative deviations (AARD) (5.22%) values for the testing data sets, and 98% of the data points lie within the 15% of AARD deviations. Furthermore, SHapley additive explanation (SHAP) analysis was employed to interpret the ML results and rationalize the viscosity predictions. The result is an ML approach that accurately predicts viscosity and will aid in accelerating the design of appropriate DESs for industrial applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Data-Driven Model Predictive Control for Temperature Management of Heat Pipe Microreactor

A data-driven model predictive control (MPC) was developed to enable the self-regulating capability of heat pipe (HP) nuclear microreactors. The MPC can proactively respond to potential disturbances of HP microreactors using three approaches for system identifications: linear state-space model, feedforward neural network, and recurrent neural networks with long short-term memory units. We present numerical results of data-driven MPCs to control the temperatures of selected HPs in a 37-HP test article. Our results show qualitatively that all data-driven MPCs produced similar control actions, while quantitatively, with artificial neural nets (especially feedforward neural nets), MPC can better follow drastic changes in setpoints with small errors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Adaptive Data-Driven Model Predictive Control for Heat Pipe Microreactors

To establish a technical basis for self-regulating microreactors, a model predictive control (MPC) system is investigated to proactively respond to anomalies and disturbances in anticipation of potential deviations from operating setpoints. Due to the difficulty of developing a physics-based surrogate model that can accurately match plant data in various operating conditions, machine learning algorithms are used in MPC, which allow for learning from both simulation and operation data, thus efficiently describing the targeted transient with arbitrary accuracy. However, one of the biggest concerns in applying ML algorithms like artificial neural networks (ANNs) is that the predictive capabilities of ANN are limited by training data. If there are gaps between the training and target domain, the accuracy of an ANN can degrade significantly when it is used to predict unseen data. To improve the predictive capability of ANN and enable a confident use of data-driven MPCs outside the training data, this study proposes an adaptive data-driven MPC framework. The system will monitor the discrepancy between plant responses and surrogate predictions, fine-tune the ANN-based surrogate when a large discrepancy is detected, and continue MPC operation with updated surrogates. The framework is demonstrated on a point kinetic model for microreactors. The hyperparameters of the update strategy, including layers to update, error thresholds, learning rate discount, and number of data points used for fine-tuning, are optimized so the simulated microreactor is able to follow changes in setpoint with the smallest of deviations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Adaptable Data Driven Model Predictive Control for Heat Pipe Microreactors

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Fuel performance evaluation of two high burnup PWR core designs during normal operation, control rod withdrawal, and control rod ejection scenarios

There is interest among utilities to extend the current, 18-month operating cycle to 24 months. Economically, this extension would require greater than 5 % enrichment and peak rod average discharge burnup levels above 62 GWd/MTU. A notable challenge of increasing enrichment is the resulting additional excess reactivity encountered during the early stages of fuel life. To accommodate, burnable absorbers beyond soluble boron are introduced into the fuel system. In high burnup fuels, the possibilities of cladding lift-off and fuel melting increase due, in part, to increased rod internal pressures and limited fuel thermal conductivity, respectively. This work collaboratively employs PARCS, RELAP5-3D, and BISON to compare the fuel performance of two high burnup fuel candidates with higher than 5 % enrichment. Here, the fuel performance parameters were compared to current NRC guidance. The results demonstrate an annular fuel design with homogenously blended gadolinium as a burnable absorber operates with greater safety margins during normal operation, allowing for additional operational flexibility. During normal operation, the core design utilizing Integral Fuel Burnable Absorber pins contained fuel pins which reached plenum pressures above 15.5 MPa by the end of the first fuel cycle and fuel pins experienced cladding hoop strains above 1 %. In the Gd core design, only two observed pins experienced plenum pressures above 15.5 MPa and no pins exceeded 1 % cladding hoop strain. During the control rod withdrawal scenario, plenum pressures for pins in both designs marginally exceeded system pressure, however neither experienced excessive hoop strain. The Gd core design experienced a maximum fuel temperature of 2418 K, which is significantly higher than the Integral Fuel Burnable Absorber design at 2157 K, but still within regulatory guidance. We predicted that the fuel in both could return to service after the CRW event. We also predicted that cladding would not fail during the Control Rod Ejection in either core design. Generally, the Integral Fuel Burnable Absorber core design performed with greater safety margin with regards to temperature during normal operation and the transient events. However, the Gd core design performed with greater safety margin regarding plenum pressure and hoop strain limits during normal operation and both transient events.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