Adaptability analysis of linear continuous control systems with reference model

Abstract

The problem of analyzing the tuning parameters of linear continuous controllers related to the class of state models is studied. To do this, algorithms for adjusting the controller are used, which are based on estimates of the plant parameters. Within the framework of this study, the adaptability property of the system is considered, and the primary goal is to determine the possibility of finding an exact solution to the problem of tuning the control loop for a given reference transient. Moreover, the study extends to a whole class of input actions, such as piecewise continuous functions of time. Based on the analysis of the convergence properties of the identification residual in a closed control system, additional simplified conditions for the adaptability of control systems using an identifier and a reference model are put forward, which supplement the already existing knowledge on this topic.

Formalization of Tasks to Ensure the Safety of Emergency and Explosive Operations in the Mining Industry

“…Therefore, it is of interest to predict the expected tensile strains and to determine the beginning of element failure, i.e. -the beginning of cracking or delamination process at the contact of layers [15][16][17][18][19][20][21][22][23][24][25][26]. The ultimate stresses in the tensile region in the "Geomechanics" program are limited by the tensile strength limit, and they are automatically assumed to be equal to C/5 for elements that do not go into the plastic, and equal to zero for elements that go into the plastic at the previous iteration cycles.…”