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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy *

Abstract Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane n e , s e p O M P and the electron temperature at the outer divertor T e , s e p d i v . Note that T e , s e p d i v is not necessarily the peak value of T e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in T e , s e p d i v , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in n e , s e p O M P and 5%–10% in T e , s e p d i v for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in n e , s e p O M P using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Development and assessment of a model predictive controller enabling anticipatory control strategies for a heat-pipe system

To support the reliable and resilient operation of modular reactors and microreactors, anticipatory control strategies have been proposed for achieving faster-than-real-time predictions and decision-making capabilities in anticipation of potential anomalies, including setpoint changes and cyber incidents. Here this work presents how anticipatory control strategies can be implemented via model predictive control (MPC) of a single heat pipe’s temperature. Considering the uncertainty in developing and applying MPC, this work evaluates MPC performance given three different model forms: a linear response surface model, an artificial neural network (ANN), and an autoregressive model with exogenous input (ARX). This work also evaluates the impacts of different input biases and variance on MPC performance in order to account for potential sensor reading variations due to cyber incidents. We observe that nonparametric models such as the ANN and ARX result in more fluctuated control actions compared to the MPC applied to the linear response surface model. However, when the cyber incidents are of a large magnitude, the linear response surface model produces smaller feasible regions than the nonparametric models under identical constraints.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Stochastic Model Predictive Control With Gaussian Wind Direction Preview for Wake Steering

This article addresses the problem of wake steering control for wind farms that explicitly consider the tradeoff between farm-level power generation and yaw duty cycle under variable and uncertain wind conditions. A novel stochastic model predictive control (MPC) algorithm is presented, which utilizes a stochastic model of the freestream wind field components in a receding horizon framework to compute optimal yaw set points that maximize the expected value of the farm power while constraining the yaw actuation. Different configurations of the algorithm are evaluated using a steady-state wind farm simulator. The proposed stochastic MPC algorithm can plan control actions over a future prediction horizon based on probabilistic estimates of the incoming wind magnitude and direction.

17 WIND ENERGY↗

DOE OSTI2022

Model Predictive Control of Discrete-Continuous Energy Systems via Generalized Disjunctive Programming

Generalized Disjunctive Programming (GDP) provides an alternative framework to model optimization problems with both discrete and continuous variables. The key idea behind GDP involves the use of logical disjunctions to represent discrete decisions in the continuous space, and logical propositions to denote algebraic constraints in the discrete space. Compared to traditional mixed-integer programming (MIP), the inherent logic structure in GDP yields tighter relaxations that are exploited by global branch and bound algorithms to improve solution quality. In this paper, we present a general GDP model for optimal control of hybrid systems that exhibit both discrete and continuous dynamics. Specifically, we use GDP to formulate a model predictive control (MPC) model for piecewise-affine systems with implicit switching logic. As an example, the GDP-based MPC approach is used as a supervisory control to improve energy efficiency in residential buildings with binary on/off, relay-based thermostats. A simulation study is used to demonstrate the validity of the proposed approach, and the improved solution quality compared to existing MIPbased control approaches.

Bhattacharya, Arnab↗

DOE OSTI2022

MPC4CLR (Model-Predictive-Control-for-Critical-Load-Restoration-in-Power-Distribution-Systems) [SWR-22-24]

Model predictive control (MPC) is a system or process control technique for making decisions under uncertainty via rolling look-ahead optimizations at each control step where only the current step decisions are applied, and the rest are discarded. In this work, we developed an MPC for a critical load restoration (CLR) in power distribution systems to recover system service (electricity delivery) following an extreme event-triggered substation outage. The method considers the problem of controlling distributed energy resources (DERs) of the distribution system with the objective of achieving maximum load pick up while satisfying distribution network flow and voltage constraints. A linearized optimal power flow (OPF) model is employed to represent the physics of the network. The problem formulation is augmented with a ramping (up) reserve product for the DERs to ensure improved and upward monotonic load restoration as time evolves. Simulation analysis and performance tests are performed using a modified IEEE 13-bus test feeder integrated with wind, solar, microturbine, and energy storage battery. The software is developed using various software packages in Julia and Python. The MPC model is implemented using the JuMP optimization language in Julia while the data analytics including renewable generation and load demand forecasts, running the MPC simulation and visualizations is performed in Python.

