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DOE OSTI2022

Field demonstration and implementation analysis of model predictive control in an office HVAC system

Model Predictive Control (MPC) is a promising technique to address growing needs for heating, ventilation, and air-conditioning (HVAC) systems to operate more efficiently and with greater flexibility. However, due to a number of factors, including the required implementation expertise, lack of high quality data, and a risk-adverse industry, MPC has yet to gain widespread adoption. While many previous studies have shown the advantages of MPC, few analyzed the implementation effort and associated practical challenges. In addition, previous work has developed an open-source, Modelica-based tool-chain that automatically generates optimal control, parameter estimation, and state estimation problems aimed at facilitating MPC implementation. Therefore, this study demonstrates usage of this tool-chain to implement MPC in a real office building, discusses practical challenges of implementing MPC, and estimates the implementation effort associated with various tasks in order to inform the development of future workflows and serve as an initial benchmark for their impact on reducing implementation effort. This study finds that the implemented MPC saves approximately 40% of HVAC energy over the existing control during a two-month trial period and that tasks related to data collection and controller deployment activities can each require as much effort as model generation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Model predictive control for robust quantum state preparation

A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces model predictive control (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Simulation Evaluation of a Large-Scale Implementation of Virtual-Phase Link-Based Model Predictive Control

Traffic congestion is a serious problem in the US, and traffic signal control is one of the effective solutions to congestion. Previous research on model predictive control (MPC)-based traffic signal control showed substantial benefits over conventional methods. This study focused on implementing MPC over a large-scale network with complex intersections and the impact of cycle length, network size, and imperfect state estimation on performances. This study implemented a virtual phase link (VPL)-based model predictive control method which used the number of vehicles in each VPL as input state variables and was suitable for National Electrical Manufacturing Association (NEMA) ring-barrier control. To test the impact of network size, the performance of distributed MPC (36 intersections in the network are divided into five subnetworks) was compared with that of MPC over the full network for a set of cycle lengths. To test the impact of imperfect state estimation, we synthetically infused estimation error and developed two scenarios, MPC-error and MPC-error narrow, which had higher and lower estimation errors, respectively. The performance of these MPC methods was compared with that of the existing time-of-day (TOD) method and an offline method that used Webster's method for split and MULTIBAND for cycle length and offset optimization. Trajectory and linkwise signal performance measures were collected from the simulation to evaluate performance. The distributed MPC method with perfect state estimation had the lowest delay and highest energy efficiency of all the methods. The performance of MPC decreased as the prediction inaccuracy increased. MPC-error had 7% and 11% more delay than MPC-error narrow in the morning and evening peaks, respectively. Overall, simulation results suggest that even with imperfect state estimation, MPC methods will outperform offline methods significantly.

large-scale simulation↗

DOE OSTI2022

Model Predictive Control for a Grid-interactive Efficient Thermal Storage-integrated Heat Pump System

Building heating and cooling systems can be used to overcome the mismatch between the intermittent supply of renewable power and the fluctuating demand for electricity. A novel underground thermal energy storage integrated with a dual-source heat pump has been proposed to mitigate the mismatch while meeting the thermal demand of buildings efficiently. Conventional thermostat control with heuristic rules cannot provide intelligent decisions to maximize the thermal efficiency and flexibility of the proposed system. Advanced control strategies like model predictive control (MPC) have provided a new paradigm for grid-interactive efficient building operation with the advancement of computation and sensing. This study developed an MPC for the proposed system to provide grid service for Demand Side Management and minimize the operating cost of building owners. A control-oriented dynamic model of the proposed system has been developed. Given an objective function and proper constraints, an optimization problem is formulated to determine the optimal control strategy of the system. Dynamic Programming is adopted to solve the optimization problem. A rule-based control (RBC) is also developed to achieve similar goals. Short-term simulations are conducted to compare the system performance resulting from the two controls. The simulation results indicate that the MPC performs more intelligently than the RBC in charging thermal energy storage and selecting heat pump sources by taking advantage of the predicted cooling demands of the building and the performance of the integrated system. As a result, the MPC could save energy and reduce operating costs compared with the RBC. A case study shows that, for a 3-day operation, the MPC saves 36.9% energy and reduces 38.5% operating cost compared with the RBC.

