van de N Nathan Wouw

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.

Controller synthesis for networked control systems

This paper presents a discrete-time model for networked control systems (NCSs) that incorporates all network phenomena: time-varying sampling intervals, packet dropouts and time-varying delays that may be both smaller and larger than the sampling interval. Based on this model, constructive LMI conditions for controller synthesis are derived, such that stabilizing state-feedback controllers can be designed. Besides the proposed controller synthesis conditions a comparison is made between the use of parameter-dependent Lyapunov functions and Lyapunov-Krasovskii functions for stability analysis. Several examples illustrate the effectiveness of the developed theory.

Prediction of regenerative chatter by modelling and analysis of high-speed milling

High-speed milling is widely used in the manufacturing industry. For the efficiency of the milling process, high demands on the material removal rate and the surface generation rate are posed. The process parameters, determining these two rates, are restricted by the occurrence of regenerative chatter. Chatter is an undesired instability phenomenon, which causes both a reduced product quality and rapid tool wear. In this paper, the milling process is modelled, based on dedicated experiments on both the material behaviour of the workpiece material and the machine dynamics. These experiments show that both the material properties and the machine dynamics are dependent on the spindle speed. Furthermore, a method for the prediction of the chatter boundaries is proposed and applied in order to predict the chatter boundaries as a function of process parameters, such as spindle speed and depth-of-cut, for spindle speed varying material and machine parameters. Finally, experiments are performed to estimate these chatter boundaries in practice. The modelled chatter boundaries are compared to the experimental results in order to validate the model and the stability analysis.

Cooperative adaptive cruise control: Network-aware analysis of string stability

In this paper, we consider a Cooperative Adaptive Cruise Control (CACC) system, which regulates intervehicle distances in a vehicle string, for achieving improved traffic flow stability and throughput. Improved performance can be achieved by utilizing information exchange between vehicles through wireless communication in addition to local sensor measurements. However, wireless communication introduces network-induced imperfections, such as transmission delays, due to the limited bandwidth of the network and the fact that multiple nodes are sharing the same medium. Therefore, we approach the design of a CACC system from a Networked Control System (NCS) perspective and present an NCS modeling framework that incorporates the effect of sampling, hold, and network delays that occur due to wireless communication and sampled-data implementation of the CACC controller over this wireless link. Based on this network-aware modeling approach, we develop a technique to study the so-called string stability property of the string, in which vehicles are interconnected by a vehicle following control law and a constant time headway spacing policy. This analysis technique can be used to investigate tradeoffs between CACC performance (string stability) and network specifications (such as delays), which are essential in the multidisciplinary design of CACC controllers. Finally, we demonstrate the validity of the presented framework in practice by experiments performed with CACC-equipped prototype vehicles.

Reconfigurable control of piecewise affine systems with actuator and sensor faults: Stability and tracking

A reconfigurable control approach for continuous-time piecewise affine (PWA) systems subject to actuator and sensor faults is presented. The approach extends the concept of virtual actuators and virtual sensors from linear to PWA systems on the basis of the fault-hiding principle that provides the underlying conceptual idea: the fault is hidden from the nominal controller and the fault effects are compensated. Sufficient linear matrix inequality (LMI) conditions for the existence of virtual actuators and virtual sensors are given that guarantee the recovery of closed-loop stability and the tracking of constant reference inputs. Since LMIs are efficiently solvable, this solution leads to a tractable computational algorithm that solves the reconfiguration problem. The approach is proven to be robust against model uncertainties and inaccurate fault diagnosis, and is evaluated using an example system of interconnected tanks.

Analysis of friction-induced limit cycling in an experimental drill-string system

In this paper, we aim for an improved understanding of the causes for torsional vibrations that appear in rotary drilling systems used for the exploration of oil and gas. For this purpose, an experimental drill-string setup is considered. In that system, torsional vibrations with and without stick-slip are observed in steady state. In order to obtain a predictive model, a discontinuous static friction model is proposed. The steady-state behavior of the drill-string system is analyzed both numerically and experimentally. A comparison of numerical and experimental bifurcation diagrams indicates the predictive quality of the model. Moreover, specific friction model characteristics can be linked to the existence of torsional vibrations with and without stick-slip.

Technical communique: On polytopic inclusions as a modeling framework for systems with time-varying delays

One of the important issues in networked control systems is the appropriate handling of the nonlinearities arising from uncertain time-varying delays. In this paper, using the Cayley-Hamilton theorem, we develop a novel method for creating discrete-time models of linear systems with time-varying input delays based on polytopic inclusions. The proposed method is compared with existing approaches in terms of conservativeness, scalability and suitability for controller synthesis.

Frequency Response Functions for Nonlinear Convergent Systems

Convergent systems constitute a practically important class of nonlinear systems that extends the class of asymptotically stable linear time-invariant systems. In this note, we extend frequency response functions defined for linear systems to nonlinear convergent systems. Such nonlinear frequency response functions for convergent systems give rise to nonlinear Bode plots, which serve as a graphical tool for performance analysis of nonlinear convergent systems in the frequency domain. The results are illustrated with an example.

Friction compensation in a controlled one-link robot using a reduced-order observer

In this paper, friction compensation in a controlled one-link robot is studied. Since friction is generally velocity dependent and controlled mechanical systems are often equipped with position sensors only, friction compensation requires some form of velocity estimation. Here, the velocity estimate is provided by a reduced-order observer. The friction is modeled by a set-valued velocity map including an exponential Stribeck curve. For the resulting discontinuous closed-loop dynamics, both the case of exact friction compensation and nonexact friction compensation are investigated. For the case of exact friction compensation, design rules in terms of controller and observer parameter settings, guaranteeing global exponential stability of the set-point are proposed. If the proposed design rules are not fulfilled, the system can exhibit a nonzero steady-state error and limit cycling. Moreover, in the case of nonexact friction compensation, it is shown that undercompensation leads to the existence of an equilibrium set and overcompensation leads to limit cycling. These results are obtained both numerically and experimentally.

Brief paper: A discrete-time framework for stability analysis of nonlinear networked control systems

In this paper we develop a prescriptive framework for the stabilising controller design based on approximate discrete-time models for nonlinear Networked Control Systems (NCSs) with time-varying sampling intervals, large time-varying delays and packet dropouts. As opposed to emulation-based approaches where the effects of sampling-and-hold and delays are ignored in the phase of controller design, we propose an approach in which the controller design is based on approximate discrete-time models constructed for a set of nominal (non-zero) sampling intervals and nominal delays while taking into account sampling-and-hold effects. Subsequently, sufficient conditions for the global exponential stability of the closed-loop NCS are provided.