Complex order control for improved loop-shaping in precision positioning

This paper presents a complex order filter developed and subsequently integrated into a PID-based controller design. The nonlinear filter is designed with reset elements to have describing function based frequency response similar to that of a linear (practically non-implementable) complex order filter. This allows for a design which has a negative gain slope and a corresponding positive phase slope as desired from a loop-shaping controller-design perspective. This approach enables improvement in precision tracking without compromising the bandwidth or stability requirements. The proposed designs are tested on a planar precision positioning stage and performance compared with PID and other state-of-the-art reset based controllers to showcase the advantages of this filter

A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page

A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution - II

We present a semi-decision procedure to tackle first order differential equations, with Liouvillian functions in the solution (LFOODEs). As in the case of the Prelle-Singer procedure, this method is based on the knowledge of the integrating factor structure.Comment: 11 pages, late

The mass and environmental dependence on the secular processes of AGN in terms of morphology, colour, and specific star-formation rate

Galaxy mass and environment play a major role in the evolution of galaxies. In the transition from star-forming to quenched galaxies, Active galactic nuclei (AGN) have also a principal action. However, the connections between these three actors are still uncertain. In this work we investigate the effects of stellar mass and the large-scale environment (LSS), on the fraction of optical nuclear activity in a population of isolated galaxies, where AGN would not be triggered by recent galaxy interactions or mergers. As a continuation of a previous work, we focus on isolated galaxies to study the effect of stellar mass and the LSS in terms of morphology (early- and late-type), colour (red and blue), and specific star formation rate (quenched and star-forming). To explore where AGN activity is affected by the LSS we fix the stellar mass into low- and high-mass galaxies. We use the tidal strength parameter to quantify their effects. We found that AGN is strongly affected by stellar mass in 'active' galaxies (namely late-type, blue, and star-forming), however it has no influence for 'quiescent' galaxies (namely early-type, red, and quenched), at least for masses down to $\rm 10^{10}\,[M_\odot]$. In relation to the LSS, we found an increment on the fraction of SFN with denser LSS in low-mass star forming and red isolated galaxies. Regarding AGN, we find a clear increment of the fraction of AGN with denser environment in quenched and red isolated galaxies, independently of the stellar mass. AGN activity would be 'mass triggered' in 'active' isolated galaxies. This means that AGN is independent of the intrinsic property of the galaxies, but on its stellar mass. On the other hand, AGN would be 'environment triggered' in 'quiescent' isolated galaxies, where the fraction of AGN in terms of sSFR and colour increases from void regions to denser LSS, independently of its stellar mass.Comment: 14 pages, 9 figures (11 pages and 6 figures without appendix), accepted for publication in Astronomy & Astrophysic