Robust Model Predictive Control Framework Research Articles

Data-driven robust model predictive control for greenhouse temperature control and energy utilisation assessment

The greenhouse microclimate, especially temperature, is highly complex, and controlling it requires significant resources due to the greenhouses' inefficient design. The application of model predictive control is a promising strategy for temperature control and efficient greenhouse management. However, it does not account for the inaccuracies and uncertainties existing in the system, leading to sub-optimal temperatures. Therefore, this study proposes a comprehensive data-driven robust model predictive control framework for greenhouse temperature control and its energy utilisation assessment in the presence of uncertainties. First, an analytical model based on mass and energy balance and a data-driven model based on an artificial neural network is developed, and their prediction performance is compared. The artificial neural network demonstrates a higher prediction accuracy and is used as the system model in the proposed control framework. A robust model predictive control strategy, based on the minimax objective function and particle swarm optimisation algorithm, is developed to handle the uncertainties in the system. Results illustrate that in the presence of uncertainties, the robust model predictive control strategy outperforms the existing greenhouse climate management system and basic model predictive control with an RMSE of 0.32 °C and 0.60 °C for a two-day simulation period in winter and summer, respectively. Furthermore, the robust model predictive control strategy leads to an energy reduction of 9.67% and 23.61% in winter and summer. The proposed framework is flexible and general and can be applied to other greenhouses with different configurations and cultivated crops by fine-tuning it on the new data set.

Recursively Feasible Data-Driven Distributionally Robust Model Predictive Control With Additive Disturbances

In this letter we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over a linearly interpolated initial state constraint in combination with a simplified affine disturbance feedback policy. We consider a moment-based ambiguity set with data-driven radius for the second moment of the disturbance, where we derive a minimum number of samples in order to ensure user-given confidence bounds on the chance constraints and closed-loop performance. This letter closes with a numerical example, highlighting the performance gain and chance constraint satisfaction based on different sample sizes.

Distributionally robust model predictive control for wind farms

In this paper, we develop a distributionally robust model predictive control framework for the control of wind farms with the goal of power tracking and mechanical stress reduction of the individual wind turbines. We introduce an ARMA model to predict the turbulent wind speed, where we merely assume that the residuals are sub-Gaussian noise with statistics contained in an moment-based ambiguity set. We employ a recently developed distributionally model predictive control scheme to ensure constraint satisfaction and recursive feasibility of the control algorithm. The effectiveness of the approach is demonstrated on a practical example of five wind turbines in a row.

Renewable energy-powered semi-closed greenhouse for sustainable crop production using model predictive control and machine learning for energy management

Renewable energy consumption in agriculture is ascending, catering to the food needs of the rising population and protecting the environment. Maximizing renewable energy usage efficiency is essential for achieving sustainable development goals. In this work, a nonlinear integrated controlled environment agriculture model is constructed to correlate the impact of weather disturbances, temperature control actuators, humidity control actuators, fertilization, and irrigation to the states of crop production facilities and crop growing conditions. Linearization of the model is performed to reduce the computation time while retaining the accuracy of the nonlinear model. A robust model predictive control framework is developed to maximize renewable energy power usage efficiency and maintain a hospitable sustainable cultivation environment. To improve the robustness of control to hedge against the forecast uncertainties, the disjunctive data-driven uncertainty sets built upon the historical forecast errors are constructed by using machine learning methods, including principal component analysis and kernel density estimation. This work also presents the result of the simulation of controlling a renewable energy-powered semi-closed greenhouse growing tomatoes located in Ithaca, New York. Compared to other model predictive control frameworks, which do not leverage the machine learning approaches, the proposed control framework enables a 0.7%–66.9% reduction in renewable energy usage and a 0.7 wt% to 16.1 wt% increase in crop production. Further analysis of this work reveals that the integrated controlled environment agriculture model can help in increasing renewable energy usage efficiency from 4.7% to 127.5%.

A Fuzzy Approximation for FCS-MPC in Power Converters

Standard model predictive control is an optimization-based control strategy that can handle multiple control objectives and system nonlinear constraints. However, it typically suffers from the limitation of the uncertainties in practical systems, such as external unknown disturbances and parametric uncertainties. Motivated by aforementioned limitation, in this article, a novel robust model predictive control framework, endowed with the merits of fuzzy logic system and finite control-set model predictive control solution, is proposed. The main objective of this article is to enhance the system robustness while guaranteeing adaptability to different conditions. More specifically, a fuzzy approximation point of view, which has a good potential to approximate the unknown nonlinear functions, is deployed and incorporated into the proposed design, which allows one to explicitly take the system nonlinear dynamics and uncertainties into account. The novelty of the proposed methodology relies on the fact that any prior knowledge and explicit information of system model parameters are not required, thereby resulting in considerable enhancement of robustness. Furthermore, the input-to-state stability of the approximation error system is proven through Lyapunov analysis, and it demonstrates that the estimated errors are uniformly ultimately bounded. Finally, the interest of the proposal is experimentally confirmed for modular multilevel converter.

