Robust model predictive control for linear systems subject to norm-bounded model Uncertainties and Disturbances: An Implementation to industrial directional drilling system

Model Predictive Control (MPC) refers to a class of receding horizon algorithms in which the current control action is computed by solving online, at each sampling instant, a constrained optimization problem. MPC has been widely implemented within the industry, due to its ability to deal with multivariable processes and to explicitly consider any physical constraints within the optimal control problem in a straightforward manner. However, the presence of uncertainty, whether in the form of additive disturbances, state estimation error or plant-model mismatch, and the robust constraints satisfaction and stability, remain an active area of research. The family of predictive control algorithms, which explicitly take account of process uncertainties/disturbances whilst guaranteeing robust constraint satisfaction and performance is referred to as Robust MPC (RMPC) schemes. In this thesis, RMPC algorithms based on Linear Matrix Inequality (LMI) optimization are investigated, with the overall aim of improving robustness and control performance, while maintaining conservativeness and computation burden at low levels. Typically, the constrained RMPC problem with state-feedback parameterizations is nonlinear (and nonconvex) with a prohibitively high computational burden for online implementation. To remedy this issue, a novel approach is proposed to linearize the state-feedback RMPC problem, with minimal conservatism, through the use of semidefinite relaxation techniques and the Elimination Lemma. The proposed algorithm computes the state-feedback gain and perturbation online by solving an LMI optimization that, in comparison to other schemes in the literature is shown to have a substantially reduced computational burden without adversely affecting the tracking performance of the controller. In the case that only (noisy) output measurements are available, an output-feedback RMPC algorithm is also derived for norm-bounded uncertain systems. The novelty lies in the fact that, instead of using an offline estimation scheme or a fixed linear observer, the past input/output data is used within a Robust Moving Horizon Estimation (RMHE) scheme to compute (tight) bounds on the current state. These current state bounds are then used within the RMPC control algorithm. To reduce conservatism, the output-feedback control gain and control perturbation are both explicitly considered as decision variables in the online LMI optimization. Finally, the aforementioned robust control strategies are applied in an industrial directional drilling configuration and their performance is illustrated by simulations. A rotary steerable system (RSS) is a drilling technology that has been extensively studied over the last 20 years in hydrocarbon exploration and is used 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. To address this problem, a simplified model described by ordinary differential equations (ODE) is first proposed, and then taking into account disturbances and system uncertainties that arise from design approximations, the proposed RMPC algorithm is used to automate the directional drilling system.Open Acces

Bilinear modelling, control and stability of directional drilling

This paper proposes an approach for the attitude control of directional drilling tools for the oil and gas industry. A bilinear model of the directional drilling tool is proposed and it characterises the nonlinear properties of the directional drilling tool more accurately than the existing linear model, hence broadens the range of adequate performance. The proposed bilinear model is used as the basis for the design of a Bilinear Proportional plus Integral (BPI) controller. The stability of the proposed BPI control system is proven using stability notions for LTI and LPV systems. The transient simulation results show that the proposed BPI controller is more effective, robust and stable for the attitude control of the directional drilling tool than the existing PI controller. The proposed BPI controller provides improved invariant azimuth responses and significantly reduces the adverse effects of measurement delays and disturbances with respect to stability and performance of the directional drilling tool

Tracking control for directional drilling systems using robust feedback model predictive control

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

Design and analysis of robust controllers for directional drilling tools

Directional drilling is a very important tool for the development of oil and gas deposits. Attitude control which enables directional drilling for the efficient placement of the directional drilling tools in petroleum producing zones is reviewed along with the various engineering requirements or constraints. This thesis explores a multivariable attitude governing plant model as formulated in Panchal et al. (2010) which is used for developing robust control techniques. An inherent input and measurement delay which accounts for the plant's dead-time is included in the design of the controllers. A Smith Predictor controller is developed for reducing the effect of this dead-time. The developed controllers are compared for performance and robustness using structured singular value analysis and also for their performance indicated by the transient response of the closed loop models. Results for the transient non-linear simulation of the proposed controllers are also presented. The results obtained indicate that the objectives are satisfactorily achieved

Wood wasp inspired space and earth drill

In this chapter, we explain why the low gravity encountered on Mars or on the Moon and the low mass of the probes, landers and rovers that carry drilling devices limit classical drilling techniques. Novel boring solutions optimised in mass and power consumption are thus needed for space applications. Biologists have identified the wood wasp, an insect that is capable of "drilling" into wood to lay its eggs. A low mass and low power system, like an insect, capable of drilling into wood is of the highest interest for planetary drilling and terrestrial drilling alike. The general working principle of the wood wasp drill ("dual reciprocating drilling") will be exposed and the potential benefits of imitating the wood wasp for planetary drilling will be highlighted. Since the nature of wood is highly fibrous but the nature of extraterrestrial and terrestrial soils are not, it is necessary to adapt the wood wasp ovipositor to our target soils. A test bench to evaluate the influence of the different geometries and operational parameters was produced and is presented here. The dual reciprocating drilling experimental results obtained on this test bench are also highlighted. They should lead to a new and enhanced model and comprehension of dual-reciprocating-drilling

Applying a modified Smith predictor-bilinear proportional plus integral control for directional drilling

Recently, a Bilinear Proportional plus Integral (BPI) controller was proposed for the control of directional drilling tools commonly used in the oil industry However, there are delays in the measurement signals which reduces the system performance. Here, the BPI controller is extended by addition of a modified Smith predictor. The effectiveness, robustness and stability of the proposed modified Smith Predictor (SP)-BPI controller are analysed. Transient simulations are presented and compared with that of the earlier BPI controller. From the results, it can be surmised that the proposed modified SP-BPI controller significantly reduces the adverse effects of disturbances and time delay on the feedback measurements with respect to stability and performance of the directional drilling tool

Unconventional gas: potential energy market impacts in the European Union

In the interest of effective policymaking, this report seeks to clarify certain controversies and identify key gaps in the evidence-base relating to unconventional gas. The scope of this report is restricted to the economic impact of unconventional gas on energy markets. As such, it principally addresses such issues as the energy mix, energy prices, supplies, consumption, and trade flows. Whilst this study touches on coal bed methane and tight gas, its predominant focus is on shale gas, which the evidence at this time suggests will be the form of unconventional gas with the most growth potential in the short- to medium-term. This report considers the prospects for the indigenous production of shale gas within the EU-27 Member States. It evaluates the available evidence on resource size, extractive technology, resource access and market access. This report also considers the implications for the EU of large-scale unconventional gas production in other parts of the world. This acknowledges the fact that many changes in the dynamics of energy supply can only be understood in the broader global context. It also acknowledges that the EU is a major importer of energy, and that it is therefore heavily affected by developments in global energy markets that are largely out of its control.JRC.F.3-Energy securit

Directional drilling attitude control with input disturbances and feedback delay

This paper presents a general approach for the attitude control of directional drilling tools for the oil and gas industry. It extends the recent work where a kinematic bilinear model of the directional drilling tool was developed and used as the basis for Constant Build Rate (CBR) controller design. The CBR controller in combination with a modified Smith Predictor (SP) is implemented for the attitude control of the directional drilling. The results of a transient simulation of the proposed modified SP-CBR controller are presented and compared with that from the CBR controller of the earlier studies. It is shown that the modified SP-CBR controller significantly reduces the adverse effects of input disturbances and time delay on the feedback measurements with respect to stability and performance