In this paper we present a framework for achieving constrained optimal real-time control for large-scale systems with fast dynamics. The methodology uses the explicit solution of the model predictive control (MPC) problem combined with model reduction, in an output-feedback implementation.The explicit solution of the MPC problem leads to online MPC functionality without having to solve an optimization problem at each time step.Reduced-order models are derived using a goal-oriented, model-constrained optimization formulation that yields efficient models tailored to the control application at hand. The approach is illustrated on a challenging largescale flow problem that aims to control the shock position in a supersonic diffuser. I. IntroductionWith the increasing interest in fluid flow control over the last decade, there arises a need for control methodology that can achieve constrained optimal real-time control of distributed systems with fast dynamics, such as in mechatronics, MEMS, rotating machinery and acoustics. Computational fluid dynamic (CFD) models of such systems typically have order * PhD Student, Department of Engineering Cybernetics; svein.hovland@itk.ntnu.no.
In this paper, we present a systematic procedure for obtaining closed-loop stable output-feedback model predictive control based on reduced-order models. The design uses linear state estimators, and applies to open-loop stable systems with hard input-and soft state constraints. Robustness against the model reduction error is obtained by choosing the cost function parameters so as to satisfy a linear matrix inequality condition. We also show by means of an example, that performance is maintained even when the model reduction error is relatively large.
In this paper we present a methodology for achieving real-time control of systems modeled by partial differential equations. The methodology uses the explicit solution of the model predictive control (MPC) problem combined with model reduction. The explicit solution of the MPC problem leads to online MPC functionality without having to solve an optimization problem at each time step. Reduced-order models are derived using a goal-oriented, model-based optimization formulation that yields efficient models tailored to the application at hand. The approach is demonstrated for reduced-order output feedback control of a large-scale linear time invariant state space model of the discretized heat equation.
An advanced dynamic flow and temperature model was used to optimize and control MPD operations in real time on the Gullfaks field in the North Sea. The well to be drilled only had a 7 bar window between the pore and fracture pressure according to prognosis. However, drilling objectives were eventually fulfilled aided by very accurate downhole pressure control. This paper addresses the model specific challenges, analyzes the differences between model calculations and downhole pressure data, and discusses how to bring hydraulic modelling further in accordance with future operational needs. Challenges related to how to tune the system efficiently and accurately, data quality issues, displacement operations, etc., are described and enlightened by downhole memory data made available when the string was back on surface. Ideas on how to build a more robust and easy to use system without sacrificing the advantages of having a high fidelity model in the real time loop are discussed. The experience and ideas described contribute to the development of a very accurate and reliable MPD system, which is capable of automatic pressure control during the whole sequence of drilling, tripping, circulation, displacements etc. An important goal for the future will be to reduce the offshore crew dedicated to the modelling function to a minimum, with the provision of onshore support during operations.
In this paper we propose to use model reduction techniques to make explicit model predictive control possible and more attractive for a larger number of applications and for longer control horizons. The main drawback of explicit model predictive control is the large increase in controller complexity as the problem size increases. For this reason, the procedure is limited to applications with low-order models, a small number of constraints and/or short control horizons. The proposed use of model reduction techniques is demonstrated for several applications, among others for control of fuel cell breathing. In all applications, a significant reduction in controller complexity is achieved.
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