HD-RMPC: A Hierarchical Distributed and Robust Model Predictive Control Framework for Urban Traffic Signal Timing

Due to the nonlinearity and dynamics of transportation systems, traffic signal control (TSC) in urban traffic networks has always been an important challenge. In recent years, model predictive control (MPC) has shown extraordinary potential in TSC due to its outstanding ability to model dynamic systems. However, the relatively complex online computing, lack of reasonable setpoints for target solving, and uncertainty of traffic network hinder MPC from being further applied. To address these problems, we propose a hierarchical, distributed, and robust model predictive control (HD-RMPC) framework for urban TSC. At the slow-update layer, the road network is dynamically divided into several subareas according to regional attributes and real-time traffic demand. Meanwhile, the volume is coordinated in a robust way for the purpose of traffic equilibrium and overflow prevention. Then, the set-point matrix of each subarea is calculated to equalize the flow in the subarea. This distributed framework guarantees the real-time performance of MPC in urban traffic networks. At the fast-update layer, we adopt an improved prediction model by explicit modeling of the disturbance and reduce the prediction error. Finally, the objective function is reconstructed and solved at the control layer to obtain the optimal control law. Through continuous and asynchronous optimization of the set point and prediction model, the framework significantly improves the control effect. Simulation evaluation based on a real-world road network demonstrates that the proposed HD-RMPC method outperforms all baselines and maintains excellent real-time performance.

Hybrid Physics-based and Data-driven Model Predictive Control for Multi-Zone Building's Thermal Comfort Under Disjunctive Uncertainty

This paper develops a hybrid approach that utilizes the distributional information of the disjunctive uncertainty sets and incorporates them into the model predictive control (MPC). This approach aims at the multi-zone building control to the thermal comfort, and it's robust to the uncertain weather forecast errors. The control objective is to maintain each zone's temperature and relative humidity within the specified ranges using the minimum cost of energy of the underlying heating system. The hybrid model is constructed using a physics-based and regression method for the temperature and relative humidity of each zone in the building. The uncertainty space is based on historical weather forecast error data, which are captured by a group of disjunctive uncertainty sets using k-means clustering algorithm. Machine learning approaches based on principal component analysis and kernel density estimation are used to construct each basic uncertainty set and reduce the conservatism of resulting robust control action under disturbances. A robust MPC framework is developed based on the proposed hybrid model and data-driven disjunctive uncertainty set. An affine disturbance feedback rule is employed to obtain a tractable approximation of the robust MPC problem. A case study of controlling temperature and relative humidity of a multi-zone building in Ithaca, New York, USA, is presented. The results demonstrate that the proposed hybrid approach can reduce 9.8% to 17.9% of total energy consumption compared to conventional robust MPC approaches. Moreover, the proposed hybrid approach can essentially satisfy the thermal constraints that certainty equivalent MPC and robust MPC largely violate.

Compact Cooperative Adaptive Cruise Control for Energy Saving: Air Drag Modelling and Simulation

This paper studies the value of communicated motion predictions in the longitudinal control of connected automated vehicles (CAVs). We focus on a safe cooperative adaptive cruise control (CACC) design and analyze the value of vehicle-to-vehicle (V2V) communication in the presence of uncertain front vehicle acceleration. The interest in CACC is motivated by the potential improvement in energy consumption and road throughput. In order to quantify this potential, we characterize experimentally the relationship between inter-vehicular gap, vehicle speed, and (reduction of) energy consumption for a compact plug-in hybrid electric vehicle. The resulting model is leveraged to show efficacy of our control design, which pursues small inter-vehicle gaps between consecutive CAVs and, therefore, improved energy efficiency. Our proposed control design is based on a robust model predictive control framework to systematically account for the system uncertainties. We present a set of thorough simulations aimed at quantifying energy efficiency improvement when vehicle states and predictions exchanged via V2V communication are used in the control law.

