Phenomen by Fuller in the Problems of Analytical Construction High-Speed Regulatorsстатья
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Дата последнего поиска статьи во внешних источниках: 8 апреля 2022 г.
Аннотация:The problem of synthesis of a controlled system with a quadratic quality criterion in which the optimal control has an infinite number of switching points on a finite time interval is discussed. This phenomenon is called the "Fuller phenomenon." Fuller himself received an explicit solution to this problem for a second-order controlled system consisting of two series-connected integrators in 1960. And for 60 years now, the Fuller problem has been stirring the minds of scientists and is very relevant and far from solved for mathematicians, especially for high-order nonlinear multidimensional systems and, all the more, in an explicit, analytical form accurate to the record of the control law.The aim of this work is to demonstrate the theoretical aspects and practical features of the method of synthesis of optimal control systems by the high speed criterion using the example of solving problems related to the Fuller phenomenon.The essence of solving problems associated with the Fuller phenomenon can be expressed by Michelangelo Buonarroti's answer to the question: “How do you make your sculptures?” - "I take a stone and cut off all unnecessary." Indeed, if the best optimal control accuracy is known for an object: optimal control for high speed, then it is very simple to obtain the worst optimal control for accuracy from it (by a criterion that does not explicitly depend on the control, which is the Fuller criterion), by in the control object accuracy criteria. A nice bonus is to increase accuracy to the optimum value and reduce the steady-state error to a theoretically strictly zero control error, and all error coefficients (of position, speed, acceleration, acceleration derivative, etc.) are also equal to zero in the presence of external and internal interference.