SETTING OF PID-REGULATOR BASED ON DIRECT SYTHESIS METHOD FOR THE SECOND ORDER OBJECTS PLUS TIME DELAY

Abstract

For the construction of modern systems of automation in greater part of cases PІ-, PID-regulators are used, this is stipulated by their simplicity, lack of static regulation error and availability of the programming units in the automation devices being used. Setting of such regulators is a relevant problem as the available methods do not meet the requirements of the needed quality or are rather complicated for practical application.

The given paper contains the method for PID-regulator parameters setting, based on the direct-synthesis method for the second-order objects with delay on the channel task-output. The method is based on the reduction of the transfer function of the closed-loop system on the task-output channel to the simplified form. This occurs by means of Pade approximation of the first order for the delay time element and establishing time integration coefficient and time of PID-regulator differentiation, connected with the coefficients of the control object model. The paper presents mathematical analysis of the simplified transfer function of the closed-loop system. Ranges of the general gain coefficient of PID-regulator at which the transient process of the closed-loop system is presented by the oscillating, conservative elements or by the aperiodic element of the second order and its stability is provided, are determined. Taking into account the substantiated requirements, concerning the quality of the transient process in the task-output channel the expression for the calculation of the general gain coefficient of PID-regulator is analytically obtained.

The study of the suggested method and comparison with the methods of Zigler-Nickols, CHP and IMC for tuning PID-regulator of the objects of the second order with delay has been performed. According to the results of the study it is established that the suggested method improves quality indices of the transient process namely: reduces the dynamic error and regulation time and can be applied for the objects of control with different response time. Results of the study show the great potential of the suggested method for rapid tuning of PID-regulator parameters, using only parameters of the object model for their calculation.