Shi, Liang↗

DOE OSTI2023

Reducing Urban Traffic Congestion Using Deep Learning and Model Predictive Control

This article proposes a deep learning (DL)-based control algorithm—DL velocity-based model predictive control (VMPC)—for reducing traffic congestion with slowly time-varying traffic signal controls. This control algorithm consists of system identification using DL and traffic signal control using VMPC. For the training process of DL, we established a modeling error entropy loss as the criteria inspired by the theory of stochastic distribution control (SDC) originated by the fourth author. Herein, simulation results show that the proposed algorithm can reduce traffic congestion with a slowly varying traffic signal control input. Results of an ablation study demonstrate that this algorithm compares favorably to other model-based controllers in terms of prediction error, signal varying speed, and control effectiveness.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Experimental test of model predictive control in a variable air volume system

Model predictive control (MPC) has been widely studied as a promising approach for improving energy efficiency and operational flexibility in buildings, yet its real-world performance for commercial variable air volume (VAV) systems remains insufficiently characterized. In particular, the impacts of model mismatch on control robustness, real-time computational burden, and device-level operation are rarely evaluated using long-term field data. Here, this study presents a comprehensive experimental evaluation of MPC applied to a full-scale VAV system in Oak Ridge National Laboratory’s Flexible Research Platform-2 building with constant cooling/heating temperature setpoints and no occupancy. The study offers three key advantages over existing work: (1) it uses a representative building in a full-scale experimental test, capturing realistic system dynamics and complexity; (2) it evaluates a relatively sophisticated MPC formulation using two different optimization solvers (Gurobi and PSO), fully accounting for computational complexity and methodological diversity; and (3) it systematically assesses potential negative impacts on various building devices, benchmark against a well-established baseline, ASHRAE Guideline 36 (G36). To isolate zone- and air-handling-unit–level supervisory control effects, the supply fan was operated with a fixed static pressure setpoint under all strategies, and the trim-and-response static pressure reset in G36 was not enabled. Results show that MPC maintained thermal comfort while improving energy efficiency. Abrupt solar radiation variations degraded performance. Computation times ranged from ∼1 s (Gurobi) to ∼ 70 s (PSO). Compared with G36, MPC achieves 33% energy savings and reduces median reheat coil output by approximately a factor of 5–10 for a representative cooling day under matched weather conditions. However, it increases the maximum discomfort deviation from 0.5 to 1°C and results in a 32% increase in staging frequency. In addition, PSO-based MPC introduced damper oscillations, also affecting actuator longevity.

ASHRAE guideline 36↗

DOE OSTI2024

Practical challenges of model predictive control (MPC) for grid interactive small and medium commercial buildings

To the urgent call for mitigating climate change, substantial initiatives have been undertaken to deploy grid-interactive heating, ventilation, and air-conditioning (HVAC) controls, such as model predictive control (MPC) for buildings. These efforts typically aim to curtail peak energy demand, shift load and enhance overall energy efficiency. With the recent development of low-cost MPC technologies that don’t require extensive instrumentation or manual modeling, small and medium commercial buildings (SMCBs), which rarely utilize advanced HVAC control systems, have become candidates for grid-interactive efficient buildings (GEBs). However, despite the potential benefits and maturity of the technology itself, several practical challenges remain in real-world implementation. In this paper, we share the practical challenges that we have encountered in implementing and testing three types of MPC solutions (ON/OFF unit, dualfuel, and VRF systems) on multiple SMCB sites. We describe the MPC deployment process and discuss the lessons learned. The site selection, eligibility, and retrofit availability (e.g., utility price structure, thermostat communications, etc.) are the main discussion points at the beginning of the project. Also, the modeling automation and the best practices for interacting with endusers and handling erroneous situations are presented for successful operations.

woo Ham, Sang↗

DOE OSTI2025

Closing the loop: model-predictive control for a closed-circuit reverse osmosis system

This article presents a model-predictive controller (MPC) for the maximization of the energy efficiency of a closed-circuit desalination reverse osmosis (CCRO) system. CCRO is a process for producing drinking water that is based on a cyclic operation with the following two phases: (a) filtration and (b) drain. In this article, we test model predictive control for optimal control of this process. The most important features of our approach are as follows: (a) the selection of a model structure that enables reliable forecasts of the filtration phase (up to 3 h), (b) an on-line model calibration strategy that ensures model forecast reliability, and (c) the satisfaction of equipment safety and operational constraints on the selected setpoints. We challenge this through deliberate introduction of changes in the unmeasured feed concentration and the applied constraints. Our results indicate that frequent model parameter updates are critical to maintain model reliability for MPC purposes. In addition, we illustrate that parameter identifiability is not guaranteed and that deliberate variation in flow rates is necessary even though the process never operates in steady state. Finally, MPC can compute flow rate setpoints that maximize the energy efficiency of the CCRO process while satisfying the applicable equipment and safety constraints.

closed-circuit reverse osmosis↗

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 OSTI2022

Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach

In this paper, we develop a novel form of differentiable predictive control (DPC) with safety and robustness guarantees. DPC is a form of approximate model predictive control (MPC), wherein the control policy is a neural network that learns a receding horizon, optimal control law. The proposed approach exploits a new form of sampled-data barrier function to enforce safety, while only interrupting the neural network-based controller near the boundary of the safe set. The effectiveness of the proposed approach is demonstrated in simulation.

