A new method of multi-inertial systems identification by the Strejc model

Abstract

The paper presents a new method of active identification by the use of nth order Strejc model with time delay. The model approximates the dynamics of multi-inertial system based on its step response. The basic and inconvenient version of identification method for this model was published by Strejc in 1959. Different results of research on this model were published in other works. In almost all these methods a key role is played by the graphic procedures for setting coordinates of the inflection point in step response of the system, drawing a tangent line in this point and finally determining the specific intervals given by this line. Based on the Strejc table one can then determine the hypothetical order and the time constant of the model. The reasons for the model approximation errors in this method are the inaccuracy of location of the inflection point, the procedure of tangent line drawing and the main idea that the step response of a real system and the model response are equal only in the one point. The method presented in this work, is based on the condition that the normalized step responses of the system and of the nth order Strejc model must be equal in two chosen points spaced from each other that will guarantee a good matching of the whole step characteristics and hence a good approximation model. As it turned out, the simple analytical formulas can be received which enable fast and simple determination of Strejc model parameters (for any specifying order n≥1). The most important features of this method are lack of procedure for the location of the inflection point and the tangent line drawing procedure, as well as the non-assumption in advance of the order of the model (in contrast to the Strejc method). The presented method is suitable for easy implementation in PLC controllers with self-tuning.