Stick-slip vibrations decrease the performance, reliability, and fail safety of drilling systems. The aim of this paper is to design a robust output-feedback control approach to eliminate torsional stick-slip vibrations in drilling systems. Current industrial controllers regularly fail to eliminate stick-slip vibrations, especially when multiple torsional flexibility modes play a role in the onset of stick-slip vibrations. As a basis for controller synthesis, a multimodal model of the torsional dynamics for a real drill-string system is employed. The proposed controller design strategy is based on skewed-μ DK iteration and aims at optimizing the robustness with respect to uncertainty in the nonlinear bit-rock interaction. Moreover, a closed-loop stability analysis for the nonlinear drill-string model is provided. This controller design strategy offers several benefits compared with existing controllers. First, only surface measurements are employed, therewith avoiding the need for down-hole measurements. Second, multimodal drill-string dynamics are effectively dealt with in ways inaccessible to state-of-practice controllers. Third, robustness with respect to uncertainties in the bit-rock interaction is explicitly provided and closed-loop performance specifications are included in the controller design. Case study results confirm that stick-slip vibrations are indeed eliminated in realistic drilling scenarios using the designed controller in which state-of-practice controllers fail to achieve this.

The comparison between time-varying hybrid trajectories is crucial for tracking, observer design and synchronisation problems for hybrid systems with state-triggered jumps. In this paper, a generic distance function is designed that can be used for this purpose. The so-called “peaking phenomenon”, which occurs when using the Euclidean distance to compare two hybrid trajectories, is circumvented by taking the hybrid nature of the system explicitly into account. Based on the proposed distance function, we define the stability of a trajectory and present sufficient Lyapunov-type conditions for hybrid system with state-triggered jumps. A constructive Lyapunov function design is presented for hybrid systems with affine flow and jump maps and a jump set that is a hyperplane. The stability conditions can then be verified using linear matrix conditions. Finally, for this class of systems, we present a tracking controller that asymptotically stabilises a given hybrid reference trajectory and we illustrate our results with an example.

This paper addresses the controlled synchronization problem of mechanical systems subjected to a geometric unilateral constraint as well as the design of a switching coupling law to obtain synchronization. To define the synchronization problem, we propose a distance function induced by the quotient metric, which is based on an equivalence relation using the impact map. A Lyapunov function is constructed to investigate the synchronization problem for two identical one-dimensional mechanical systems. Sufficient conditions for the individual systems and their controlled interaction are provided under which synchronization can be ensured. We present a (coupling) control law which ensures global synchronization, also in the presence of grazing trajectories and accumulation points (Zeno behavior). The results are illustrated using a numerical example.

This paper proposes feedback control strategies for the mitigation of torsional stick-slip oscillations in drilling systems using drag bits. Herein, we employ a model for the coupled axial-torsional drill-string dynamics in combination with a rate-independent bit-rock interaction law including both cutting and frictional effects. Using a singular perturbation and averaging approach, we show that the dynamics of this model generate an apparent velocity-weakening effect in the torque-on-bit, explaining the onset of torsional stick-slip vibrations. Based on this dynamic analysis, the (decoupled) torsional dynamics can be described by a delay-differential equation with a state-dependent delay. Using this model, we propose both state-and output-feedback control strategies for the mitigation of torsional stick-slip oscillations, where the latter strategy uses surface measurements only. The effectiveness of the proposed approaches is shown in a simulation study.

To enable access to unconventional reservoirs of oil and (shale-) gas, geothermal energy and minerals, complex curved boreholes need to be drilled in the earth's crust. Directional drilling techniques, incorporating down-hole robotic actuation systems called rotary steerable systems, are used to generate these curved boreholes. In practice, however, boreholes drilled with such systems often show instability-induced borehole spiraling, which negatively affects the borehole quality and increases drag losses while drilling. As a basis for controller synthesis, we present a directional drilling model in terms of delay differential equations. Next, the problem of curved well-bore generation is formulated as a tracking problem and a model-based robust control strategy is developed, solving this tracking problem while guaranteeing the prevention of borehole spiraling. The effectiveness of the proposed approach is illustrated by representative case studies for the generation of curved boreholes.

