Discretization of control law for a class of variable structure control systems

A new method for the discretization of a class of continuous-time variable structure control systems, based on the linear complementarity theory, is proposed. The proposed method consists two steps. In the first step, the motion projected on the sliding manifold (the fast dynamics) is discretized by means of backward Euler time-step method. In the second step, the sampled and hold control law is determined such that the trajectories of the discrete-time closed loop system projected on the sliding manifold coincide with the trajectories of discretized fast dynamics. The discrete-time closed-loop system exhibits discrete-time sliding motion. It means that the trajectories of the discrete-time closed loop system reach the sliding manifold in a finite number of steps and stay on it after that. Also, it is proved that control law is a continuous function. Therefore, the closed loop system is chattering free. The theoretically obtained results are verified on the example of the non-holonomic integrator. \u

The wave equation as a port-Hamiltonian system and a finite-dimensional approximation

The problem of approximating a distributed parameter system with free boundary conditions is solved for the 2-dimensional wave equation. To this end we first model the wave equation as a distributed-parameter port-Hamiltonian system. Then we employ the idea that it is natural to use different finite elements for the approximation of di?erent geometric variables (forms) describing a distributed-parameter system, to spatially discretize the system and we show that we obtain a ?nite-dimensional port-Hamiltonian system, which also preserves the conservation laws

Tools for analysis of Dirac structures on Hilbert spaces

In this paper tools for the analysis of Dirac structures on Hilbert spaces are developed. Some properties are pointed out and two natural representations of Dirac structures on Hilbert spaces are presented. The theory is illustrated on the example of the ideal transmission line. \u

Hamiltonian formulation of planar beams

This paper deals with the port-Hamiltonian formulation of planar beams. It is shown how this formulation can be related to the linear beams models: the Timoshenko beam model and the rod model

Harmonic oscillators in the Nos\'e - Hoover thermostat

We study the dynamics of an ensemble of non-interacting harmonic oscillators in a nonlinear dissipative environment described by the Nos\'e - Hoover model. Using numerical simulation we find the histogram for total energy, which agrees with the analysis of the Nos\'e - Hoover equations effected with the method of averaging. The histogram does not correspond to Gibbs' canonical distribution. We have found oscillations at frequency proportional to $\sqrt{\alpha/m}$, $\alpha$ the dissipative parameter of thermostat and $m$ the characteristic mass of particle, about the stationary state corresponding to equilibrium. The oscillations could have an important bearing upon the analysis of simulating molecular dynamics in the Nos\'e - Hoover thermostat.Comment: 7 pages, 4 figure

N-Butyl-Cyanoakrylatkleber versus Titanklammerstapler zur Netzfixierung bei der laparoskopischen transabdominalen präperitonealen Leistenhernioplastik

Hintergrund: Unterschiedliche Medien kommen zur Netzfixierung bei der Leistenbruchchirurgie zum Einsatz. Bei nahezu gleichwertiger technischer Effektivität unterscheiden sie sich bei unterschiedlicher Invasivität bezüglich Fremdkörpergefühl und Nervenirritationen. Patienten und Methoden: Insgesamt 300 TAPP Operationen wurden bei 197 Patienten zwischen 8/04 und 1/07 analysiert. Verglichen wurde der Ethicon-EMS(r)-Stapler mit dem vollsynthetischen Kleber Glubran2(r). Nach 1/2 Jahr wurden Lebensqualitätsdaten erhoben. Nach 1 Jahr fand eine körperliche Nachuntersuchung auf Rezidive statt. Ergebnisse: Bei einem follow up von 100% zeigten die mittleren VAS Werte für Schmerz (1,19 vs. 1,71; p<0,05), Fremdkörpergefühl (0,64 vs. 1,01; p<0,05) sowie Zufriedenheit (9,2 vs. 8,9; p<0,05) signifikante Vorteile für die Glubran2(r)-Gruppe. Diskussion: Glubran2(r) ist ebenbürtig zum etablierten EMS(r)-Stapler, verbunden mit geringeren Raten an Schmerz und Fremdkörpergefühl bei höherer Verfahrensakzeptanz