Real-time Model Predictive Control Research Articles

Accelerating chiller sequencing using dynamic programming

Effective management of heating, ventilation, and air conditioning (HVAC) systems is crucial for enhancing building energy efficiency. Chillers, a significant component of HVAC systems, are responsible for more than 50 % of energy usage of the whole cooling plant, underscoring the importance of optimizing chiller sequencing. Although Model Predictive Control (MPC) has demonstrated efficacy in enhancing chiller performance, its widespread adoption is hindered by its high computational complexity. This study introduces a dynamic programming approach coupled with a 2-step optimization method to expedite chiller sequencing optimization while upholding MPC’s real-time control capabilities. The MPC method implemented in this study integrates a load forecasting model with an artificial neural network (ANN) based chiller model. Through simulation tests utilizing historical HVAC operational data from a commercial building located in Shanghai, the proposed chiller sequencing strategy achieves a 9.73 % decrease in energy consumption. Moreover, the dynamic programming approach, especially in conjunction with the 2-step optimization process, significantly reduces the MPC solution time at each control step from 165 min to 3.61 s, making it a viable solution for real-time MPC deployment. Additionally, the research delves into the influence of the chiller model’s complexity, the optimization strategy, and control horizon on computational efficiency. This research provides a feasible solution to implement chiller sequencing in real buildings to pick up the low-hanging fruits in an effective way.

Real-time robust nonlinear model predictive control with monotonically increasing weight for quadruped locomotion

Real-time robust nonlinear model predictive control with monotonically increasing weight for quadruped locomotion

Hierarchical MPC-based authority allocation strategy for human–machine shared vehicles considering human–machine conflict

The uncertainty of driver behavior is an important factor affecting the safety of human–machine co-driving vehicles. Traditional rule-based models often fail to capture the nonlinear and complex characteristics of human steering behavior. To overcome this, we propose a data network-driven approach utilizing gated recurrent unit (GRU) neural networks to accurately predict driver steering behavior. The GRU-based driver model is integrated with vehicle dynamics to construct a control-oriented driver–vehicle model. Considering that human–machine conflict may cause vehicle instability, an exponential function combining proportional–integral–derivative is proposed to quantify the human–machine conflict level based on steering difference. To reasonably allocate human–computer permissions based on human–machine interaction, a hierarchical authority allocation framework is proposed. The upper layer provides a reference authority allocation via an exponential function, while the lower layer employs a real-time model predictive control (MPC) optimizer to track this reference, ensuring optimal vehicle path tracking and stability. The proposed system’s effectiveness is validated through driver-in-the-loop testing, demonstrating significant improvements in safety and performance. The results show that in the human–machine conflict scenario, the proposed authority allocation strategy can still ensure the path tracking and safety of the vehicle.

Smart home power management algorithm using real-time model predictive control for a stand-alone PV system with battery energy storage

A smart home power management system is critical for stand-alone home-photovoltaic (HPV) with battery energy storage. Existing approaches often focus on maximizing power extraction from PV systems without considering real-time power adjustments or battery state of charge (SoC), which can lead to over-current or over-voltage issues that damage the battery. To address these limitations, this paper proposes a home power management algorithm that dynamically adjusts the power flow between the PV system, home loads, and the battery based on real-time system power measurements and battery SoC. This dynamic adjustment ensures an uninterrupted power supply to the home loads while maintaining battery safety. The proposed home manager algorithm features multiple operating modes: Maximum power point (MPP) charging, partial charging, fast charging, float charging, and partial discharging. Each mode is integrated with its dedicated model predictive controller (MPC) to achieve its specific control objective. Finally, through a semi-experimental simulation using a process-in-the-loop (PIL) test approach with the embedded board eZdsp TMS320F28335, testing under various irradiance levels shows that the home manager achieves significant improvement over conventional approaches. For instance, over the MPP mode it achieve a power efficiency of 99.36% with a 2.05% SoC increase, while fast charging mode resulted in 87.44% efficiency with an 11.2% SoC increase. However, float charging mode maintained an 87.27% efficiency with a 2.6% SoC increase, and partial discharging led to a 1.3% SoC decrease. The overall battery efficiency reached 96.45%, demonstrating the algorithm’s ability to optimize power flow, ensure a reliable energy supply, and maintain battery safety under varying weather conditions.

