Torsional stick-slip vibrations decrease the performance, reliability and fail-safety of drilling systems used for the exploration and harvesting of oil, gas, min- erals and geo-thermal energy. Current industrial controllers regularly fail to eliminate stick-slip vibrations, especially when multiple torsional flexibility modes in the drill- string dynamics play a role in the onset of stick-slip vibrations. This chapter presents the experimental validation of novel robust output-feedback controllers designed to eliminate stick-slip vibrations in the presence of multiple dominant torsional flexibility modes. For this purpose, a representative experimental test setup is designed, using a model of a real-life drilling rig as a basis. The model of the dynamics of the experimental setup can be cast in Lure-type form with set-valued nonlinearities representing an (uncertain) model for the complex bit-rock interaction and the interaction between the drill-string and the borehole. The proposed controller design strategy is based on skewed-m-DK-iteration and aims at optimizing the robustness with respect to uncertainty in the non-smooth bit-rock interaction. Moreover, a closed-loop stability analysis for the non-smooth drill-string model is provided. Experimental results confirm that stick-slip vibrations are indeed eliminated using the designed controller in realistic drilling scenarios in which state-of-practice controllers have failed to achieve the same.

In this paper, we present a method aiming at pattern prediction in networks of diffusively coupled nonlinear systems. Interconnecting several globally asymptotical stable systems into a network via diffusion can result in diffusion-driven instability phenomena, which may lead to pattern formation in coupled systems. Some of the patterns may co-exist which implies the multi-stability of the network. Multi-stability makes the application of common analysis methods, such as the direct Lyapunov method, highly involved. We develop a numerically efficient method in order to analyze the oscillatory behavior occurring in such networks. We show that the oscillations appear via a Hopf bifurcation and therefore display sinusoidal-like behavior in the neighborhood of the bifurcation point. This allows to use the describing function method in order to replace a nonlinearity by its linear approximation and then to analyze the system of linear equations by means of the multivariable harmonic balance method. The method cannot be directly applied to a network consisting of systems of any structure and here we present the multivariable harmonic balance method for networks with a general system's structure and dynamics.

In this paper, we introduce the split-path nonlinear integrator (SPANI) as a novel nonlinear filter designed to improve the transient performance of linear systems in terms of overshoot, while preserving good rise-time and settling behavior. In particular, this nonlinear controller targets the well-known trade-off induced by integral action, which removes steady-state errors due to constant external disturbances, but deteriorates transient performance in terms of increased overshoot. The rationale behind the proposed SPANI filter is to ensure that the integral action has, at all times, the same sign as the closed-loop error signal, which, as we will show, enables a reduction in overshoot thereby leading to an overall improved transient performance. The resulting closed-loop dynamics is modeled by a hybrid dynamical system, for which we provide sufficient Lyapunov-based conditions for stability. Furthermore, we illustrate the effectiveness, the design and the tuning of the proposed controller in a benchmark simulation study of an industrial pick-and-place machine.