Reply Reply to the Discussions on ‘‘New stabilization and tracking control laws for electrohydraulic servomechanisms’’ Ioan Ursu n , Adrian Toader, Andrei Halanay, Silvia Balea Elie Carafoli National Institute for Aerospace Research À INCAS, Systems Department, Bd. Iuliu Maniu 220, Bucharest 061126, Romania We would like first to highlight the excellent idea of EJC to allocate space for a Discussion Section. Here can be traced some of the great spirit of the old periodicals, which ensured the fame of the old Academies from London, Paris and so on. First we want to thank Professor MingQuing Xiao and remem- ber his quote taken from V. I. Arnold: ‘‘In every mathematical investigation, the question will arise whether we can apply our mathematical results to the real worlds’’. Our belief is broadly positive, but not without a certain skepticism (see [1,2]). The difficulties, and the challenges too, arise from the fact that the mathematical thinking, a meta-reality, operates upon the real world through mathematical models. The paradox is that some incompatibilities arise between the mathematical thinking, namely a theory, and a mathematical model. This is exactly what happened in this article, when the tracking problem could not be definitively solved in the framework of the geometric theory, but it has been solved in the framework of the backstepping approach. The ‘‘culprit’’ was a mathematical model, of switching type, which could not be ‘‘acclimatized’’ with the geometric theory. Professor Xiao invoked a possible approach to the problem of optimal servo synthesis using the HJB equation, relying on the paper of Beard, Saridis and Wen. The first author can make a confession. About 10 years ago, he asked Professor R. W. Beard for an advice, who had published several articles in the field, to recommend a method able to be implemented for the synthesis of a hydraulic servo. In its response, Professor Beard recommended without hesitation a PID algorithm, although he had published works on electrohydraulic servo control synthesis that used the HJB equation. Today, many things are changed, especially with the advent of powerful computers, and we think Professor Xiao recommendation is welcome. So far, as shown in the paper references, we successfully had implemented the neuro-fuzzy control in electrohydraulic actuators. Our thanks are also addressed to Professor Tingwen Huang for the attention with which he read the manuscript and for his recommendations. We should only mention that the subject of the control saturation for hydraulic servos was in the frontline of our preoccupations over time (see [3,4]). To be more specific, in the case of the backstepping tracking control À if a special antiwindup loop is not considered À the saturation occurrence can be avoided through careful tuning the weighting parameters in Proposition 5.1 (see also [2,5]). References [1] I. Ursu, Dealing with mathematical modelling in applied control, INCAS Bulletin v 3 (2) (2011) 87–93, see/http://bulletin.incas.ro/files/ursu_ioan_ v3_is2_fullr.pdfS. [2] I. Ursu, F. Ursu, F. Popescu, Backstepping design for controlling electro- hydraulic servos, Journal of The Franklin Institute, USA 343 (January) (2006) z94–110. [3] I. Ursu, G. Tecuceanu, F. Ursu, M. Vladimirescu, T. Sireteanu, From robust control to antiwindup compensation of electrohydraulic servo actuators, Aircraft Engineering and Aerospace Technology 70 (4) (1998) 259–264. [4] I. Ursu, H infinity control synthesis with antisaturating compensator, INCAS Bulletin 2 (4) (2010) 203–211, see/http://bulletin.incas.ro/files/ioan_ursu_v2 no4_1_full.pdfS. [5] I. Ursu, F. Popescu, F. Ursu, Control synthesis methodology related to an advanced nonlinear electrohydraulic servo system, Proceedings of the Romanian Academy, Series A, Mathematics, Physics, Technical Sciences, Information Science 5 (1) (2004) 39–45 January–April. Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ejcon European Journal of Control 0947-3580/$ - see front matter & 2013 European Control Association. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ejcon.2013.02.007 DOI of original articles: http://dx.doi.org/10.1016/j.ejcon.2013.02.005, http://dx.doi.org/10.1016/j.ejcon.2013.02.006 n Corresponding author. E-mail address: iursu@incas.ro (I. Ursu). European Journal of Control 19 (2013) 85