Bottom hole pressure control for oil well drilling using model reference adaptive control

Reducing Overparametrization in MRAC for Hyperbolic PDEs

“…The MRAC controller from [1] is employed in [2] for controlling the bottom hole pressure (BHP) in managed pressure drilling (MPD). MPD is a technique that enables pressure control in wells with narrow pressure windows and varying formation pressures [3].…”

“…Although the problem investigated in this paper, formally stated in Section II, is motivated from BHP control in MPD, the problem is in Section III solved for a more general class of 2 × 2 systems of hyperbolic PDEs. The derived controller is then applied to the BHP control in MPD in section VI, and compared to the overparameterized control design previously presented in [2]. Some concluding remarks are offered in Section VII.…”

“…Now that we have a system in the proper form, we can see that most of the system parameters (37) depend nonlinearly on the uncertain parameter F . It is possible to use the method proposed in [1] directly, which was what was done in [2]. However, treating the coefficients (37) as completely unknown functions of x leads to severe overparameterization.…”

“…The method from [2] was also implemented for comparison, using the same adaptation gains. The initial parameter estimates for the method from [2] were set to values corresponding to the initial value of ν, that is ν = ν 0 . 1) Case 1: The initial guess for ν was in this case set to 1.0, corresponding to a friction factor F =F .…”