Eseye, Abinet Tesfaye↗

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 OSTI2022

A machine learning approach for clinker quality prediction and nonlinear model predictive control design for a rotary cement kiln

Abstract Cement manufacturing is energy‐intensive (5Gj/t) and comprises a significant portion of the energy footprint of concrete systems. Incorporating modern monitoring, simulation and control systems will allow lower energy use, lower environmental impact, and lower costs of this widely used construction material. One of the goals of the CESMII roadmap project on the Smart Manufacturing of Cement included developing an analytical process model for clinker quality that includes the chemistry of the kiln feed and accounts for critical process variables. This predictive model will be used in nonlinear model predictive control system designed to significantly reduce process energy use while maintaining or improving product quality. In the cement manufacturing plant used in this study, the kiln feed (meal) is tested every 12 h and used to estimate the mineral composition of the cement kiln output (clinker) using the stoichiometry‐based Bogue's model and the expertise of the plant operators. During kiln operation, kiln output (clinker) is sampled and tested every 2 h to measure its chemical and mineral composition. The predicted and measured values of the clinker composition are used by the plant operators to adjust the kiln input stream and the production process characteristics to maintain stable operation and uniform product quality. However, the time delay between prediction and testing, along with inaccuracies inherent in the Bogue's model have made any process changes designed to minimize energy use problematic, especially in‐light of potential clinker quality issues that process changes often pose. A new analytical model that integrates quality information and process operation information has been developed from data collected from 2 years of production from an operating cement facility. To make the model fuel‐type‐independent, consumed heat energy was computed in the model instead of fuel type and amount. A Feedforward Network was trained and tailored from collected data. Many data‐based simulations were conducted to quantitatively evaluate the proposed model and the 5‐fold cross‐validation procedure was used to test the models. The resulting predictive model was shown to have a low root mean square error (MSE) with respect to the estimated clinker mineral composition compared to that using the industry standard “Bogue’ model”. The end goal of this work was to develop a single machine learning tool that allows the use of quality control data and process control variables to improve energy efficiency of the process in a continuous fashion. The proposed nonlinear model predictive control system (NMPC) can generate predicted kiln production characteristics based on manipulated variables in manner that accurately follows the target product quality values. Simulation results also show that the proposed model produced accurate predictions of kiln outputs that fell within the required constraints, while manipulating control variables within typical operational ranges.

Ali, Asem M.↗

DOE OSTI2023

Limits on the Range and Rate of Change in Power Take-Off Load in Ocean Wave Energy Conversion: A Study Using Model Predictive Control

Previous work comparing power take-off (PTO) architectures for ocean wave-powered reverse osmosis suggests that variable displacement in the wave energy converter (WEC)-driven pump does not offer a significant performance advantage. A limitation of that study is that the WEC was subject to a constant load within a given sea state (“Coulomb damping”) and did not account for controlled, moment-to-moment variation of the PTO load enabled by a variable displacement pump. This study explores the potential performance advantage of a variable PTO load over Coulomb damping. Model predictive control is used to provide optimal load control with constraints on the PTO load. The constraints include minimum and maximum loads and a limit on the rate of load adjustment. Parameter studies on these constraints enable conclusions about PTO design requirements in addition to providing an estimated performance advantage over Coulomb damping. Numerical simulation of the Oyster 1 WEC is carried out with performance weighted by historical sea state data from Humboldt Bay, CA. The results show a performance advantage of up to 20% higher yearly-average power absorption over Coulomb damping. Additionally, the parameter studies suggest that the PTO load should be adjustable down to at least 25% of the maximum load and should be adjustable between the minimum and maximum loads within a few seconds.

