The paper presents a new family of strategies for swinging up a pendulum. They are derived from physical arguments based on two ideas: shaping the Hamiltonian for a system without damping; and providing damping or energy pumping in relevant regions. A two-parameter family of simple strategies without switches with nice properties is obtained. The main result is that all solutions that do not st...

We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for stabilization and asymptotic stabilization by applying a fast oscillating control to the string. In the first situation studied we assume that system is subject to a da...

We investigate the scalar field perturbations of the 4+1-dimensional Schwarzschild black hole immersed in a Gödel Universe, described by the Gimon-Hashimoto solution. This may model the influence of the possible rotation of the Universe upon the radiative processes near a black hole. In the regime when the scale parameter j of the Gödel background is small, the oscillation frequency is linearly...

We obtain a class of oscillation modes with damping and absorption that are connected to the classical harmonic oscillator modes through the supersymmetric one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schrödinger equations in particle physics. A single coupling parameter characterizes both the damping and absorption features of these modes, which ...

It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3...

This paper presents a novel method of PID controller tuning suitable for higher-order aperiodic processes and aimed at step response-based auto-tuning applications. The PID controller tuning is based on the identification of so-called n-th order lag (PTn) process model and application of damping optimum criterion, thus facilitating straightforward algebraic rules for the adjustment of both the ...

Dynamic properties of the soils at the Lotung test site, Lotung, Taiwan, are estimated from seismic vertical array measurements (input± output data sets) using both time-invariant and time-variant parametric modeling methods (system identi®cation). Soil properties are directly mapped from model parameters to an equivalent lumped mass model of the soil interval. Shear stiffness and damping ratio...