scholarly journals Sensitivity Analysis of Optimal Control for a Class of Parabolic PDEs Motivated by Model Predictive Control

2019 ◽  
Vol 57 (4) ◽  
pp. 2753-2774 ◽  
Author(s):  
Lars Grüne ◽  
Manuel Schaller ◽  
Anton Schiela
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Parabolic Pdes

scholarly journals Time Adaptivity in Model Predictive Control

2021 ◽  
Vol 90 (1) ◽  
Author(s):  
Alessandro Alla ◽  
Carmen Gräßle ◽  
Michael Hinze
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Error Control ◽  
Time Discretization ◽  
Posteriori Error ◽  
Parabolic Pdes ◽  
Prediction Horizon ◽  
Control Concept ◽  
Adaptive Time

AbstractThe core of the Model Predictive Control (MPC) method in every step of the algorithm consists in solving a time-dependent optimization problem on the prediction horizon of the MPC algorithm, and then to apply a portion of the optimal control over the application horizon to obtain the new state. To solve this problem efficiently, we propose a time-adaptive residual based a-posteriori error control concept based on the optimality system of this optimal control problem. This approach not only delivers an adaptive time discretization of the prediction horizon, but also suggests an adaptive time discretization of the application horizon, whose length could be either adaptive or fixed. We apply this concept for systems governed by linear parabolic PDEs and present several numerical examples which demonstrate the performance and the robustness of our adaptive MPC control concept.

An Economic Model Predictive Control Approach for Wind Power Smoothing and Tower Load Mitigation

2018 ◽  
Author(s):  
Mohamed M. Alhneaish ◽  
Mohamed L. Shaltout ◽  
Sayed M. Metwalli
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Model Predictive Control ◽  
Wind Power ◽  
Predictive Control ◽  
Economic Model ◽  
Control Algorithm ◽  
Fatigue Load ◽  
Economic Model Predictive Control ◽  
Control Framework

An economic model predictive control framework is presented in this study for an integrated wind turbine and flywheel energy storage system. The control objective is to smooth wind power output and mitigate tower fatigue load. The optimal control problem within the model predictive control framework has been formulated as a convex optimal control problem with linear dynamics and convex constraints that can be solved globally. The performance of the proposed control algorithm is compared to that of a standard wind turbine controller. The effect of the proposed control actions on the fatigue loads acting on the tower and blades is studied. The simulation results, with various wind scenarios, showed the ability of the proposed control algorithm to achieve the aforementioned objectives in terms of smoothing output power and mitigating tower fatigue load at the cost of a minimal reduction of the wind energy harvested.

Direct Optimal Control and Model Predictive Control

2017 ◽  
pp. 263-382 ◽  
Author(s):  
Mario Zanon ◽  
Andrea Boccia ◽  
Vryan Gil S. Palma ◽  
Sonja Parenti ◽  
Ilaria Xausa
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Direct Optimal Control

scholarly journals Sensitivity Analysis of the Battery Model for Model Predictive Control: Implementable to a Plug-In Hybrid Electric Vehicle

2018 ◽  
Vol 9 (4) ◽  
pp. 45 ◽  
Author(s):  
Nicolas Sockeel ◽  
Jian Shi ◽  
Masood Shahverdi ◽  
Michael Mazzola
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Fuel Consumption ◽  
Electric Vehicle ◽  
Predictive Control ◽  
Hybrid Electric Vehicle ◽  
Control Solution ◽  
Current Time ◽  
Battery Model ◽  
Hybrid Electric

Developing an efficient online predictive modeling system (PMS) is a major issue in the field of electrified vehicles as it can help reduce fuel consumption, greenhouse gasses (GHG) emission, but also the aging of power-train components, such as the battery. For this manuscript, a model predictive control (MPC) has been considered as PMS. This control design has been defined as an optimization problem that uses the projected system behaviors over a finite prediction horizon to determine the optimal control solution for the current time instant. In this manuscript, the MPC controller intents to diminish simultaneously the battery aging and the equivalent fuel consumption. The main contribution of this manuscript is to evaluate numerically the impacts of the vehicle battery model on the MPC optimal control solution when the plug hybrid electric vehicle (PHEV) is in the battery charge sustaining mode. Results show that the higher fidelity model improves the capability of accurately predicting the battery aging.

scholarly journals MODEL PREDICTIVE CONTROL TOOLBOX DESIGN FOR NONSTATIONARY PROCESS

2021 ◽  
Author(s):  
Oleksandr V. Stepanets ◽  
Yurii I. Mariiash
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Complex Structure ◽  
Nonstationary Process ◽  
Actual State ◽  
Quadratic Functional ◽  
Linear Quadratic ◽  
Prediction Horizon

Background. Model predictive control (MPC) approach is the basic feedback scheme, combined with high adaptive properties, which determines its successful use in the practice of design and operation of control systems. These advantages allow managing multidimensional objects with a complex structure, including nonlinearity, optimizing processes in real time within the constraints on controlled and managed variables, taking into account uncertainties in the task of objects and perturbations. Objective. The purpose of the paper is to design and analyse control system of carbon monoxide oxidation in the convector cavity based on MPC with linear-quadratic cost functional with constraint. Methods. The design of MPC is based on mathematical model of an object (relatively simple). At the current step, the prediction of object dynamic response on some final period of time (prediction horizon) is carried out; control optimization is performed, the purpose of which is to approximate the control variables of the prediction model to the corresponding setpoint on the predict horizon. The found optimal control is applied and measurement of an actual state of object at the end of a step is carried out. The prediction horizon is shifted one step further, and this algorithm are repeated. Results. The results of modeling the automatic control system show that the MPC approach provides maintenance of carbon dioxide content when changing oxygen consumption and overshoot caused by introduction bulk does not exceed 0.6 % that meets the technological requirements of the process. Conclusions. A fuse of the MPC and the quadratic functional given the constraints on the input signals is proposed. The problems of control degree of carbon oxidation in the convector cavity include non-stationarity, so the use of classical control methods is difficult. The MPC approach minimizes the cost function that characterizes the quality of the process. The predicted behaviour of a dynamic system will usually differ from its actual motion. The obtained quadratic functional is optimized to find the optimal control of degree of CO oxidation to CO2.

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