The problem of controlling objects with time delay is quite complicated. The presence of a delay in the control loop leads to an increase in the phase shift, which can provoke instability of the system. The paper proposes a study of a nonlinear multi-connected system of automatic control (MSAC) of an object with a delay by frequency methods, based on the method of harmonic linearization and a system description of the characteristics of a multi-connected automatic control system. A nonlinear multi-connected automatic control system with delay in direct channels and cross-channels is considered. The nonlinear multi-connected automatic control system with delay consists of a set of identical separate subsystems and mutual connections between subsystems are single. With the help of frequency methods, the parameters of periodic motions (PM) in nonlinear homogeneous multi-connected automatic control systems with delay (amplitude and frequency of self-oscillations) are determined and their stability is estimated according to the proposed criteria. The paper presents examples that demonstrate the use of the proposed techniques to assess the stability of a nonlinear multi-connected system of automatic control of the object with delay both in direct communication channels and cross and finding the parameters (amplitude and frequency) of periodic movements. The results of the study were confirmed by simulation using MATLAB SIMULINK package.
The article deals with the development of fuzzy cognitive models of the processes of analysis and management of the quality of education as a multifactor system. The approach based on definition of trajectories of achievement of target indicators of education quality with the use of technologies of knowledge engineering is offered. The functional scheme of the model of education quality management is developed. The structuring of factors influencing the quality of education is carried out: management and target indicators, as well as indicators characterizing the current state of the education system are identified. Cognitive modeling is carried out to analyze and support of making decisions on education quality management. Fuzzy cognitive map (FCM) is developed on the basis of statistical data using methods of statistical and intelligent analysis. The analysis of the integrated system indicators of the constructed FCM, the results of which identified the most significant concepts that have the greatest impact on the state of the education system is carried out. The algorithm of Silov is applied for searching for the ways of direct and indirect influence of concepts on each other through the matrix of interaction between concepts, representing intelligent cognitive agent; the search procedure is based on the use maxtriangular operation with fuzzy matrices using the T -and S-norms. The maximum positive and negative ways between the management and target concepts of the FCM are formed, which are considered as possible scenarios for the use of budgetary funds to improve the quality of education. The constructed ways represent a chain of fuzzy rules of the form "if-then" and can be the basis for the formation of recommendations for decision-making in the management of the quality of education.
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