Accelerated MPC: A real-time model predictive control acceleration method based on TSMixer and 2D block stochastic configuration network imitative controller

Modern industrial processes demand real-time model predictive control (MPC) method within the constraints of limited computing resources. This paper introduces an accelerated MPC method to address the issue. Specifically, we employ the time series mixing model (TSMixer) to construct a predictive model capable of accurately forecasting the behavior of the system under control. Furthermore, we extend the capabilities of TSMixer by integrating a feature classification model (TSMixer with FCM). This enhanced version takes into account both future information and static variables, resulting in superior accuracy compared to the transformer model while maintaining a significantly smaller parameter count. Finally, to further enhance MPC’s responsiveness, we develop a two-dimensional block stochastic configuration network (2D-BSCN) imitative controller. This innovative network clones the behavior of rolling optimization, effectively replacing online optimization to reduce computational time. The experimental results show that the accelerated MPC has an excellent performance in numerical simulation and actual industrial processes. Notably, the algorithm achieves a smaller FLOPs and tracking time than other state-of-the-art models, well within the requirement for industrial process control.

Real-time deep learning-based model predictive control of a 3-DOF biped robot leg

Our research utilized deep learning to enhance the control of a 3 Degrees of Freedom biped robot leg. We created a dynamic model based on a detailed joint angles and actuator torques dataset. This model was then integrated into a Model Predictive Control (MPC) framework, allowing for precise trajectory tracking without the need for traditional analytical dynamic models. By incorporating specific constraints within the MPC, we met operational and safety standards. The experimental results demonstrate the effectiveness of deep learning models in improving robotic control, leading to precise trajectory tracking and suggesting potential for further integration of deep learning into robotic system control. This approach not only outperforms traditional control methods in accuracy and efficiency but also opens the way for new research in robotics, highlighting the potential of utilizing deep learning models in predictive control techniques.

Data-driven auto-tuning strategy for RTO-MPC based on Bayesian optimization

Real-time optimization (RTO) and model predictive control (MPC) are extensively employed in industrial processes to enhance economic objectives. However, the tuning of the system remains a challenge, in particular, for cases where an explicit model relating the RTO objective and the process dynamics is unknown. To address this issue, an online data-driven auto-tuning strategy leveraging two Bayesian optimization (BO) techniques is proposed. This strategy is useful for situations where the RTO objective and the process dynamics are detectable but their exact functional forms are unclear. The proposed strategy views the RTO objective as a black-box objective and interprets the steady-state conditions as black-box equality constraints within the RTO layer. In this context, the upper-trust-bound based constrained BO (UTB-CBO) method is adopted to optimize the setpoints and enhance solution feasibility. Additionally, the proposed approach can take into account measurable disturbance inputs explicitly and account for their consequential influence on objective optimization by considering disturbance variations as contextual information. Simultaneously, another contextual BO scheme is implemented to automatically tune the MPC controller parameters for improving tracking performance upon accepting the setpoints optimized by the RTO. Simulation results based on a continuous stirred-tank reactor system are given to illustrate the effectiveness of the proposed approach.

Influence of usage and model inaccuracies on the performance of smart hot water heaters: lessons learned from a demand response field test

Domestic hot water heaters are considered to be easily integrated as flexible loads for demand response. While literature grows on reproducible simulation and lab tests, real-world implementation in field tests considering state estimation and demand prediction-based model predictive control approaches is rare. This work reports the findings of a field test with 16 autonomous smart domestic hot water heaters. The heaters were equipped with a retrofittable sensor/actuator setup and a real-time price-driven model predictive control unit, which covers state estimation, demand prediction, and optimization of switching times. With the introduction of generic performance indicators (specific costs and thermal efficiency), the results achieved in the field are compared by simulations to standard control modes (instantaneous heating, hysteresis, night-only switching). To evaluate how model predictive control performance depends on the user demand prediction and state estimation accuracy, simulations assuming perfect predictions and state estimations are conducted based on the data measured in the field. Results prove the feasible benefit of RTP-based model predictive control in the field compared to a hysteresis-based standard control regarding cost reduction and efficiency increase but show a strong dependency on the degree of utilization.