In this paper, a novel distributed consensus control approach for vehicular platooning systems is proposed. In formalizing the underlying consensus problem, a realistic vehicle dynamics model is considered and a velocity-dependent spacing-policy between two consecutive vehicles is realized. For a generic communication topology, conditions for asymptotic platoon stability are proposed. As a particular case, these results allow to consider bi-directional vehicle interaction, which improves the coherence between the vehicles in the platoon. The theoretical results are experimentally validated using a three-vehicle platoon consisting of (longitudinally) automated vehicles equipped with wireless inter-vehicle communication and radar-based sensing.

In this paper, we consider active trailer steering control as a means to improve the maneuverability of (long) truck-trailer combinations during cornering. Hereto, we formulate the problem of reducing the so-called swept path width during cornering and that of eliminating unsafe tail swing of the trailer as a tracking control problem. We present a kinematic tractor-trailer model including off-axle hitching, on the basis of which we design nonlinear control strategies solving this tracking problem. The effectiveness of the proposed approach is evidenced experimentally on a robotic tractor-trailer platform.

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.

Directional drilling systems generate complex curved boreholes in the earth's crust for the exploration and harvesting of oil, gas and geothermal energy. In practice, boreholes drilled with such systems often show instability-induced borehole spiraling, which negatively affects the borehole quality and increases drag losses while drilling. This paper presents a dynamic state-feedback controller design approach for the stable generation of complex, three-dimensional borehole geometries, while avoiding undesired borehole spiraling. The design is based on a model for three-dimensional borehole propagation in terms of nonlinear delay differential equations. After casting the problem of borehole propagation into a tracking problem, it is shown that complex, three-dimensional borehole geometries can be asymptotically stabilized with the proposed controller. The effectiveness of the proposed approach is evidenced in an illustrative benchmark study.

A reset integral controller is discussed that induces improved low-frequency disturbance rejection properties under double integrator control without giving the unwanted increase of overshoot otherwise resulting from adding an extra linear integrator. To guarantee closed-loop stability, a (conditional) reset condition is used that restricts the input-output behavior of the dynamic reset element to a [0,α]-sector with α a positive (finite) gain. As a result, stability can be guaranteed on the basis of a circle criterion-like argument and checked through (measured) frequency response data. Both stability and performance of the control design will be discussed via measurement results obtained from a wafer stage system of an industrial wafer scanner.

It is well-known that fundamental performance limitations exist when using linear feedback control for linear systems. In this note, we present an example of a nonlinear control strategy that can achieve a time-domain performance specification that cannot be obtained by any linear controller. In particular, we present a variable-gain control approach that meets an overshoot requirement that cannot be met by any linear controller.

The analysis of incremental stability properties typically involves measuring the distance between any pair of solutions of a given dynamical system, corresponding to different initial conditions, at the same time instant. This approach is not directly applicable for hybrid systems in general. Indeed, hybrid systems generate solutions that are defined with respect to hybrid times, which consist of both the continuous time elapsed and the discrete time, that is the number of jumps the solution has experienced. Two solutions of a hybrid system do not a priori have the same time domain, and we may therefore not be able to compare them at the same hybrid time instant. To overcome this issue, we invoke graphical closeness concepts. We present definitions for incremental stability depending on whether incremental asymptotic stability properties hold with respect to the hybrid time, the continuous time, or the discrete time, respectively. Examples are provided throughout the paper to illustrate these definitions, and the relations between these three incremental stability notions are investigated. The definitions are shown to be consistent with those available in the literature for continuous-time and discrete-time systems.

Active trailer steering control can improve the manoeuvrability of (long) truck-trailer combinations during cornering. To assess the effectiveness of trailer steering control, we formulate the problem of reducing the so-called swept-path width during cornering, and that of eliminating unsafe tail swing of the trailer, as a tracking control problem. We present a kinematic tractor-trailer model including off-axle hitching, on the basis of which nonlinear control strategies solving this tracking problem are developed. The effectiveness of the proposed approach is evidenced by means of a benchmark simulation study.

In this paper, a structure-preserving model reduction approach for a class of nonlinear delay differential equations with time-varying delays is proposed. Benefits of this approach are, firstly, the fact that the delay nature of the system is preserved after reduction, secondly, that input-output stability properties are preserved and, thirdly, that a computable error bound reflecting the accuracy of the reduction is provided. These results are also applicable to large-scale linear delay differential equations with constant delays. The effectiveness of the results is evidenced by means of an illustrative example involving the nonlinear delayed dynamics of the turning process.