In automatic control systems (ASR), industrial processes of various types with a delay with a limit on the amount of overregulation, a PID controller with a real differentiating link (hereinafter referred to as the PID controller) is widely used. As is known, a sign of the presence of a large delay in the object of regulation is the ratio τob/Tob ≥ 1, where τob is the value of the delay time and Tob is maximum time constant of the object of control. In the presence of a large delay and limitation in the ASR, the parametric synthesis of the PID controller by well-known frequency methods becomes difficult, which leads to interest in the development of numerical searchless algorithms for parametric optimization based on the use of sensitivity functions to determine the gradient of the optimality criterion. In this paper, an APO algorithm is formed that calculates, based on the minimum of the integral quadratic criterion, the values of the adjustable parameters of the PID controller in the specified ASR. In order to ensure that there is no re-regulation of the resulting transient process, the authors of this article propose to introduce a restriction on the regulatory effect into the automatic system at the optimization stage, which, in turn, is taken into account by adding a penalty function to the integral criterion. The proposed algorithm is based on the method of conjugate Polak—Polyak-Ribier gradients with its known advantages. The components of the gradient vector of the optimization criterion are calculated using such sensitivity functions that allow you to obtain all the components of this vector without trial search variations of the configurable parameters. To calculate the value of the optimization step, the authors implemented an appropriate algorithm based on a gradient procedure using the sensitivity function of the output coordinate of the ASR to the step value. The convergence of the generated APO algorithm was verified using a numerical procedure based on the zone of attraction of record values of the optimization criterion, which is determined by a positive-definite Hesse matrix of the integral quadratic criterion based on the difference between the averaged and the tested transients.

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, Иркутский национальный исследовательский технический университет, 664074, г. Иркутск, ул. Лермонтова 83. Аннотация. Для повышения качества переходных процессов в автоматических системах с запаздыванием, превышающим по значению наибольшее из постоянных времени объекта, используют переключение параметров в ПИрегуляторе (РПС). Одной из задач, возникающих при промышленной реализации РПС, является определение оптимальных настраиваемых параметров, доставляющих экстремальное значение принятому критерию оптимальности. Так как используется РПС и рассматривается объект с запаздыванием, то использование аналитических подходов для его настройки затруднительно. Это приводит к необходимости применения алгоритмических методов. В основе предлагаемого алгоритма используется градиентная процедура, в которой составляющие градиента вычисляются с помощью функций чувствительности с их известными преимуществами. В данной работе формируются анализаторы чувствительности, которые могут быть основой алгоритмов автоматической параметрической оптимизации (АПО), вычисляющих, исходя из минимума критерия интегрального вида, оптимальный вектор настройки рассматриваемого ПИ-регулятора. Ключевые слова: ПИ-регулятор, анализатор чувствительности, система с переменной структурой, линия переключения, запаздывание, дискретная система, параметрический синтез Цитирование: Куликов В. В., Куцый Н. Н. Анализаторы чувствительности автоматических систем с пи-регулятором с переменными параметрами при использовании линии переключения // Информационные и математические технологии в науке и управлении. 2020. № 3 (19). С. 57-64.

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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