The main purpose of this contribution is the control of both torsional and axial vibrations occurring along a rotary oilwell drilling system. The model considered consists of a wave equation coupled to an ordinary differential equation (ODE) through a nonlinear function describing the rock-bit interaction. We propose a systematic method to design feedback controllers guaranteeing ultimate boundedness of the system trajectories and leading consequently to the suppression of harmful dynamics. The proposal of a Lyapunov-Krasovskii functional provides stability conditions stated in terms of the solution of a set of linear and bilinear matrix inequalities (LMIs, BMIs). Numerical simulations illustrate the efficiency of the obtained control laws.

The drill pipe model described by the wave equation with boundary conditions is reduced through the d'Alembert transformation to a difference equation model. Assuming that the boundary condition at the bottom is perturbed by bounded additive noise, an ultimate bound for the velocity at the bottom of the pipe is obtained. The proposal of a Lyapunov functional for the distributed model allows to provide an ultimate bound for a measure of the distributed variables describing the system in terms of linear matrix inequality conditions. The two approaches are compared through an illustrative example.

This paper presents the control design for the regulation and trajectory tracking tasks of the non-minimum phase output voltage of a DC-DC Boost-type power converter. The proposed approach exploits the differential flatness property of the system leading to a control strategy whose benefits include a simple derivation based on the parameterization of the control input and a zero steady-state error in the system response due to the establishment of predefined stable error dynamics. The main contribution of this paper is that the proposed controller is robust against power supply variations that may arise from the use of renewable energy sources. Furthermore, it is also robust against load variations that are normally related to energy consumption demands. These aspects are disregarded in most of the existing control techniques. A successful validation of the effectiveness of the flatness-based control system is carried out through numerical simulations and experimental tests performed in a built prototype of the system.