Shaw Cortez, Wenceslao E.↗

DOE OSTI2024

Transformer Neural Networks with Spatiotemporal Attention for Predictive Control and Optimization of Industrial Processes

In the context of real-time optimization and model predictive control of industrial systems, machine learning, and neural networks represent cutting-edge tools that hold promise for enhancing dynamic modeling. This work presents a novel transformer neural network architecture for real-time optimization and model predictive control. This network design includes a modified attention mechanism inspired by positional embedding attention from vision transformers and task-specific modifications to the input-output structure of the transformer’s decoder stack. Experiments were conducted using data from a 450 MW coal-fired power plant to evaluate this approach's effectiveness. The transformer neural network was compared with conventional recurrent models, including GRU and LSTM. The transformer exhibited a 6% increase in the R-squared (R2) value of predictions and an 83% reduction in mean squared error (MSE). Computation time was also reduced by 84% compared to conventional recurrent models.

Gallup, Ethan R.↗

DOE OSTI2025

Commercial building HVAC demand flexibility with model predictive control: Field demonstration and literature insights

Model Predictive Control (MPC) for building Heating Ventilation and Air Conditioning (HVAC) systems is beginning to gain traction in the market, with a few controls companies incorporating it into their product offerings. However, it remains difficult to assess whether the energy cost savings are enough to justify the cost of MPC implementation for a particular building, given the limited number of reported demonstrations. For small commercial and residential buildings with relatively uniform systems, standardized approaches can help lower implementation costs. In contrast, for large buildings or district systems, the potential magnitude of cost savings could justify more customized solutions. Estimating the cost-effectiveness of MPC becomes more challenging for medium and large commercial buildings, where a one-size-fits-all solution may not be suitable, and the potential energy cost savings may be insufficient to justify a customized solution. To make MPC technology more appealing, incorporating additional value streams beyond energy efficiency alone can significantly increase its attractiveness. One such revenue stream is demand flexibility, in response to dynamic electricity prices, where MPC can leverage the thermal mass of the building to shift the load and support the grid. Building on an extensive literature review of MPC field studies focused on cost savings and demand flexibility, this paper presents the results of implementing MPC control in a large office building HVAC system in Berkeley, CA. Four different dynamic electricity price profiles were integrated into the MPC objective function to shift building demand while maintaining comfort, and field testing was performed with each price profile across four seasons. The results show potential for 40–65 % demand decrease percentage and up to 61 % annual cost savings compared to the existing rule-based control strategy, under the tested dynamic price scenarios. This paper also presents a sensitivity analysis on the cost savings with respect to the price profile variability, discusses the implementation effort for the price-responsive MPC, and compares the cost savings found in this study to those found in literature on the basis of dynamic price variability, or so-called Electricity Price Relative Standard Deviation.

Zanetti, Ettore↗

DOE OSTI2026

Near-Optimal Performance of Stochastic Model Predictive Control

Here, this article presents a regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finite-dimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. Although this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: under stabilizability and detectability conditions, the regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.

93E20, 93B45↗

DOE OSTI2025

A Model Predictive Control to Improve Grid Resilience

The following article details a model predictive control (MPC) to improve grid resilience when faced with variable generation resources. This topic is of significant interest to utility power systems where distributed intermittent energy sources will increase significantly and be relied on for electric grid ancillary services. Previous work on MPCs has focused on narrowly targeted control applications such as improving electric vehicle (EV) charging infrastructure or reducing the cost of integrating Energy Storage Systems (ESSs) into the grid. In contrast, this article develops a comprehensive treatment of the construction of an MPC tailored to electric grids and then applies it integration of intermittent energy resources. To accomplish this, the following article includes a description of a reduced order model (ROM) of an electric power grid based on a circuit model, an optimization formulation that describes the MPC, a collocation method for solving linear time-dependent differential algebraic equations (DAEs) that result from the ROM, and an overall strategy for iteratively refining the behavior of the MPC. Next, the algorithm is validated using two separate numerical experiments. First, the algorithm is compared to an existing MPC code and the results are verified by a numerically precise simulation. It is shown that this algorithm produces a control comparable to existing algorithms and the behavior of the control carefully respects the bounds specified. Second, the MPC is applied to a small nine bus system that contains a mix of turbine-spinning-machine-based and intermittent generation in order to demonstrate the algorithm’s utility for resource planning and control of intermittent resources. This study demonstrates how the MPC can be tuned to change the behavior of the control, which can then assist with the integration of intermittent resources into the grid. The emphasis throughout the paper is to provide systematic treatment of the topic and produce a novel nonlinear control compatible design framework applicable to electric grids and the control of variable resources. This differs from the more targeted application-based focus in most presentations.

