The filtered split-path nonlinear integrator (F-SPANI) is a generic nonlinear controller designed to improve the transient performance of linear (motion) systems in terms of overshoot. The main idea underlying F-SPANI is that the amplitude and phase of an integrator can be tuned using independent filters, resulting in more efficient use of the buffer of the integrator. In this article, a general description of F-SPANI is presented. In addition, a stability analysis result is presented that provides sufficient conditions in the form of linear matrix inequalities (LMIs) for closed-loop stability analysis on the basis of construction of a common quadratic Lyapunov function (CQLF). The ease of the design, implementation, and the potential of the proposed controller are illustrated both in simulations and in experiments on an industrial pick-and-place machine.

A microgrid in the islanded mode is considered where a fleet of fuel cell cars is used as a distributed power generation system. The objective of the proposed control system is to minimize the operational cost of the system, subject to the physical and operational constraints of the system. In order to deal with uncertainty in the prediction of the microgrid's load, two model predictive control methods, a min-max (MM) approach and disturbance feedback MM approach, are proposed. We develop three distributed control algorithms and we show that by using these algorithms, the driving patterns of the fuel cell cars can be kept private. In other words, no privacy sensitive data on the usage of the cars are collected by a central control agent. Numerical case studies are presented to demonstrate the excellent performance of the proposed control methods.

Cooperative adaptive cruise control (CACC) is a potential solution to decrease traffic jams caused by shock waves, increase the road capacity, decrease fuel consumption and improve safety. This paper proposes an integrated solution to a combination of four challenges in these CACC systems. One of the technological challenges is how to guarantee string stability (the ability to avoid amplification of dynamic vehicle responses along the string of vehicles) under nominal operational conditions. The second challenge is how to apply this solution to heterogeneous vehicles. The third challenge is how to maintain confidentiality of the vehicle parameters. Finally, the fourth challenge is to find a method which improves robustness against wireless packet loss. This paper proposes a model predictive control approach in combination with a feed-forward control design, which is based on a shared vector of predicted accelerations over a finite time horizon. This approach is shown to be applicable to a heterogeneous sequence of vehicles, while the vehicle parameters remain confidential. In previous works such an approach has shown to increase robustness against packet losses. Conditions for string stability are presented for the nominal operational conditions. Experimental results are presented and indeed demonstrate string stable behavior.

Shimmy oscillations are undesired vibrations in aircraft landing gears. In this chapter, the onset of shimmy vibrations, marked by Hopf bifurcations, is investigated in the parameter space of high-fidelity, flexible multibody landing gear models. Such a bifurcation analysis is performed by combining the Virtual.Lab Motion multibody solver with the numerical continuation software AUTO. The resulting quasi-2-parameter bifurcation diagrams, involving aircraft velocity and normal load, are verified using conventional time-simulation methods and are shown to be computationally more efficient. A sensitivity study reveals the influence of design parameters, such as the shimmy damping coefficient, mechanical trail, and steering actuator stiffness, on the occurrence of shimmy.

Sensitivity analysis for hybrid systems with state-triggered jumps is experiencing renewed attention for the control of robots with intermittent contacts. The basic assumption that enables this type of analysis is that jumps are triggered when the state reaches, transversally, a sufficiently smooth switching surface. In many scenarios of practical relevance, however, this switching surface is just piecewise smooth and, moreover, a perturbation of the initial conditions or the input leads to a different number of jumps than the nominal trajectory's. This work extends the sensitivity analysis in this context, under the assumptions that (i) at least locally, the intermediate perturbation-dependent jumps lead the system to reach always the nominal post-impact mode and (ii) once a switching and corresponding intermediate jump has occurred, its corresponding constraint remains active until reaching the nominal post-impact mode. Numerical simulations complement and validate the theoretical findings.

We consider a distributed axial-torsional drill-string model with a rate-independent bit-rock interaction law to study the occurrence and non-local characteristics of axial and torsional self-excited vibrations as caused by the regenerative effect. A first contribution of the paper is the derivation of a non-dimensional version of the full non-linear distributed drill-string–bit-rock interaction model and showing how it relates to the minimal set of characteristic quantities. Using this model the study shows how multiple axial modes of the drill-string are excited, or attenuated, depending on the bit rotation rate. This indicates that a lumped drill-string model approximation is insufficient for the general case. Then, a comprehensive simulation study is performed to create a stability map for the occurrence of stick-slip oscillations. In particular, the significance of the axial topside boundary condition, i.e., constant velocity vs. constant hook-load, is evaluated. A central finding is that increasing the axial loop gain (determined by the bit-rock parameters) tends to both increase the area of stable torsional dynamics and increase the rate of penetration for a constant imposed weight on bit. This also corresponds to a more severe axial instability.