16 TIDAL AND WAVE POWER↗

DOE OSTI2023

Bayesian filtering for model predictive control of stochastic gene expression in single cells

This study describes a method for controlling the production of protein in individual cells using stochastic models of gene expression. By combining modern microscopy platforms with optogenetic gene expression, experimentalists are able to accurately apply light to individual cells, which can induce protein production. Here we use a finite state projection based stochastic model of gene expression, along with Bayesian state estimation to control protein copy numbers within individual cells. We compare this method to previous methods that use population based approaches. We also demonstrate the ability of this control strategy to ameliorate discrepancies between the predictions of a deterministic model and stochastic switching system.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Comparative Analysis of Model Predictive Control and MPC-Informed Rule-Based Control for Thermal Storage Operation in Ultra-Low Temperature 4th Generation District Heating Networks

The integration of thermal storage and heat pumps in district heating networks (DHNs) can significantly enhance operational flexibility and energy efficiency; however, the practical deployment of advanced control strategies is often hindered by forecasting requirements and computational complexity. This study presents a comparative analysis of thermal storage control strategies in an ultra-low-temperature fourth-generation DHN, focusing on the development of a simplified rule-based control (RBC) explicitly informed by Model Predictive Control (MPC) behavior. The proposed methodology systematically analyzes the charging and discharging decisions of an MPC-controlled system under ideal forecasting conditions and extracts recurrent control patterns as a function of key system variables, including outdoor temperature, thermal demand, and electricity price. These patterns are translated into a set of structured time- and condition-based rules, resulting in an MPC-informed RBC that embeds predictive insights while preserving implementation simplicity and operational transparency. The approach is validated on a realistic mixed-use urban district in Denver, Colorado, USA, equipped with a centralized air-source heat pump, distributed water-to-water heat pumps, and a central thermal storage unit. Results show that the tuned RBC attains approximately 96% of ideal MPC economic performance (-27% of costs), preserves values of technical and environmental indicators (reduction only of 2-3%), and substantially reduces complexity. Sensitivity analyses further demonstrate the robustness of the RBC under varying operational conditions (i.e., ambient temperature, electricity price). Overall, the study demonstrates that MPC-informed rule-based control represents an effective trade-off between control performance and real-world applicability, enabling the integration of additional system components while maintaining simplicity, robustness, and ease of implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Koopman Model Predictive Control for Eco-Driving of Automated Vehicles

In this paper, we develop a data-driven process for building a model predictive control (MPC) for eco-driving of automated vehicles. The process involves performing system identification in which the non-linear vehicle dynamics model is approximated by the Koopman operator, a linear predictor of higher state-dimension, in a data-driven framework. This approach allows us to formulate the eco-driving problem in a constrained quadratic program that leads to a computationally fast MPC. The MPC is then implemented as a closed-loop control of an electric vehicle in numerical simulations for demonstration.

autonomous vehicle↗

DOE OSTI2022

Superconvergence of Online Optimization for Model Predictive Control

We develop a one-Newton-step-per-horizon, online, lag-L, model predictive control (MPC) algorithm for solving discrete-time, equality-constrained, nonlinear dynamic programs. Based on recent sensitivity analysis results for the target problems class, we prove that the approach exhibits a behavior that we call superconvergence; that is, the tracking error with respect to the full horizon solution is not only stable for successive horizon shifts, but also decreases with increasing shift order to a minimum value that decays exponentially in the length of the receding horizon. The key analytical step is the decomposition of the one-step error recursion of our algorithm into algorithmic error and perturbation error. We show that the perturbation error decays exponentially with the lag between two consecutive receding horizons, while the algorithmic error, determined by Newton’s method, achieves quadratic convergence instead. Overall this approach induces our local exponential convergence result in terms of the receding horizon length for suitable values of L. In conclusion, numerical experiments validate our theoretical findings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A tutorial review of machine learning-based model predictive control methods

Abstract This tutorial review provides a comprehensive overview of machine learning (ML)-based model predictive control (MPC) methods, covering both theoretical and practical aspects. It provides a theoretical analysis of closed-loop stability based on the generalization error of ML models and addresses practical challenges such as data scarcity, data quality, the curse of dimensionality, model uncertainty, computational efficiency, and safety from both modeling and control perspectives. The application of these methods is demonstrated using a nonlinear chemical process example, with open-source code available on GitHub. The paper concludes with a discussion on future research directions in ML-based MPC.

