This Master’s Thesis introducing active preload control of machine tool head supported by a company TOSHULIN, a.s. It presents a way of creating models from rigid body models to flexible bodies and finally to multi-body systems with control loop. The goal of this thesis is create active preload control using a piezo-stack system for simplified linear model of ma-chine tool head.

In this paper, we investigate the question of the spectrally equivalence of the so- called Pseudo-Laplacian to the usual discrete Laplacian in order to use hierarchical preconditioners for this more complicate matrix. The spectral equivalence is shown to be equivalent to a Brezzi-type inequality, which is fulfilled for the finite element spaces considered here.

In Analysis and Numerik differential-algebraischer Gleichungen P. Kunkel and V. Mehrmann give a survey of relevant conditions for consistent systems, for existence and uniqueness of solutions, and touch numerical procedures for obtaining the solutions.

We study linear descriptor systems with rectangular variable coefficient matrices. Using local and global equivalence transformations we introduce normal and condensed forms and get sets of characteristic quantities. These quantities allow us to decide whether a linear descriptor system with variable coefficients is regularizable by derivative and/or proportional state feedback or not. Regularizable by feedback means for us that their exist a feedback which makes the closed loop system uniquely solvable for every consistent initial vector.

We discuss the pole placement problem for single-input or multi-input control models of the form _x=Ax+Bu. This is the problem of determining a linear state feedback of the formu=F xsuch that in the closed-loop system _x= (A+BF)x, the matrixA+BFhas a prescribed set of eigenvalues. We analyze the conditioning of this problem and show that it is an intrinsically ill-conditioned problem, and especially so when the system dimension is large. Thus even the best numerical methods for this problem may yield very bad results. On the other hand, we also discuss the question of whether one really needs to solve the pole placement problem. In most circum- stances what is really required is stabilization or that the poles are in a specified region of the complex plane. This related problem may have much better conditioning. We demonstrate this via the example of stabilization.

Two alternative technologies of communication inside a parallelized Conjugate-Gradient algorithm are presented and compared to the well known hypercubecommunication. The amount of communication is diskussed in detail. A large range of numerical results corroborate the theoretical investigations.

A collection of benchmark examples is presented for the numerical solution of continuous-time algebraic Riccati equations. This collection may serve for testing purposes in the construction of new numerical methods, but may also be used as a reference set for the comparison of methods.

This is the second part of a collection of benchmark examples for the numerical solution of algebraic Riccati equations. After presenting examples for the continuous-time case in Part I, our concern in this paper is discrete-time algebraic Riccati equations. This collection may serve for testing purposes in the construction of new numerical methods, but may also be used as a reference set for the comparison of methods.

In the paper we construct exact three-point discretizations of linear and nonlinear two-point boundary value problems with boundary conditions of the first kind. The finite element approach uses basis functions defined by the coefficients of the differential equations. All the discretized boundary value problems are of inverse isotone type and so are its exact discretizations which involve tridiagonal M-matrices in the linear case and M-functions in the nonlinear case.

Introduction In recent years, domain decomposition methods have been used extensively to efficiently solve boundary value problems for partial differential equations in complex{form domains. On the other hand, multilevel techniques on hierarchical data structures also have developed into an effective tool for the construction and analysis of fast solvers. But direct realization of multilevel techniques on a parallel computer system for the global problem in the original domain involves difficult communication problems. I this paper, we present and analyze a combination of these two approaches: domain decomposition and multilevel decomposition on hierarchical structures to design optimal preconditioning operators.