The analysis of incremental stability typically involves measuring the distance between any two solutions of a given dynamical system at the same time instant, which is problematic when studying hybrid dynamical systems. Indeed, hybrid systems generate solutions defined with respect to hybrid time instances (that consists of both the continuous time elapsed and the discrete time, which is the number of jumps experienced so far), and two solutions of the same hybrid system may not be defined at the same hybrid time instant. To overcome this issue, we present novel definitions of incremental stability for hybrid systems based on graphical closeness of solutions. As we will show, defining incremental asymptotic stability with respect to the hybrid time yields a restrictive notion, such that we also investigate incremental asymptotic stability notions with respect to the continuous time only or the discrete time only, respectively. In this manner, two (effectively dual) incremental stability notions are attained, called jump- and flow incremental asymptotic stability. To present Lyapunov conditions for these two notions, in both cases, we resort to an extended hybrid system and we prove that the stability of a well-defined set for this extended system implies incremental stability of the original system. We can then use available Lyapunov conditions to infer the set stability of the extended system. Various examples are provided throughout this paper, including an event-triggered control application and a bouncing ball system with Zeno behavior, that illustrate incremental stability with respect to continuous time or discrete time, respectively.

This paper addresses the synchronization problem of mechanical systems subjected to a single geometric unilateral constraint. The impacts of the individual systems, induced by the unilateral constraint, generally do not coincide even if the solutions are arbitrarily ‘close’ to each other. The mismatch in the impact time instants demands a careful choice of the distance function to allow for an intuitively correct comparison of the discontinuous solutions resulting from the impacts. We propose a distance function induced by the quotient metric, which is based on an equivalence relation using the impact map. The distance function obtained in this way is continuous in time when evaluated along jumping solutions. The property of maximal monotonicity, which is fulfilled by most commonly used impact laws, is used to significantly reduce the complexity of the distance function. Based on the simplified distance function, a Lyapunov function is constructed to investigate the synchronization problem for two identical one-dimensional mechanical systems. Sufficient conditions for the uncoupled individual systems are provided under which local synchronization is guaranteed. Furthermore, we present an interaction law which ensures global synchronization, also in the presence of grazing trajectories and accumulation points (Zeno behavior). The results are illustrated using numerical examples of a 1-DOF mechanical impact oscillator which serves as stepping stone in the direction of more general systems.

In this paper, we introduce a variable-gain control strategy for mechanical ventilators in the respiratory systems. Respiratory systems assist the patients who have difficulty breathing on their own. For the comfort of the patient, fast pressure buildup (and release) and a stable flow response are desired. However, linear controllers typically need to balance between these conflicting objectives. In order to balance this tradeoff in a more desirable manner, a variable-gain controller is proposed, which switches the controller gain based on the magnitude of the patient flow. The effectiveness of the control strategy is demonstrated in experiments on different test lungs.

This paper involves the dynamic (stability) analysis of distributed drill-string systems. A minimal set of parameters characterizing the linearized, axial-torsional dynamics of a distributed drill string coupled through the bit-rock interaction is derived. This is found to correspond to five parameters for a simple drill string and eight parameters for a two-sectioned drill-string (e.g., corresponding to the pipe and collar sections of a drilling system). These dynamic characterizations are used to plot the inverse gain margin of the system, parametrized in the non-dimensional parameters, effectively creating a stability map covering the full range of realistic physical parameters. This analysis reveals a complex spectrum of dynamics not evident in stability analysis with lumped models, thus indicating the importance of analysis using distributed models. Moreover, it reveals trends concerning stability properties depending on key system parameters useful in the context of system and control design aiming at the mitigation of vibrations.

This paper introduces a robust observer-based output feedback control strategy that enables the generation of complex three-dimensional borehole trajectories created by directional drilling systems, while avoiding undesired transient behavior. The model-based controller relies on a set of nonlinear delay differential equations describing the borehole evolution. Herein, only local orientation measurements of the bottom hole assembly of the drilling system are employed. Controller and observer gains are synthesized by optimizing the location of the rightmost pole of the closed-loop dynamics, using a spectral approach for delay differential equations. Moreover, the strategy is extended to cope with the uncertainty of key system parameters in the directional drilling process. The effectiveness of the designed controller is tested in an illustrative benchmark study.

