novtexmechМехатроника, автоматизация, управлениеMekhatronika, Avtomatizatsiya, Upravlenie1684-64272619-1253Commercial Publisher «New Technologies»10.17587/mau.21.530-534novtexmech-877Research ArticleРОБОТЫ, МЕХАТРОНИКА И РОБОТОТЕХНИЧЕСКИЕ СИСТЕМЫROBOT, MECHATRONICS AND ROBOTIC SYSTEMSГрадиентный алгоритм параметрической оптимизации ПИ-регулятора с переменной структурой с зоной нечувствительностиThe Gradient-Based Algorithm for Parametric Optimization of a Variable Structure PI Controller with Dead BandКуликовВ. В.KulikovV. V.Godefire@mail.ruКуцыйА. П.KutsyiA. P.osha1993irk@yandex.ruКуцыйН. Н.KutsyiN. N.

Доктор технических наук

Иркутск

Kutsyi Nikoly N., D. Sc.

Irkutsk, 664074

kucyinn@mail.ruИркутский национальный исследовательский технический университетРоссияIrkutsk National Research Technical UniversityRussian FederationИркутский национальный исследовательский технический университет; Иркутский государственный университет путей сообщенияРоссияIrkutsk National Research Technical University; Irkutsk State Transport UniversityRussian Federation202007092020219530534Copyright © Commercial Publisher «New Technologies», 20202020Commercial Publisher «New Technologies»Commercial Publisher «New Technologies»https://mech.novtex.ru/jour/about/submissions#copyrightNoticehttps://mech.novtex.ru/jour/article/view/877

Наличие в автоматической системе объекта с запаздыванием, превышающего по значению максимального временного параметра объекта регулирования, снижает качество работы типовых регуляторов (интегральный, пропорционально-интегральный, пропорционально-интегрально-дифференциальный). Присутствие в системе такого запаздывания требует обращения к тому или иному классу регуляторов, компенсирующих отрицательные влияния запаздывания.  В  настоящей  работе  рассматривается  известный  своими  преимуществами  ПИ  регулятор  с  пере менными или переключаемыми параметрами, относящийся к классу регуляторов с переменной структурой (РПС), не использующих скользящий режим. Ввиду того, что используемый регулятор содержит переключаемые параметры и рассматривается объект с запаздыванием, то использование аналитических подходов к параметрической оптимизации системы крайне сложно. Это приводит к необходимости обращаться к алгоритмическим методам.

В  настоящей  работе  используется  градиентный  алгоритм,  в  котором  составляющие  градиента  вычисляются с  помощью  функций  чувствительности  с  их  известными  преимуществами.  Сформированный  алгоритм  автоматической параметрической оптимизации (АПО) вычислил оптимальные параметры РПС для заданного объекта исходя из  минимума  интегрального  квадратичного  критерия.  Достоверность  найденного  вектора  настройки  регулятора, сформированного алгоритмом АПО, подтверждается вычислительной методикой. Алгритм АПО с достаточной для практики точностью решил поставленную задачу параметрической оптимизации. Полученный положительный опыт оптимизации ПИ регулятора с переменными параметрами позволяет применить его к другим РПС, не использующим скользящий режим и, таким образом, в дальнейшем расширить практику применения градиентного алгоритма на основе функций чувствительности для такого класса РПС при различных законах переключения структур регулятора.

In the automatic system, the presence of an object with a delay that exceeds the value of the maximum time parameter of the controlled object reduces the operating quality of generic controllers (integral, proportionally-integral, proportionally-integral-differential). The occurrence of this kind of delay in the system requires addressing a particular class of regulators that compensate for the negative effects of the delay. This paper examines the PI controller known for its advantages with variable or switchable parameters, which belongs to the class of controllers with variable structure (henceforward — VSC) that do not use sliding mode. Due to the fact that the controller used contains switchable parameters and the object with delay is considered, it is extremely difficult to use analytical approaches to parametric optimization of the system. This lays one under a necessity to use algorithmic methods. This work employs a gradient-based algorithm in which the components of the gradient are calculated using sensitivity functions with their known advantages. The generated Automatic Parametric Optimization (APO) Algorithm calculated the optimal VSC parameters for a given object, based on the minimum of the integrated quadratic criterion. The reliability of the found vector of the controller setting, formed by the APO algorithm, is confirmed by the computational methodology. With accuracy sufficient for practice, the APO algorithm solved the problem of parametric optimization. The positive experience of optimizing the PI controllers with variable parameters allows one to apply it to other VSC, which do not use a sliding mode, and thus further expand the practice of using a gradient-based algorithm based on sensitivity functions for such a class of VSC under various laws of switching structures of the controller.

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The authors declare that there are no conflicts of interest present.