Control systems with vector relays

The paper presents the evolution of discontinuous control systems starting from a relay with only two output constant values. The relay systems were widely used at the early stage of the feedback control system history. The analysis and design methods for them were developed by Ya. Tsypkin and discussed in his monograph “Theory of relay control systems,” published in 1956. It is shown how a relay function is modified in the so-called variable structure systems, when the relay output cab be equal to one of two continuous state functions. The next step is made in the framework of variable structure systems with vector control. The design procedure for systems with vector relay control relies on selection of a discontinuity surface for each control component. High efficiency of such designed systems results from enforcing sliding modes on the surfaces. Finally, the vector relay unit control is offered. The method is free of the component-wise design and proved to be applicable for infinite-dimensional systems.