This paper proposes a new approach to control the grid-side current of LCL-grid connected voltage source converters using hysteretic relay feedback controllers. The closed loop system is stabilized by designing a local feedback around the relay element. The compensator allows the use of relay feedback controllers by making the controlled plant almost strictly positive real. The article proposes the use of the locus of the perturbed relay system as analysis and design tool and studies orbital stability for several plant and controller conditions. The approach is validated by means of simulation testing.
We study the maximum number of limit cycles that can bifurcate from a degenerate center of a cubic homogeneous polynomial differential system. Using the averaging method of second order and perturbing inside the class of all cubic polynomial differential systems we prove that at most three limit cycles can bifurcate from the degenerate center. As far as we know this is the first time that a complete study up to second order in the small parameter of the perturbation is done for studying the limit cycles which bifurcate from the periodic orbits surrounding a degenerate center (a center whose linear part is identically zero) having neither a Hamiltonian first integral nor a rational one. This study needs many computations, which have been verified with the help of the algebraic manipulator Maple.
In this note we present an application of a new tool (the Gröbner cover method, to discuss parametric polynomial systems of equations) in the realm of automatic discovery of theorems in elementary geometry. Namely, we describe, through a relevant example, how the Gröbner cover algorithm is particularly well suited to obtain the missing hypotheses for a given geometric statement to hold true. We deal with the following problem: to describe the triangles that have at least two bisectors of equal length. The case of two inner bisectors is the well known, XIX century old, Steiner-Lehmus theorem, but the general case of inner and outer bisectors has been only recently addressed. We show how the Gröbner cover method automatically provides, while yielding more insight than through any other method, the conditions for a triangle to have two equal bisectors of whatever kind.
Benadero, L.; Giral, R.; Aroudi, A.; Calvente, J. Mathematics and computers in simulation Vol. 71, num. 4-6, p. 256-269 DOI: 10.1016/j.matcom.2006.02.009 Data de publicació: 2006-06-19 Article en revista
This paper deals with the analysis of a single inductor switching dc–dc power electronics converter which is used to regulate two, in general non-symmetric, positive and negative outputs. A PWM control with a double PI feedback loop is used for the regulation of both output voltages. The steady state properties of this converter are first discussed and then stability is studied in terms of both power stage and control parameters.