Real-time time-varying economic nonlinear model predictive control for wind turbines

Economic nonlinear model predictive control is a great choice to tackle the control issues appearing in the current wind energy industry. In this paper, instead of generator power, aerodynamic power is employed in the economic cost function to establish the required conditions of stability and convergence of the economic performance, such as turnpike and problem convexity. However, since aerodynamic power depends on time-varying wind speed, conventional time-invariant economic nonlinear model predictive controllers cannot guarantee the stability and convergence of economic performance. This paper proposes a new time-varying economic nonlinear model predictive controller for wind turbine control that considers an economic trajectory, instead of a steady-state, in its optimization problem. The proposed time-varying economic cost function directly considers aerodynamic power, the activity of pitch angle and generator torque, and fatigue loads on the shaft and tower. Therefore, this controller can maximize power extraction and reduce fatigue load on the tower, drivetrain, and actuators. Furthermore, a fast-parallel Newton-type method is used to implement the proposed controller in actual wind turbines. An accurate aeroelastic model is used to validate the performance of the proposed control scheme. The proposed controller is also compared with two tracking nonlinear model predictive controllers, the baseline controller, and a newly developed method, under fatigue and extreme load scenarios in the presence and absence of uncertainty. The simulation results show the superior economic performance of the proposed approach. Moreover, the real-time results verify the computational speed that the proposed controller requires to deploy actual wind turbines.

Autonomous Needle Navigation in Subretinal Injections via iOCT.

Subretinal injection is an effective method for direct delivery of therapeutic agents to treat prevalent subretinal diseases. Among the challenges for surgeons are physiological hand tremor, difficulty resolving single-micron scale depth perception, and lack of tactile feedback. The recent introduction of intraoperative Optical Coherence Tomography (iOCT) enables precise depth information during subretinal surgery. However, even when relying on iOCT, achieving the required micron-scale precision remains a significant surgical challenge. This work presents a robot-assisted workflow for high-precision autonomous needle navigation for subretinal injection. The workflow includes online registration between robot and iOCT coordinates; tool-tip localization in iOCT coordinates using a Convolutional Neural Network (CNN); and tool-tip planning and tracking system using real-time Model Predictive Control (MPC). The proposed workflow is validated using a silicone eye phantom and ex vivo porcine eyes. The experimental results demonstrate that the mean error to reach the user-defined target and the mean procedure duration are within an acceptable precision range. The proposed workflow achieves a 100% success rate for subretinal injection, while maintaining scleral forces at the scleral insertion point below 15mN throughout the navigation procedures.

Towards a digital twin framework in additive manufacturing: Machine learning and bayesian optimization for time series process optimization

Laser directed-energy deposition (DED) offers notable advantages in additive manufacturing (AM) for producing intricate geometries and facilitating material functional grading. However, inherent challenges such as material property inconsistencies and part variability persist, predominantly due to its layer-wise fabrication approach. Critical to these challenges is heat accumulation during DED, influencing the resultant material microstructure and properties. Although closed-loop control methods for managing heat accumulation and temperature regulation are prevalent in DED literature, few approaches integrate real-time monitoring, physics-based modeling, and control simultaneously in a cohesive framework. To address this, we present a digital twin (DT) framework for real-time model predictive control of process parameters of the DED for achieving a specific process design objective. To enable its implementation, we detail the development of a surrogate model utilizing Long Short-Term Memory (LSTM)-based machine learning which uses Bayesian Inference to predict temperatures across various spatial locations of the DED-built part. This model offers real-time predictions of future temperature states. In addition, we introduce a Bayesian Optimization (BO) method for Time Series Process Optimization (BOTSPO). Its foundational principles align with traditional BO, and its novelty lies in our unique time series process profile generator with a reduced dimensional representation. BOTSPO is used for dynamic process optimization in which we deploy BOTSPO to determine the optimal laser power profile, aiming to achieve desired mechanical properties in a DED build. The identified profile establishes a process trajectory that online process optimizations aim to match or exceed in performance. This paper elucidates components of the digital twin framework, advocating its prospective consolidation into a comprehensive digital twin system for AM.