Data-driven robust model predictive control framework for stem water potential regulation and irrigation in water management

In this work, we propose a data-driven robust model predictive control (DDRMPC) framework that utilizes stem water potential (SWP) as a basis for effective irrigation control of high value-added crops. By linearizing and discretizing a nonlinear dynamic model of water dynamics, we develop a state-space model that predicts the dynamic state of SWP. In the model, soil, root, and stem are the three compartments to describe current water status of the system. In addition, evapotranspiration and precipitation are the driving force and the water inlet, respectively. A robust optimal control problem is formulated to maintain SWP above a safe level to avoid detrimental effects on crops. To describe the uncertainty within prediction errors of evapotranspiration and precipitation, a data-driven approach is adopted, which achieves a desirable tradeoff between constraint satisfaction and water saving. Meanwhile, it is shown that the proposed DDRMPC ensures both feasibility and stability. A case study based on almond tree is carried out to showcase the effectiveness of the DDRMPC strategy relative to on–off control, certainty equivalent MPC and robust MPC. In particular, the control of tree stem water potential through DDRMPC can reduce the water consumption by 7.9% compared with on–off control while maintaining zero probability of constraint violation.

A robust model predictive control framework for the regulation of anesthesia process with Propofol

AbstractIn this work, we present a robust Model Predictive Control (MPC) strategy based on linear matrix inequalities (LMIs) for the intravenous administration of Propofol, a drug which is used for anesthesia during surgeries. The controller is designed for a population of patients and takes into account constraints on the amount of administered drug and on the drug concentration profile. A detailed compartmental mathematical model available in the literature is adjusted to the available data and provides the future predictions of the process. In the context of the application, only the depth of anesthesia (BIS index) is assumed to be measured—as it is common in practice. The state of the system (drug amount in organs) is estimated in real‐time by incorporating a state observer. The derived control scheme, along with the designed state observer are able to deal with major challenges in controlling the depth of anesthesia which are inter‐ and intra‐patient variability, model nonlinearity, and model uncertainty. The controller is able to satisfy the divergent characteristics of the patients of the dataset, while satisfying in parallel all the imposed constraints. Moreover, we show that by considering smaller groups of patients with similar characteristics the corresponding responses are significantly improved.

Robust model predictive control of an anaesthesia workstation ventilation unit

Abstract Respiratory support is a key element of modern medical care, ranging from oxygen therapy to full ventilatory support. A central component of mechanical ventilation is the control of the resulting pneumatic quantities such as pressure and flow. In this article the use of robust model predictive control for pressure-controlled mechanical ventilation is proposed, with the goal of increasing the safety of the patient by considering physiological safety constraints. The uncertainty in the estimation of physiological model parameters as well as model uncertainties are considered as disturbances to the system, which are taken into account through the proposed robust model predictive control framework. The practical applicability of this control approach is illustrated in an implementation on a research demonstrator of the ventilation unit from an anaesthesia workstation.

Constrained robust model predictive control embedded with a new data‐driven technique

In the control field, the adaptive model predictive control (AMPC) has the capability of taking effective control actions on unknown-but-bounded time-independent or slowly time-varying systems coupling with constraints. In essence, AMPC estimates the uncertain parameters or uncertainty set online by utilising historian data to extract model information. The model estimation procedure imposes some specific conditions on data and these extra conditions have restricted its practical use. To overcome these problems, a new data-driven control methodology is presented that integrates the data-driven concept into robust model predictive control (RMPC) architecture for unknown-but-bounded time-independent or slowly time-varying plant. The key novelty is to employ historian data to derive control policy and make a prediction in replacement with the complicated procedure of utilising data to estimate model parameters. A data-driven RMPC algorithm is developed within the robust model predictive control framework with the fulfilment of recursive feasibility and stability. The authors display the highlights of the data-driven model predictive control controller through two simulation examples. The resulting controller is verified to reduce conservativeness and increase the closed-loop performance of the system.

Robust MPC for temperature management on electrical transmission lines

Abstract In the current context of high integration of renewable energies, maximizing infrastructures capabilities for electricity transmission is a general need for Transmission System Operators (TSO). The French TSO, RTE, is developing levers to control power flows in realtime: renewable production curtailment is already employed and large battery storage systems are planned to be installed for congestion management in early 2020. The combination of these levers with the use of Dynamic Line Rating (DLR) helps exploiting the lines at the closest of their limit by managing their temperature in real-time. Unnecessary margins can be reduced, avoiding congestion and excessive generation curtailment. In particular, there is a possible interesting correlation between the transits increase due to high wind farms generation and the cooling effect of wind on power lines in the same area. In order to optimize the electrical transmission network capacities, the present paper advocates the use of a temperature management model, mixing production curtailment and large batteries as control variables. A robust Model Predictive Control framework for local control on electrical lines temperature is presented based on the regulation within tubes of trajectories. Simulations on the French electrical network are conducted to show the effectiveness of the optimization-based control design.