Graphical analysis and design of limit cycles in autonomous relay control systems

An exact graphical analysis and design technique is presented which is based on closed-form expressions for Tsypkin'a infinite summations. The technique is developed from the observations that the closed-form expressions can be written in a compact notation, and that this new notation simplifies the evaluation of Tsypkin'a necessary conditions for the existence of a simple limit cycle. A set of basic analysis curves is derived for several simple 0(s) forms. It is shown that simple paper and pencil computations are often all that are required to construct a design curve for a more general G(s) function.