The existing Polish gravity control (POGK) established in the last few years of 20th century according to the international standards is spanned on 12 absolute gravity stations surveyed with four different types of absolute gravimeters. Relative measurements performed by various groups on nearly 350 points of POGK with the use of LaCoste&Romberg (LCR) gravimeters were linked to those 12 stations. The construction of the network, in particular the limited number of non homogeneously distributed absolute gravity stations with gravity determined with different instruments in different epochs is responsible for systematic errors in g on POGK stations. The estimate of those errors with the use of gravity measurements performed in 2007-2008 is given and their possible sources are discussed. The development of absolute gravity measurement technologies, in particular instruments for precise field absolute gravity measurements, provides an opportunity to establish new type of gravity control consisting of stations surveyed with absolute gravimeters. New gravity control planned to be established in 2012-2014 will consist of 28 fundamental points (surveyed with the FG5 – gravimeter), and 169 base points (surveyed with the A10 gravimeter). It will fulfill recent requirements of geodesy and geodynamics and it will provide good link to the existing POGK. A number of stations of the new gravity control with precisely determined position and height will form the national combined geodetic network. Methodology and measurement schemes for both absolute gravimeters as well as the technology for vertical gravity gradient determinations in the new gravity control were developed and tested. The way to assure proper gravity reference level with relation to ICAG and ECAG campaigns as well as local absolute gravimeter comparisons are described highlighting the role of metrology in the project. Integral part of the project are proposals of re-computation of old gravity data and their transformation to a new system (as 2nd order network) as well as a definition of gravity system as “zero-tide” system. Seasonal variability of gravity has been discussed indicating that the effects of environmental changes when establishing modern gravity control with absolute gravity survey cannot be totally neglected .
Research activities of Polish research groups in a period of 2015–2019 on reference frames and reference networks are reviewed and summarised in this paper. The summary contains the results concerning the implementation of latest resolutions on reference systems of the International Union of Geodesy and Geophysics and the International Union of Astronomy with special emphasis on the changes in the Astronomical Almanac of the Institute of Geodesy and Cartography, Warsaw. It further presents the status of the implementation of the European Terrestrial Reference System 1989 (ETRS89) in Poland, monitoring the terrestrial reference frame, operational work of GNSS permanent IGS/EPN stations in Poland, operational work of the laser ranging station in Poland of the International Laser Ranging Service (ILRS), active GNSS station network for the realization of ETRS89 in Poland, validation of recent ETRS89 realization, expressed in ETRF2000 in Poland, and maintenance of the vertical control in Poland (PL-KRON86-NH). Extensive research activities are observed in the field of maintenance and modernization of gravity control not only in Poland, but also in Sweden and in Denmark, as well as establishment of gravity control in Ireland based on absolute gravity survey. The magnetic control in Poland was also regularly maintained. The bibliography of the related works is given in references.
The summary of research activities concerning reference frames and reference networks performed in Poland in a period of 2011–2014 is presented. It contains the results of research on implementation of IUGG2011 and IAU2012 resolutions on reference systems, implementation of the ETRS89 in Poland, operational work of permanent IGS/ EUREF stations in Poland, operational work of ILRS laser ranging station in Poland, active GNSS station networks in Poland, maintenance of vertical control in Poland, maintenance and modernization of gravity control, and maintenance of magnetic control in Poland. The bibliography of the related works is given in references.
Swing-up control of a single pendulum from the pendant to the upright position is ﬁrstly surveyed. The control laws are comparatively studied based on swing-up time from a given initial state to the upright position. The State Dependent Riccati Equation is found eﬀective for designing the swing-up control law under saturating control input. The control law is extended to a linear combination of sine function of the angle and the angular velocity, and a variable structure control with a sliding mode given by the linear combination. Making the swing-up time correspond to a colour, which is similar to the Fractal analysis, colour maps of the swing-up time for given control parameters and initial conditions yield interesting Fractal-like ﬁgures.