The paper considers the joint effect of the control delay and speed sensor output signal limiting on the stability of the relay dynamic system under the constant disturbance. It is shown that in this case a new property is detected in the system – the appearance of the unstable limit cycle. Phase trajectories are drawn to a stable limit cycle only from the area of initial conditions where their boundaries are determined by the trajectory of an unstable limit cycle. Using the method of Poincare mappings, the parameters of fixed points defining the unstable limit cycle as the boundary of the stability region are found. A simplified method for approximate determination of simple limit cycles and stability in the “large” is proposed based on the property of dynamic symmetry of the system. The method allows the study of the problem under consideration to be limited to applying shift and symmetry mappings to the switching lines.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.