ACTA IMEKO ISSN: 2221-870X June 2018, Volume 7, Number 2, 65-72 ACTA IMEKO | www.imeko.org June 2018 | Volume 7 | Number 2 | 65 Numerical Investigation of Optimal Dynamic Measurements Aleksandr L. Shestakov, Georgy A. Sviridyuk, Alevtina V. Keller, Alyona A. Zamyshlyaeva, Yurii V. Khudyakov South Ural State University,Lenina, 76, Chelyabinsk, Russia Section: RESEARCH PAPER Keywords: mathematical model of measuring transducer; optimal dynamic measurement; set of admissible measurements Citation: Aleksandr L. Shestakov, Georgy A. Sviridyuk, Alevtina V. Keller, Alyona A. Zamyshlyaeva, Yurii V. Khudyakov, Numerical Investigation of Optimal Dynamic Measurements, Acta IMEKO, vol. 7, no. 2, article 12, June 2018, identifier: IMEKO-ACTA-07 (2018)-02-12 Section Editor: Franco Pavese, Italy Received December 16, 2017; In final form May 11, 2018; Published June 2018 Copyright: © 2018 IMEKO. This is an open-access article distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited Funding: The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011 Corresponding author: Alevtina Keller, e-mail: kellerav@susu.ru 1. INTRODUCTION Currently, the theory and practice of dynamic measurements are developing in various directions. For a long time the theory of inverse problems [1], methods of direct and inverse Fourier transforms were the mathematical basis of dynamic measurements. In addition, for more than 20 years methods of the remote control theory were successfully applied for solving various problems of dynamic measurements. In the recent years, a new approach was developed [2] to restore the input signal distorted by the measuring transducer and external interference, called by the authors “the theory of optimal dynamic measurements”. We emphasize that the theory of optimal dynamic measurements is based on three fundamental components: 1) the solution of dynamic measurements problems using the ideas and methods of the remote control theory; 2) the development of the descriptor systems theory and its applications [3]; 3) the development of methods for the solution of Sobolev type equations and corresponding optimal control problems, including numerical methods for solving optimal control problems for Leontief type systems. Leontief type systems are finite-dimensional case of Sobolev-type equations and a special case of descriptor systems (with constant matrices). This report presents recent results in the theory of optimal dynamic measurements. 2. MATHEMATICAL MODELING OF OPTIMAL DYNAMIC MEASUREMENTS We first introduce mathematical model of optimal dynamic measurements (Figure 1). Mathematical model of measuring transducer (MT) is represented by the Leontief type system of equations , , Lx Ax Bu G y Cx D ς η = + +   = +   (1) where L and A are matrices that characterize the structure of the MT. In some cases it is possible that det 0 L = (this will be discussed in the next section); () xt and () xt  are vector functions of the state of the MT and the velocity of the state change, respectively; y(t) is a vector-function of observation; C and D are rectangular matrices characterizing the interrelation between the system state and observation; () ut is a vector- function of measurements; B is the matrix characterizing the ABSTRACT The basic ideas of mathematical modeling of optimal dynamic measurements are presented. The key thing is to construct a mathematical model of the measuring transducer, which allows simulating also a complex measuring transducer. In this manuscript we propose such a mathematical model and we discuss its results obtained through numerical studies in a variety of cases: from the simplest, without considering disturbances, to the case when a deterministic disturbance, for example resonances, occur at the input and at the output of the measuring transducer. Lastly, the importance of the description of the set of admissible measurements in the modeling of dynamic measurements is discussed.