An energy management strategy for fuel cell hybrid electric vehicle based on a real-time model predictive control and pontryagin’s maximum principle

ABSTRACT In order to maintain the battery SOC, the fuel cell power will fluctuate dramatically, as well as frequent start-stop, which will greatly increase the life attenuation of the fuel cell and reduce the durability. An optimization-based energy management strategy with a real-time model predictive control and pontryagin’s maximum principle for FCHEV is proposed in this paper, both the fuel economy and the fuel cell durability are considered in the optimization. A novel model predictive control is studied to achieve energy distribution. After the calculation of predicted speed sequence through back propagation neural network, pontryagin’s maximum principle is introduced to solve the optimal control problem in each prediction horizon and obtain the ideal control strategy. In addition, the fuel cell degradation model is introduced in the modeling process, the minimum power point of the fuel cell system is designed to improve the fuel economy and durability of the fuel cell. Compared with the rule-based strategy, the proposed MPC strategy has better performance to reduce the total equivalent hydrogen consumption, which can save up to 8.44% in the test case of the mid-size fuel cell passenger car while maintaining the stability of the battery’s state of charge.

Real-time Learning-based Nonlinear Model Predictive Control of a virtual motorcycle employing grey-box modeling through Gaussian processes

Virtual prototyping tools simulations are nowadays largely adopted methods in the automotive industry. However, to achieve effective simulative tests for two-wheeled vehicles, a virtual rider, i.e. a controller for virtual motorcycles, is typically needed due to the inherent instability of the system. Different control strategies have been employed to deal with this control task, and promising results have been obtained using Nonlinear Model Predictive Control (NMPC). Yet, performance of NMPC highly relies on the plant characterization, that can be highly complex to obtain analytically for 2-wheel vehicles. To improve it, learning dynamics approaches can be used within a Learning-based Nonlinear Model Predictive Control (LbNMPC) framework, exploiting the combination of data-driven techniques and NMPC strategy. In this manuscript, we present a tailored real-time capable LbNMPC for a virtual motorcycle that relies on a continuous grey-box model based on Gaussian Processes (GPs), method that has proven to be effective for 4-wheel vehicle applications. To cope with the real-time requirement, a feature selection procedure and sparse GP approximations have been adopted. A comparison with a physics-based model NMPC implementation taken from the literature has been carried out, analyzing the impact of different sparse GP representations. Remarkable improvements in both model accuracy and tracking performance have been obtained, and the generalization properties of the grey-box model have been assessed.

Real-time Model Predictive Contouring Control via Block Successive Convex Approximation

The real-time implementation of model predictive control (MPC) in robotics field is known to be challenging due to the inherent non-convex and nonlinear dynamics involved, as well as the need for a longer prediction horizon for better control performance. This paper presents a real-time model predictive contouring control (MPCC) scheme by utilizing the block successive convex approximation (BSCA) method. By adopting this method, the original computationally intensive non-convex problem can be decomposed into smaller subproblems with explicit solutions. We show the effectiveness and the real-time performance of the proposed method through a wheeled mobile robot path following task using MPCC controller in simulation.

