Tracking and estimation of bottom-hole unmeasured pressure states using a fuzzy observer

Abstract

This paper focuses on sustaining a constant bottomhole pressure, a widely used approach in Managed Pressure Drilling (MPD). MPD is a multifaceted, nonlinear process that uses various control methods for estimation and stabilization of the pressure at the bottom of the well. Applying the T–S fuzzy modeling method and the concept of parallel distributed compensation (PDC), an observer-based fuzzy controller is developed to ensure that the bottom-hole pressure tracks the desired target value without exceeding the pressure window, even in the presence of uncertainties and disturbances, such as pore and fracture pressures, while concurrently addressing cases where the system states are inaccessible. To accomplish this, an observer is developed using estimated antecedent variables to address practical challenges. To begin, the wellbore model is introduced, followed by the use of the T–S fuzzy model (TSFM) approach to represent the precise dynamics of the wellbore’s nonlinear system. Next, a tracking controller based on PDC is employed to achieve the control objectives. The Lyapunov method, together with the $H_{\infty }$ criterion, ensures the stability of the controlled wellbore system, with sufficient criteria established through an LMI optimization process. The results of the simulation reveal the improvement and merits of the proposed observer-based controller.