Nathan van de Wouw

Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance

There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.

Design and experimental evaluation of cooperative adaptive cruise control

Road throughput can be increased by driving at small inter-vehicle time gaps. The amplification of velocity disturbances in upstream direction, however, poses limitations to the minimum feasible time gap. String-stable behavior is thus considered an essential requirement for the design of automatic distance control systems, which are needed to allow for safe driving at time gaps well below 1 s. Theoretical analysis reveals that this requirement can be met using wireless inter-vehicle communication to provide real-time information of the preceding vehicle, in addition to the information obtained by common Adaptive Cruise Control (ACC) sensors. In order to validate these theoretical results and to demonstrate the technical feasibility, the resulting control system, known as Cooperative ACC (CACC), is implemented on a test fleet consisting of six passenger vehicles. Experiments clearly show that the practical results match the theoretical analysis, thereby indicating the possibilities for short-distance vehicle following.

Stability and Convergence of Mechanical Systems with Unilateral Constraints

Stability of motion is a central theme in the dynamics of mechanical systems. While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book starts with the treatise of the mathematical background on non-smooth analysis, measure and integration theory and an introduction to the field of non-smooth dynamical systems. The unilateral constraints are modelled in the framework of set-valued force laws developed in the field of non-smooth mechanics. The embedding of these constitutive models in the dynamics of mechanical systems gives rises to dynamical models with impulsive phenomena. This book uses the mathematical framework of measure differential inclusions to formalise such models. The book proceeds with the presentation of stability results for measure differential inclusions. These stability results are then applied to nonlinear mechanical systems with unilateral constraints. The book closes with the study of the convergence property for a class of measure differential inclusions; a stability property for systems with time-varying inputs which is shown to be highly instrumental in the context of the control of mechanical systems with unilateral constraints. While the book presents a profound stability theory for mechanical systems with unilateral constraints, it also has a tutorial value on the modelling of such systems in the framework of measure differential inclusions. The work will be of interest to engineers, scientists and students working in the field of non-smooth mechanics and dynamics.

Lp String Stability of Cascaded Systems: Application to Vehicle Platooning

Nowadays, throughput has become a limiting factor in road transport. An effective means to increase the road throughput is to employ a small intervehicle time gap using automatic vehicle-following control systems. String stability, i.e., the disturbance attenuation along the vehicle string, is considered an essential requirement for the design of those systems. However, the formal notion of string stability is not unambiguous in literature, since both stability and performance interpretations exist. Therefore, a novel definition for string stability of nonlinear cascaded systems is proposed, using input-output properties. This definition is shown to result in well-known string stability conditions for linear cascaded systems. The theoretical results are experimentally validated using a platoon of six passenger vehicles equipped with cooperative adaptive cruise control.

Controller Synthesis for String Stability of Vehicle Platoons

Cooperative adaptive cruise control (CACC) allows for short-distance automatic vehicle following using intervehicle wireless communication in addition to onboard sensors, thereby potentially improving road throughput. In order to fulfill performance, safety, and comfort requirements, a CACC-equipped vehicle platoon should be string stable, attenuating the effect of disturbances along the vehicle string. Therefore, a controller design method is developed that allows for explicit inclusion of the string stability requirement in the controller synthesis specifications. To this end, the notion of string stability is introduced first, and conditions for L2 string stability of linear systems are presented that motivate the development of an H∞ controller synthesis approach for string stability. The potential of this approach is illustrated by its application to the design of controllers for CACC for one- and two-vehicle look-ahead communication topologies. As a result, L2 string-stable platooning strategies are obtained in both cases, also revealing that the two-vehicle look-ahead topology is particularly effective at a larger communication delay. Finally, the results are experimentally validated using a platoon of three passenger vehicles, illustrating the practical feasibility of this approach.

