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

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

Linear feedback control of transient energy growth and control performance limitations in subcritical plane Poiseuille flow

Suppression of the transient energy growth in subcritical plane Poiseuille flow via feedback control is addressed. It is assumed that the time derivative of any of the velocity components can be imposed at the walls as control input, and that full-state information is available. We show that it is impossible to design a linear state-feedback controller that leads to a closed-loop flow system without transient energy growth. In a subsequent step, full-state feedback controllers -- directly targeting the transient growth mechanism -- are designed, using a procedure based on a Linear Matrix Inequalities approach. The performance of such controllers is analyzed first in the linear case, where comparison to previously proposed linear-quadratic optimal controllers is made; further, transition thresholds are evaluated via Direct Numerical Simulations of the controlled three-dimensional Poiseuille flow against different initial conditions of physical interest, employing different velocity components as wall actuation. The present controllers are effective in increasing the transition thresholds in closed loop, with varying degree of performance depending on the initial condition and the actuation component employed

Bilinear modelling and bilinear PI control of directional drilling

This paper presents the design of an inclination- and azimuth-hold controllers and their subsequent stability and performance analysis for directional drilling tools as typically used in the oil industry. Using an input transformation developed in earlier work that partially linearizes and decouples the plant dynamics of the directional drilling tool, a bilinear model of the directional drilling tool is developed and is used as the basis for Bilinear PI controller design. Results for a transient simulation of the proposed BPI controller are presented and compared with that of the PI controller of the earlier work. It is presented that BPI controller gives more consistent responses over a broader operating range compared to the PI controller. In addition, the effect of time delay on the feedback measurements with respect to the stability and performance is investigated in the simulations

Quasi-bilinear modelling and control of directional drilling

A quasi-bilinear proportional-plus-integral (QBPI) controller is proposed for the attitude control of directional drilling tools for the oil and gas industry; and it is designed based on the proposed quasi-bilinear model of the directional drilling tool. The quasi-bilinear model accurately depicts the nonlinear characteristics of the directional drilling tool to a greater extent than the existing linear model, thus extends the scope of appropriate performance. The proposed QBPI control system is an LTI system and it is shown to be exponentially stable. The proposed QBPI controller outstandingly diminishes the deleterious impact of disturbances and measurement delay regarding to performance and stability of the directional drilling tool, and it yields invariant azimuth responses. Drilling cycle scheme which captures the drilling cycle and toolface actuator dynamics of the directional drilling tool, is developed. The servo-velocity and servo-position loops of the toolface servo-control architecture are proven to be robustly stable using Kharitonov's Theorem

A robust controller design method for feedback substitution schemes using genetic algorithms

Controllers for feedback substitution schemes demonstrate a trade-off between noise power gain and normalized response time. Using as an example the design of a controller for a radiometric transduction process subjected to arbitrary noise power gain and robustness constraints, a Pareto-front of optimal controller solutions fulfilling a range of time-domain design objectives can be derived. In this work, we consider designs using a loop shaping design procedure (LSDP). The approach uses linear matrix inequalities to specify a range of objectives and a genetic algorithm (GA) to perform a multi-objective optimization for the controller weights (MOGA). A clonal selection algorithm is used to further provide a directed search of the GA towards the Pareto front. We demonstrate that with the proposed methodology, it is possible to design higher order controllers with superior performance in terms of response time, noise power gain and robustness

A robust controller design method for feedback substitution schemes using genetic algorithms

Controllers for feedback substitution schemes demonstrate a trade-off between noise power gain and normalized response time. Using as an example the design of a controller for a radiometric transduction process subjected to arbitrary noise power gain and robustness constraints, a Pareto-front of optimal controller solutions fulfilling a range of time-domain design objectives can be derived. In this work, we consider designs using a loop shaping design procedure (LSDP). The approach uses linear matrix inequalities to specify a range of objectives and a genetic algorithm (GA) to perform a multi-objective optimization for the controller weights (MOGA). A clonal selection algorithm is used to further provide a directed search of the GA towards the Pareto front. We demonstrate that with the proposed methodology, it is possible to design higher order controllers with superior performance in terms of response time, noise power gain and robustness