Розробленн я методу оптимально го налаштуван ня ПІ-регулят� �рів.pdf

O. Romashevich, V. S. Lovyakin, A. P. Liasko, and V. V. Makarets from the National University of Life and Environmental Sciences of Ukraine. The goal is to consider constraints in the regulation process and minimize unwanted quality indicators of automatic regulation.

The methodology involves formulating the task of optimal PI regulator tuning in general form, analyzing its elements, and replacing them to minimize specific criteria. A generalized criterion is developed, containing individual criteria and weight coefficients that differ significantly in value, creating a desired topology of the generalized (complex) criterion.

The results include a method for optimal PI regulator tuning with constraints, ensuring stability, meeting constraints, and minimizing a complex optimization criterion. The method is linked to a MISO (Multiple Input Single Output) function, which is minimized during calculations and is based on the mathematical model of the regulated object. The method does not impose strict requirements on the mathematical properties of the task.

The scientific novelty lies in the first method for optimal PI regulator tuning with constraints, applicable to objects of any order. It allows minimizing multiple optimization criteria, considering the importance of each, and ensuring stability during regulation. The method can also be generalized for PID regulators and automatic regulators of any structure (including nonlinear).

Practically, the method significantly reduces the integral squared error (ISE) compared to other engineering methods for PI regulator tuning. For example, for an object described by the transfer function G(s)=1/(s+1)², ISE decreased by 1.87-3.14 times, and for G(s)=1/(s+1)³, it decreased by 1.32-2.10 times. The method can also be used to minimize other unwanted integral or positional indicators.

The introduction notes that PI regulators are the most common type, used in 90-95% of regulators in various industries. The first PI regulator tuning method was developed by Ziegler and Nichols in 1942, and thousands of methods have since been developed. However, optimal PI regulator tuning remains an open issue due to the complexity of technological processes. The authors emphasize the need for approaches that can tune regulators even in nonlinear or poorly formalized mathematical models.