Abstract:This paper presents a constrained finite horizon model predictive control (MPC) scheme for regulation of the annular pressure in a well during managed pressure drilling from a floating vessel subject to heave motion. In addition the robustness of a controller to deal with heave disturbances despite uncertainties in the friction factor and bulk modulus is investigated. The stochastic model describing sea waves in the North Sea is used to simulate the heave disturbances. The results show that the closed-loop simulation without disturbance has a fast regulation response, without any overshoot, and is better than a proportional-integralderivative (PID) controller. The constrained MPC for managed pressure drilling shows further improved disturbance rejection capabilities with measured or predicted heave disturbance. Monte Carlo simulations show that the constrained MPC has a good performance to regulate set point and attenuate the effect of heave disturbance in case of significant uncertainties in the well parameter values.

Heave motion of floating rigs complicates the control of pressure in MPD. During connections, the drill string is detached from the draw-works and moves with the heaving rig, causing downhole pressure fluctuations. As a step towards designing control schemes to actively attenuate the fluctuations, a fit-for-purpose mathematical model of well hydraulics is derived based on a finite volumes discretization. The model incorporates various MPD operations, including circulating in new mud, vertical motion and rotation of the drill string. Using field data from UllRigg - a full-scale experimental drilling facility - the model is validated with respect to the different MPD operations. Since an automatic control scheme in principle inherits the complexity of the model on which it is based, it is of great importance to develop models of minimal complexity. It is shown by simulations that significantly reduced order models obtained by applying the method of frequency-weighted balanced model reduction to large models outperform those obtained by simply reducing the number of control volumes. This result is particularly important for the dynamics involved during heave, since a significant number of control volumes are required to model this case. The contributions of this paper enable development of control systems for automated MPD operations from floaters.

SUMMARYA new robust adaptive control method is proposed, which removes the deficiencies of the classic robust multiple model adaptive control (RMMAC) using benefits of the -gap metric. First, the classic RMMAC design procedure cannot be used for systematic design for unstable plants because it uses the Baram Proximity Measure, which cannot be calculated for open-loop unstable plants. Next, the %FNARC method which is used as a systematic approach for subdividing the uncertainty set makes the RMMAC structure being always companion with the -synthesis design method. Then in case of two or more uncertain parameters, the model set definition in the classic RMMAC is based on cumbersome ad hoc methods. Several methods based on -gap metric for working out the mentioned problems are presented in this paper. To demonstrate the benefits of the proposed RMMAC method, two benchmark problems subject to unmodeled dynamics, stochastic disturbance input and sensor noise are considered as case studies. The first case-study is a non-minimum-phase (NMP) system, which has an uncertain NMP zero; the second case-study is a mass-spring-dashpot system that has three uncertain real parameters. In the first case-study, five robust controller design methods (H 2 , H ∞ , QFT, H ∞ loop-shaping and -synthesis) are implemented and it is shown via extensive simulations that RMMAC/ /QFT method improves disturbance-rejection, when compared with the classic RMMAC. In the second case-study, two robust controller design methods (QFT and mixed -synthesis) are applied and it is shown that the RMMAC/ /QFT method improves disturbance-rejection, when compared with RMMAC/ /mixed-.

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