In this paper, we introduce a switching control strategy for mechanical ventilators in medical respiratory systems. Respiratory systems assist patients that have difficulty breathing on their own. For the comfort of the patient, fast pressure buildup (and release), and a stable flow response are desired. However, linear controllers typically need to balance between these conflicting objectives. In order to balance this trade-off in a more desirable manner, a switching controller is proposed, that switches the controller gain based on the magnitude of the patient flow. The effectiveness of the control strategy is demonstrated in a model-based simulation study.

Extremum-seeking control is a useful tool for the steady-state performance optimization of plants for which the dynamics and disturbance situation can be unknown. The case when steady-state plant outputs are constant received a lot of attention, however, in many applications time-varying outputs characterize plant performance. As a result, no static parameter-to-steady-state performance map can be obtained. In this work, an extremum-seeking control method is proposed that uses a so-called dynamic cost function to cope with these time-varying outputs. We show that, under appropriate conditions, the solutions of the extremum-seeking control scheme are uniformly ultimately bounded in view of bounded and time-varying external disturbances, and the region of convergence towards the optimal tunable plant parameters can be made arbitrarily small. Moreover, its working principle is illustrated by means of the performance optimal tuning of a variable-gain controller for a motion control application.

In this paper, we consider synchronization of dynamical systems interconnected via nonlinear integral coupling. Integral coupling allows one to achieve synchronization with lower interaction levels (coupling gains) than with linear coupling. Previous results on this topic were obtained for synchronization of several systems with all-to-all interconnections. In this paper, we relax the requirement of all-to-all interconnections and provide two results on exponential synchronization under nonlinear integral coupling for networks with topologies different from all-to-all interconnections. In particular, we provide a high-gain result for an arbitrary interconnection topology and a non-high-gain method for analysis of synchronization for specific topologies. The results are illustrated by simulations of Hindmarsh-Rose neuron oscillators.

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.

Automated Managed Pressure Drilling (MPD) is a method for fast and accurate pressure control in drilling operations. The achievable performance of automated MPD is limited, firstly, by the control system and, secondly, by the hydraulics model based on which this control system is designed. Hence, an accurate hydraulics model is needed that, at the same time, is simple enough to allow for the use of high performance controller design methods. This paper presents an approach for nonlinear Model Order Reduction (MOR) for MPD systems. For a single-phase flow MPD system, a nonlinear model is derived that can be decomposed into a feedback interconnection of a high-order linear subsystem and low-order nonlinear subsystem. This structure, under certain conditions, allows for a nonlinear MOR procedure that preserves key system properties such as stability and provides a computable error bound. The effectiveness of this MOR method for MPD systems is illustrated through simulations.

Small inter-vehicle distances can increase traffic throughput on highways. Human drivers are not able to drive safely under such conditions. To this aim, cooperative adaptive cruise control (CACC) systems have been developed, which require vehicles to communicate with each other through a wireless communication network. By communicating control-relevant information, the vehicles equipped with the CACC system are able to react more quickly to disturbances caused by preceding vehicles and, therefore, are able to maintain the desired (small) inter-vehicle distance while avoiding string instability. String stability relates to the propagation of the effect of disturbance on system states over the vehicle string. Commonly used approaches to design controllers yielding string stability, involve an iterative process requiring an a priori designed controller with a priori defined communication topology. The main contribution of this paper is to propose a synthesis strategy for both local controllers and the communication structure, while guaranteeing string stability for infinite-length vehicular strings. The obtained results are illustrated by model-based case studies.

To improve traffic throughput, Cooperative Adaptive Cruise Control (CACC) has been proposed as a solution. The usage of Vehicle-to-Vehicle (V2V) communication enables short following distances, thereby increasing road capacity and fuel reduction (especially for trucks). Control designs for CACC use the wirelessly communicated intended acceleration of a preceding vehicle as a feedforward action in a following vehicle. This feedforward action may determine approximately 80% of the total control action. In case of a communication failure, this feedforward is no longer available, and a larger time gap is needed to ensure high performance and robustness in terms of stability and safety. However, such a larger time gap is not instantly realizable. Therefore, a CACC design is needed which is robust against intermittent communication failures. This paper proposes to share model-based predictions of the intended acceleration via V2V communication, which are stored in a buffer of the following vehicle. This buffer is used in case a packet dropout occurs. Further, since the communication frequency is lower than the frequency of the control-platform, this buffer is also used to virtually upgrade the communication frequency. The design has been tested in experimental vehicles and shows an increased control performance, also in periods of packet dropouts.