A Terminal State Feasibility Governor for Real-Time Nonlinear Model Predictive Control Over Arbitrary Horizons

A Terminal State Feasibility Governor for Real-Time Nonlinear Model Predictive Control Over Arbitrary Horizons

Real-Time Model Predictive Control Framework for a Point Absorber Wave Energy Converter With Excitation Force Estimation and Prediction

Real-Time Model Predictive Control Framework for a Point Absorber Wave Energy Converter With Excitation Force Estimation and Prediction

Active Battery Cell Balancing by Real-Time Model Predictive Control for Extending Electric Vehicle Driving Range

Active Battery Cell Balancing by Real-Time Model Predictive Control for Extending Electric Vehicle Driving Range

Modeling and aggregated control of large-scale 5G base stations and backup energy storage systems towards secondary frequency support

A significant number of 5G base stations (gNBs) and their backup energy storage systems (BESSs) are redundantly configured, possessing surplus capacity during non-peak traffic hours. Moreover, traffic load profiles exhibit spatial variations across different areas. Proper scheduling of surplus capacity from gNBs and BESSs in different areas can provide sustainable frequency support for the power system without compromising the operation of 5G network. In this paper, a comprehensive strategy is proposed to safely incorporate gNBs and their BESSs (called “gNB systems”) into the secondary frequency control procedure. Initially, an aggregated model is developed using a state space method to capture the state of a cluster of heterogeneous gNB systems (gNBs-cluster). Subsequently, a utility function is defined to evaluate the quality of 5G network operation in a normalized manner. Based on this utility function, an aggregated control method is proposed, including real-time available power estimation and model predictive control (MPC) for the gNBs-cluster, which ensures the 5G network operation within the security constraint during demand response processes. Simulations, utilizing actual device data, demonstrate the effectiveness of the proposed method in improving power system frequency performance while guaranteeing the safety and reliability of the 5G network.

Real-time model predictive control of urban drainage system in coastal areas

In the context of global climate change and urbanization, model predictive control (MPC) has been increasingly applied in the field of real-time control of urban drainage systems to cope with frequent urban flooding events caused by extreme rainstorms. However, the computation time of the predictive model calculation greatly hinders further development of MPC in this field. In this study, we propose two surrogate models, namely the water tank-water balance model 1 (TWBM1) and the water tank-water balance model 2 (TWBM2), to replace the storm water management model (SWMM) as the prediction model for MPC, thus improving MPC computational efficiency. Both surrogate models can obtain the total outflow process at the downstream outfall of the study area and the corresponding overflow process. In comparison with TWBM1, TWBM2 requires 26 % fewer calibration parameters, and its structure is simpler. These results have been verified in the real-time optimal scheduling of a rainwater drainage system in the Doumen area of Fuzhou City, China. The results show that TWBM1 and TWBM2 have shorter computation time compared to SWMM, which improves the efficiency of MPC computation. Additionally, in comparison with the existing scheduling results, MPC has better performance in terms of economy, security and computational efficiency.

Physically consistent deep learning-based day-ahead energy dispatching and thermal comfort control for grid-interactive communities

Grid-interactive communities are an emerging solution for optimal energy dispatching, improving grid stability, and enhancing the usage of on-site renewable energy by leveraging community flexibilities. This work introduces a novel Physically Consistent Deep Learning (PCDL)-based optimization framework for day-ahead energy dispatching and thermal comfort control within grid-interactive communities. Specifically, the PCDL model is developed to capture the thermal dynamics within the community while ensuring strict adherence to physics consistency. This consistency is defined with the aim of generating physically viable solutions in response to modified system inputs. Subsequently, the PCDL model is utilized for load estimation and indoor climate prediction within a proposed scheduling and control strategy: (1) an optimal energy dispatching plan is calculated based on the day-ahead grid market; (2) a real-time model predictive control (MPC) method is applied to minimize the utilization error and indoor comfort constraint violations caused by following the scheduled energy dispatching plan. A simulation case of a residential hall community at Cornell University with on-site renewable energy resources is implemented to demonstrate the effectiveness of the proposed approach. Comparative simulations, which include the Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Gaussian Process (GP) regression models, confirm the performance advantage of capturing community thermal dynamic and control-oriented generalization ability when using the PCDL model. These results leads to notable improvements in indoor thermal comfort control, ranging between 65.4 and 68.7%, 63.6–79.3%, and 60.4–62.2% for each comparative model, respectively. Moreover, by harnessing community demand flexibility, we achieve energy cost savings between 29.5 and 39.7% compared to the baseline controller.