Abstract. Objective. This article studies the problem of increasing the efficiency of fuzzy controller synthesis in a control system using a genetic algorithm. The best parameters of the fuzzy controller are selected using the crossing-over and mutation operators in the genetic algorithm. The operation of the mutation operator can lead to the formation of an incorrect set of parameters, which complicates the procedure for synthesizing a fuzzy controller.Methods. Arrays of parameter sets of membership functions, conclusions, and rule weights that are included in the fuzzy controller are compiled using mathematical simulation. The mechanism of operation of single-point and two-point variation operators in the genetic algorithm is described by the simulation modeling.Results. Mathematical models of single-point and two-point variation operators for the genetic algorithm are proposed. The mechanism for changing the values of elements in the array of a set of parameters of a fuzzy controller with one input and output variable is presented.Conclusion. Replacing the mutation operator with the variation operator eliminates the formation of incorrect sets of parameters of the fuzzy controller in the control system.
В статье рассматривается использование стохастических методов в решении задач оптимизации. Применение генетических алгоритмов позволяет успешно решать задачи с различными ограничениями для параметров целевой функции. Согласованная работа таких операторов, как оператор селекции, бинарной рекомбинации и мутации, обеспечивает нахождение экстремального значения целевой функции. В работе оператора мутации присутствует перестановка элементов внутри набора параметров, вследствие чего переставленный элемент может не принадлежать диапазону его возможных значений, что может привести к появлению недопустимого решения задачи. Предлагается заменить оператор мутации на оператор вариации, который изменяет случайно выбранный элемент набора параметров на определенную величину с учетом диапазона его возможных значений. В работе представлена блок-схема генетического алгоритма с операторами селекции, бинарной рекомбинации и вариации. Составлены математические модели формирования массивов значений параметров целевой функции. Рассмотрены средства программной среды MATlAB и системы имитационного моделирования Simulink для автоматизации процесса генерации случайных чисел для массивов значений параметров для задачи оптимизации и работы одноточечных операторов бинарной рекомбинации и вариации. Вид функций распределения случайных величин для генерации случайных чисел выбирается с учетом условия задачи оптимизации и начальных данных. Ключевые слова: задача оптимизации, генетический алгоритм, генератор случайных чисел, оператор бинарной рекомбинации, оператор вариации
The article considers the possibility of using a fuzzy first-order Takagi-Sugeno-Kang type controller to control the movement of an inverted pendulum in order to achieve dynamic stabilization of its unstable equilibrium. The structure of linguistic variables and the base of rules for such a fuzzy controller are proposed. Graphs of changes in the controlled quantities (horizontal carriage displacement and angle of deviation from the vertical) and the control action are constructed, they illustrating the onset of dynamic stabilization of the unstable equilibrium of an inverted pendulum.
The opinion of 190 teachers of the disciplines of physical culture of institutes and universities of Belgorod, Voronezh and Moscow as well as the opinion of more than 1,500 students of the Belgorod State Technological University named after V.G. Shukhov is presented. The problems of conducting physical education lessons in a distance education format are outlined and opinions based on the results of an electronic questionnaire are described. An organized pedagogical process with the use of electronic theoretical materials, electronic testing of knowledge, video assignments, conferences, require more individual, differentiated work from the teacher. 68 % of respondents recognize physical culture in remote form as a forced and temporary measure. Only 1 % admit the possibility of systematic use of new experience. Of the students who participated in the survey, only 57 % engaged in physical culture in a distance format actively and with pleasure. The motivation for the classes was the desire to study successfully and the habit of systematically performing physical exercises. First-year students experienced the greatest difficulties. The main difficulties for everyone were the material and technical capabilities in organizing regular classes, limited funds and space. The departments consider the need to find new strategic ways of development. 6 % of teachers consider it important to study at advanced training courses on the topic of organizing and conducting practical classes in a new distance format.
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