Volume 61, Issue 8

The contribution presents a simple method for parameter identification in linear spatially distributed systems. The approach relies on a linear system of convolution equations associated with the originally given boundary value problem. Unknown signals are eliminated from these equations by means of simple algebraic computations. The resulting equations, the numerical identification scheme is based on, are in general nonlinear with respect to the unknown parameters even if the originally posed boundary value problem is linear w. r. t. to the latter. The method is illustrated by means of two simulation examples and experimental

In this article the approximation of linear second order distributed-parameter systems is considered using a Galerkin approach. The resulting finitedimensional approximation model also has a second order structure and preserves the stability as well as the passivity. Krylov subspace methods are used for choosing the degrees of freedom appearing in the Galerkin approach to assure moment matching. Simplifications of the approximation procedure are presented for systems with collocated inputs and outputs as well as for different types of damping. The structure preserving approximation of an Euler-Bernoulli beam with Kelvin-Voigt damping demonstrates the results of the article

A novel formulation of approximate truncated balanced realization (TBR) is introduced to unify three approaches: two iterative methods for solving the underlying Lyapunov equations - the alternating directions implicit (ADI) iteration and the rational Krylov subspace method (RKSM) - and a two-step procedure that performs a Krylov-based projection and subsequently direct TBR. The framework allows to compare the three methods with respect to solvability, fidelity, numerical effort, stability preservation and global error bounds, which suggests to merge ADI with the two-step procedure Zusammenfassung Eine neue Formulierung des approximativen Balancierten Abschneidens vereinheitlicht drei Varianten: zwei iterative Lösungsverfahren der zugrundeliegenden Ljapunow-Gleichungen - Alternating Directions Implicit (ADI) Iteration und Rational Krylov Subspace Method (RKSM) - und ein Zwei-Schritt-Verfahren (ZSV), welches nacheinander eine Krylow-Projektion und Balanciertes Abschneiden durchführt. Die einheitliche Beschreibung ermöglicht den Vergleich hinsichtlich Lösbarkeit, Approximationsgüte, numerischem Aufwand, Stabilitätserhaltung und globaler Fehlerschranken, was eine Fusion von ADI und ZSV empfiehlt

The efficient simulation of elastic multibody systems can be enabled with Gramian matrix based reduction methods. Frequency weighted Gramian Matrices are well suited for the reduction of mechanical systems. For systems with many elastic degrees of freedom, the frequency weighted Gramian matrix is approximated by the Proper Orthogonal Decomposition. A reasonable choice of snapshots is decisive. Therefore, a greedy search is presented in this contribution. The necessary calculation of the error in the reduction step requires in an exact way a prohibitive computational effort for large industrial scale models. However, error estimators can be used in the iterative reduction process to reduce systems with millions degrees of freedom efficiently

This paper considers a class of nonlinear output regulation problems for the rotational rigid body equations. The equations of motion for the rigid body are written in the natural SO (3) representation. The presented design consists of an observer and a certainty equivalence implementation of an independently designed state feedback law. The proposed solution is global and achieves almost global convergence in the closed loop Zusammenfassung Dieser Beitrag beschäftigt sich mit einer Klasse von nichtlinearen Ausgangsregelungsproblemen für die Drehbewegung von Starrkörpern. Die Bewegungsgleichungen der Starrkörper werden in der SO (3) Darstellung betrachtet. Der Regler besteht aus einem Beobachter und einer davon unabhängig entworfenen Zustandsrückführung, in welcher die Beobachterzustände verwendet werden. Der Entwurf resultiert in einem geschlossenen Kreis mit garantierter Konvergenz für fast alle Anfangsbedingungen

This paper deals with networked, dynamical multi-agent systems (MAS) trying to reach consensus about their states subject to uncertain data transfer and noisy measurements. For this, an analogy between the consensus protocol and Gaussian belief propagation is established. Modeling the consensus problem as a stochastic process, uncertainties in the initial states and in the information flow can be considered. The requirements for decentral inference are derived, two decentral approximative inference protocols are developed and a Gaussian consensus protocol is realized. Furthermore, the dependency between communication density and approximation error is presented. Finally, it is shown that taking measurement noise into account leads to a decentral design of a Kalman filter for consensus systems

This paper describes the efficient fusion of optical and inertial data in a tracking system for following fast motion. The main goal is to design the data fusion in a way to provide tracking results with a high sampling rate and low latency. An invariant approach for data fusion preserves the system symmetries. A positive effect of respecting the system geometry is a reduction of computation time. The optical-inertial tracking system is low-cost and suitable for various applications, e. g. in computer-assisted surgery

This contribution presents a new method for the prevention of problems caused by a saturating sensor in an otherwise linear loop. Different from the known anti-windup schemes for input constraints the compensator is not stabilized during saturation, as this can lead to a deadlock situation in case of persistent disturbances. Instead, the integral controller action remains active during sensor saturation, and the windup effects are prevented by an appropriate modification of the numerator of the controller. A saturation indicator provides the necessary signal for this modification. As integral action is also present during saturation a robust rejection of persistent disturbances is achieved. Using a two degrees of freedom control structure one also obtains a robust reference behaviour