Wu, Zhe [Department of Chemical and Biomolecular E↗

DOE OSTI2022

Model predictive control for demand flexibility: Real-world operation of a commercial building with photovoltaic and battery systems

Hundreds of studies have investigated Model Predictive Control (MPC) for the optimal operation of building energy systems in the past two decades. However, MPC field tests are still uncommon, especially for small- and medium-sized commercial buildings and for buildings integrated with onsite renewables. This paper describes the implementation and the long-term performance evaluation of an MPC controller in a small commercial building equipped with behind-the-meter photovoltaics and electrochemical batteries. MPC controls space conditioning, commercial refrigeration, and the battery system. We tested two types of demand flexibility applications in the field: electricity bill minimization under time-of-use tariffs and responses to grid flexibility events. Results show that the proposed controller achieves 12% of annual electricity cost savings and 34% peak demand reduction against the baseline, while respecting thermal comfort and food safety. The field tests also demonstrate the ability of the MPC controller to provide a multitude of grid services including real-time pricing, demand limiting, load shedding, load shifting, and load tracking, using the same optimization framework.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

NASA NTRS2019

Partition-based Feasible Integer Solution Pre-computation for Hybrid Model Predictive Control

For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a static map from the current parameter to a suboptimal integer solution such that the remaining convex program is feasible. Convergence is proved with a new insight that the overlap among the feasible parameter sets of each integer solution governs the partition complexity. The partition is stored as a tree which makes querying the feasible solution efﬁcient. The algorithm can be used to warm start a mixed integer solver with a real-time guarantee or to provide a reference integer solution in several suboptimal MPC schemes. The algorithm is tested on randomly generated systems with up to six states, demonstrating the effectiveness of the approach.

Bayard, David S.↗

DOE OSTI2021

A Phase-Disposition PWM Enabled Model Predictive Control for a Nine-Level Inner-Interleaved Hybrid Multilevel Converter

This article brings forward a phase-disposition pulse width modulation enabled model predictive control (PDPWM-MPC) for a nine-level inner-interleaved hybrid multilevel converter (9L-IHMC). Firstly, three layers of virtual space vector diagrams (VSVD) are established based on the sign patterns of the original and virtual reference vectors in the abcframe, respectively, to achieve the phase-disposition pulse width modulation (PD-PWM) in a non-independent three-phase way. Then, three adjacent virtual vectors in the third-layer VSVD, together with their optimized duty cycles, are applied to guarantee the optimal current tracking. Finally, through the use of the duty cycle alternation approach, dc-link and floating capacitors voltages are balanced and circulating currents are mitigated as well. The proposed PDPWM-MPC can not only enable the decoupling of the low-and high-frequency stages in the 9L-IHMC, but also reduce both output current ripples and computational burden. In addition, it can achieve a constant equivalent switching frequency and address the disproportion of power losses associated with the PD-PWM. Here, both simulations and experiments on a silicon carbide device-based prototype substantiate the effectiveness of the proposed control strategy.

42 ENGINEERING↗

DOE OSTI2022

Extremum-Seeking-Based Ultra-local Model Predictive Control and Its Application to Electric Motor Speed Regulation

Electric vehicle (EV) market is rapidly expanding. As a critical component of EV, an electric motor needs to accurately follow a reference speed signal while respecting the electrical current constraint for safety. Those requirements are usually formulated as a model predictive control (MPC) problem. However, the performance of traditional model-based MPC depends on the accuracy of the system model, which may not always be guaranteed in reality. Therefore, we utilize a data-driven, model-free predictive control strategy, called ultra-local MPC (ULMPC), to control the speed of an electric motor. To further enhance the control performance of ULMPC, we employ the extremum-seeking control (ESC) to tune the control gain of the ULMPC online. Simulation and hardware experiments demonstrate the enhancement of the extremum-seeking-based ULMPC over a constant-gain ULMPC.

Zhou, Yujing↗