microgrid↗

DOE OSTI2025

HP-FLEX: Field demonstration of the semantics-driven configuration of a Model Predictive Control system to make heat pumps flexible

Model Predictive Control (MPC) has demonstrated significant potential for optimizing building operations and enabling demand flexibility. However, the widespread adoption of MPC is hindered by complex manual configuration and commissioning processes that must be conducted by control experts working alongside building operators. These challenges drive up costs and reduce scalability, particularly when technical human resources and building automation systems are limited, such as in small and medium commercial buildings (SMCBs). This paper demonstrates how semantic standards, specifically ASHRAE 223P, can accelerate the adoption of MPC applications for load flexibility in SMCBs. The authors present a replicable control framework, titled “HP-FLEX” that leverages a building’s semantic model to bootstrap the required data configuration for an MPC controller developed for optimizing heat pump systems as flexible grid resources. The semantic model helps streamline the deployment workflow, particularly for site setup, data/control commissioning, and model setup. This integration enhances portability, transferability, and scalability of the HP-FLEX MPC, which has been developed to support MPC-based supervisory HVAC controllers in SMCBs. Additionally, the paper details the required building and thermostat metadata information to enable the HP-FLEX MPC based on field demonstrations. The new workflow was tested in a small commercial building located in California, U.S., and demonstrated a load shifting performance of 9% based on a dynamic pricing signal that varies by the hour. This work provides a practical pathway for transitioning sophisticated building applications from custom to standardized semantic representations, supporting the broader adoption of advanced control strategies like MPC. The framework also establishes a foundation for evolving metadata requirements as applications mature while maintaining compatibility with industry standards.

Paul, Lazlo↗

DOE OSTI2025

HP-FLEX: Field Demonstration of the Semantics-Driven Configuration of a Model Predictive Control System to Make Heat Pumps Flexible

Paul, Lazlo↗

DOE OSTI2022

Online data-enabled predictive control

We develop an online data-enabled predictive (ODeePC) control method for optimal control of unknown systems, building on the recently proposed DeePC (Coulson et al., 2019). Our proposed ODeePC method leverages a primal-dual algorithm with real-time measurement feedback to iteratively compute the corresponding real-time optimal control policy as system conditions change. The proposed ODeePC conceptual-wise resembles standard adaptive system identification and model predictive control (MPC), but it provides a new alternative for the standard methods. ODeePC is enabled by computationally efficient methods that exploit the special structure of the Hankel matrices in the context of DeePC with Fast Fourier Transform (FFT) and primal-dual algorithm We provide theoretical guarantees regarding the asymptotic behavior of ODeePC, and we demonstrate its performance through numerical examples.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Model-based predictive control of multi-stage air-source heat pumps integrated with phase change material-embedded ceilings

This paper presents a model-based predictive control strategy to optimize the operations of phase change material (PCM) ceiling panels coupled with a multi-stage air-source heat pump. A three-stage prototype heat pump unit has been built and tested in the laboratory, with the low and medium stages designed for space heating/cooling and the high compression stage dedicated to charging of the PCM energy storage. To facilitate optimal control of the integrated heat pump system, a mixed-integer linear programming formulation is derived through linearization of the heat pump model and a mixed-integer reformulation of the PCM dynamic governing equations. A predictive control strategy is synthesized based on the resultant control formulation and implemented in a receding horizon scheme that optimizes the PCM charging and the zone temperature schedules simultaneously to leverage both the passive (associated with building construction materials) and active (PCM) storage capacities of a building. The control strategy has been tested along with three benchmarking control scenarios using a co-simulation platform for a prototypical detached house in Atlanta, GA. In this study, test results showed that application of the proposed control strategy to the PCM-integrated heat pump could provide 27.1% electricity cost savings while a fine tuned rule-based control strategy could achieve cost savings of 20.4%, compared to a baseline case without PCM storage, under a time-of-use rate tariff.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