Tracking Control for Directional Drilling Systems Using Robust Feedback Model Predictive Control Anastasis Georgiou , Simos A. Evangelou , Imad M. Jaimoukha and Geoff Downton ∗∗ Department of Electrical and Electronic Engineering, Imperial College, London SW7-2AZ, U.K.(e-mail: anastasis.georgiou16@imperial.ac.uk, i.jaimouka@imperial.ac.uk, s.evangelou@imperial.ac.uk). ∗∗ Schlumberger, Gloucester, GL10 3SX, United Kingdom (GDownton@slb.com). Abstract: A rotary steerable system (RSS) is a drilling technology which has been extensively studied and used for over the last 20 years in hydrocarbon exploration and it is expected to drill complex curved borehole trajectories. RSSs are commonly treated as dynamic robotic actuator systems, driven by a reference signal and typically controlled by using a feedback loop control law. However, due to spatial delays, parametric uncertainties and the presence of disturbances in such an unpredictable working environment, designing such control laws is not a straightforward process. Furthermore, due to their inherent delayed feedback, described by delay differential equations (DDE), directional drilling systems have the potential to become unstable given the requisite conditions. This paper proposes a Robust Model Predictive Control (RMPC) scheme for industrial directional drilling, which incorporates a simplified model described by ordinary differential equations (ODE), taking into account disturbances and system uncertainties which arise from design approximations within the formulation of RMPC. The stability and computational efficiency of the scheme are improved by a state feedback strategy computed offline using Robust Positive Invariant (RPI) sets control approach and model reduction techniques. A crucial advantage of the proposed control scheme is that it computes an optimal control input considering physical and designer constraints. The control strategy is applied in an industrial directional drilling configuration represented by a DDE model and its performance is illustrated by simulations. Keywords: Directional Drilling,Trajectory tracking, Robust MPC, LMI optimization 1. INTRODUCTION The oil and gas industry has constantly searched for more economic and efficient technologies to exploit fossil energy resources. The process for obtaining and extraction of fossil energy resources such as oil and gas, which remain the major fuels for powering today’s society, has two major difficulties. Firstly, access to energy resources requires boreholes with com- plex curves, which is not a simple task to achieve. Secondly, deep-seated and offshore hydrocarbon explorations commonly take place under an unpredictable environment and extreme working conditions while targeting resource locations in the crust of the Earth (Carpenter, 2013). These challenges are being addressed by Rotary Steerable Systems (Bayliss et al., 2012). This steering mechanism is a tool placed close to the drilling bit of a bottom hole assembly (BHA) as illustrated in Fig. 1. In this paper we study a push-the-bit RSS that controls the direc- tion of borehole propagation via force actuated pads mounted close to the bit. Currently the control actuator commands are operated with major communication delays by professionals, where they are located at the surface close to the drilling rig, using complex data sets, such as location of the reservoir, rock layer geometry, etc. Human errors and communication delays could be minimized by automating the steering commands by ⋆ This work has been funded by an EPSRC Industrial CASE Studentship award in collaboration with Schlumberger (EP/R512540/1). developing a closed-loop controller using real-time data from sensors located in the drill string. Fig. 1. Directional drilling system (Downton and Ignova, 2011). The main difficulties of developing an automated RSS system are, firstly the unpredictable and harsh working environment, secondly, key parameters vary whilst drilling and lastly the Preprints of the 21st IFAC World Congress (Virtual) Berlin, Germany, July 12-17, 2020 Copyright lies with the authors 12149