Bilinear Methods Research Articles

Vibration of cracked shafts in bending

Cracked rotating shafts exhibit a certain particular dynamic response due to the local flexibility of the cracked section. In this response, most of the features of the response of a shaft with dissimilar moments of inertia can be identified. Moreover, the non-linear behavior of the closing crack introduces the characteristics of non-linear systems. For many practical applications, the system can be considered bi-linear and analytical methods can be applied. A de Laval rotor with an open crack is investigated by way of application of the theory of shafts with dissimilar moments of inertia. Furthermore, analytical solutions are obtained for the closing crack under the assumption of large static deflections, a situation common in turbomachinery. Finally, a solution is developed for the case in which the local flexibility function is found experimentally.

Weighted minimum-variance self-tuning control

A weighted minimum-variance controller has recently been defined which is based upon a k-steps-ahead control law and which may be used for unstable and non-mimimum-phase plants. The controller includes control weighting and this results in relatively smooth control signals. The controller is also stable for ranges of control weighting where other control laws are unstable. Both explicit and implicit self-tuning algorithms are proposed based upon this controller. Some of the algorithms use bilinear identification methods developed by Åström for use in his pole-zero-placement algorithms. The self-tuning controller is related to that developed by Clarke and Gawthrop when the system is minimum-phase.

Schrödinger operators withL loc p -potentials

We discuss the question of when the closure of the Schrodinger operator, −Δ+V, acting inLp(Rl,dlx), generates a strongly continuous contraction semigroup. We prove a series of theorems proving the stability for −Δ:Lp→Lp of the property of having am-accretive closure under perturbations by functions inLlocq (1<p≦q). The connection with form sums and the Trotter product formula are considered. These results generalize earlier results of Kato, Kalf-Walter, Semenov and Beliy-Semenov in that we allow more general local singularities, including arbitrary singularities at one point, and arbitrary growth at infinity. We exploit bilinear form methods, Kato's inequality and certain properties of infinitesimal generators of contractions.

Computer Implementation of Digital Techniques and Spectral Estimation

In this paper along with a brief theoretical analysis of the design aspects of recursive and non-recursive digital filters, derivation of design algorithms and their performance characteristics are studied with the help of general-purpose digital computer, Honeywell-400. The basic mathematical tools used are the well-known z-transformation calculus and the bilinear z-transformation methods. We have presented in this paper in some detail the digital filtering with sampled spectrum frequency shift technique and its application to spectral estimation and the design procedure of a bank of filters using the methods along with the performance results.