QUESTIONS ABOUT METHODOLOGY OF ANALYSIS, CONTROL, REGULATION, IDENTIFICATION AND OBSERVATION OF GYROSCOPIC SYSTEMS - Leontieva, V. V.; Kondratieva, N. A. (Computer Science and Applied Mathematics, 2017)
The quality of mathematical models and the usefulness of research of gyroscopic systems are fundamentally depends on the chosen methodology for quantitative and qualitative research of such systems and the applied mathematical apparatus. This paper is devoted to the disclosure of the essence and presentation of the main stages of the analysis of the main features of gyroscopic systems and mathematical models describing their behavior. The general recommendations for the analysis of gyroscopic systems in order to identify the main regularities in the methodology for carrying out such analysis and also in the general methodology for research of gyroscopic systems formulated on their basis is proposed. The relationship between the analyzed properties of systems and a number of such problems as control, regulation, observation, identification and adaptation is obtained in this work. These recommendations are disclosed in the form of an algorithm that realizes the conceptual aspects of the methodology for studying gyroscopic systems. In this case, the above algorithm for analyzing gyroscopic systems and mathematical models describing their behavior is sufficiently enlarged. According to the goal of research, we propose to realize the research of gyroscopic systems and their mathematical models in the following areas: 1) carrying out the analysis for determination of possibility conditions of application of a precession theory and for selection the methods for constructing precessional equations of systems; study of nutation oscillations; 2) implementation of qualitative study of the behavior of solutions of differential equations, which consists in studying the properties of trajectories and their motions in phase space; analysis of the stability of the motion of gyroscopic systems; 3) investigation of the influence of gyroscopic forces on the character and stability of the motion of the studied system and on the stationary motion of gyroscopic systems; 4) determination of conditions for stabilization using gyroscopic forces of unstable potential and non-conservative systems; 5) determination and subsequent analysis of the set of reachability of gyroscopic systems; 6) research of such basic properties of gyroscopic systems as controllability, observability, identifiability, parametric sensitivity and adaptability. Such analysis is also possible in other areas, determined by the direct goal of the control and regulation problems. In view of the characteristic features of gyroscopic systems that affect the type of mathematical models used to describe their behavior, the selection of methods that perform model analysis of an object and the search for appropriate solutions taking into account these features, as well as the stated goal and problems of the carried out research, some certain problems based on the results of the developed methodology are allocated in this work. Such problems could be used for basic and/or additional study and modeling of gyroscopic systems and are able to allow to synthesize mathematical models of the object and/or algorithms for its control, regulation, observation, identification and adaptation. In the conclusion it should be noted that proposed methodology allows to systematize the main stages, methods and approaches for obtaining an effective algorithm for the complex investigation and regulation of a gyroscopic systems in conditions of complete and incomplete information about the studied object. The main attention is paid to the conceptual aspects and methodology of research