Uniform Output Regulation of Nonlinear Systems

The problem of asymptotic regulation of the output of a dynamical system plays a central role in control theory. An important variant of this problem is the output regulation problem, which can be used in such areas as set-point control, tracking reference signals and rejecting disturbances generated by an external system, controlled synchronization of dynamical systems, and observer design for autonomous systems. This book is one of the first systematic studies on the nonlinear output regulation problem that embraces both the local and global solvability analysis, covering such aspects as solvability conditions, controller design, and practical implementation issues. The book opens with the development of the mathematical apparatus of convergent systems—very useful for studying nonlinear control systems—laying the foundation for most of the results presented in the work. The study then proceeds to a new problem statement—the so-called uniform output regulation problem. A comprehensive solvability analysis of this problem is provided in the next part of the work. Based on the solvability analysis, constructive controller design methods for the global uniform output regulation problem are presented for various classes of nonlinear systems. In an attempt to bridge the gap between theory and practice, the authors conclude with a presentation of an experimental case study. The experiment—one of the first in the field of nonlinear output regulation—deals with control of a translational oscillator with a rotational actuator, illustrating the applicability of the nonlinear output regulation theory in experiments and raising a number of questions to be addressed in future research. The scope of questions addressed in the book, the uniformity of their treatment, the novelty of the proposed approach, and the obtained results make this volume unique with respect to other works on the problem of nonlinear output regulation. In addition to being an excellent reference for the uniform output regulation problem, the book has a tutorial value on convergent systems. The work will be of interest to control engineers, theorists, and students, and may be used as a textbook for a graduate course on nonlinear control.

Nonlinear drillstring dynamics analysis

This paper studies the dynamical response of a rotary drilling system with a drag bit, using a lumped parameter model that takes into consideration the axial and torsional vibration modes of the bit. These vibrations are coupled through a bit-rock interaction law. At the bit-rock interface, the cutting process introduces a state-dependent delay, while the frictional process is responsible for discontinuous right-hand sides in the equations governing the motion of the bit. This complex system is characterized by a fast axial dynamics compared to the slow torsional dynamics. A dimensionless formulation exhibits a large parameter in the axial equation, enabling a two-time-scales analysis that uses a combination of averaging methods and a singular perturbation approach. An approximate model of the decoupled axial dynamics permits us to derive a pseudoanalytical expression of the solution of the axial equation. Its averaged behavior influences the slow torsional dynamics by generating an apparent velocity weakening friction law that has been proposed empirically in earlier work. The analytical expression of the solution of the axial dynamics is used to derive an approximate analytical expression of the velocity weakening friction law related to the physical parameters of the system. This expression can be used to provide recommendations on the operating parameters and the drillstring or the bit design in order to reduce the amplitude of the torsional vibrations. Moreover, it is an appropriate candidate model to replace empirical friction laws encountered in torsional models used for control.

Stability Analysis of Networked Control Systems Using a Switched Linear Systems Approach

In this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, and communication constraints. Communication constraints impose that, per transmission, only one node can access the network and send its information. The order in which nodes send their information is orchestrated by a network protocol, such as, the Round-Robin (RR) and the Try-Once-Discard (TOD) protocol. In this paper, we generalize the mentioned protocols to novel classes of so-called “periodic” and “quadratic” protocols. By focusing on linear plants and controllers, we present a modeling framework for NCSs based on discrete-time switched linear uncertain systems. This framework allows the controller to be given in discrete time as well as in continuous time. To analyze stability of such systems for a range of possible transmission intervals and delays, with a possible nonzero lower bound, we propose a new procedure to obtain a convex overapproximation in the form of a polytopic system with norm-bounded additive uncertainty. We show that this approximation can be made arbitrarily tight in an appropriate sense. Based on this overapproximation, we derive stability results in terms of linear matrix inequalities (LMIs). We illustrate our stability analysis on the benchmark example of a batch reactor and show how this leads to tradeoffs between different protocols, allowable ranges of transmission intervals and delays. In addition, we show that the exploitation of the linearity of the system and controller leads to a significant reduction in conservatism with respect to existing approaches in the literature.

Formation control of unicycle mobile robots: a virtual structure approach

In this paper, the formation control problem for unicycle mobile robots is studied. A virtual structure control strategy with mutual coupling between the robots is proposed. The rationale behind the introduction of the coupling terms is the fact that these introduce additional robustness with respect to perturbations as compared to typical leader-follower approaches. The applicability of the proposed approach is shown in experiments with a group of mobile robots controlled over a wireless communication network.

String stability of interconnected vehicles under communication constraints

In this paper, we present a novel modelling and string stability analysis method for an interconnected vehicle string in which information exchange takes place via wireless communication. The usage of wireless communication introduces time-varying sampling intervals, delays, and communication constraints of which the impact on string stability requires a careful analysis. In particular, we study a Cooperative Adaptive Cruise Control (CACC) system which regulates inter-vehicle distances in a vehicle string and utilizes information exchange between vehicles through wireless communication in addition to local sensor measurements. The propagation of disturbances through the interconnected vehicle string is inspected by using the notion of so-called string stability which is formulated here in terms of an ℒ2-gain requirement from disturbance inputs to controlled outputs. This paper provides conditions on the uncertain sampling intervals and delays under which string stability can still be guaranteed. These results support the design of CACC systems that are robust to uncertainties introduced by wireless communication.