An analysis of relay servomechanisms

THE METHODS of analysis and synthesis of linear servomechanism loops have been developed to the point where they have become a common and useful tool. Comparable advances have not been made in the case of relay-type control although the latter is of great importance in many engineering fields. The reason for this failure is that the differential equations governing a relay-controlled system are nonlinear in nature and cannot be solved by conventional means. Nevertheless, it is possible to analyze such a system by accepting something less than a finite analytic expression for the solution of the governing differential equation. Application of Laplace transform theory to this problem yields the response expressed as a series of terms from which the system behavior may be found. The information obtainable in this manner indicates whether the system under consideration is stable or unstable and gives relations among the circuit parameters which must hold if the response of the system is periodic. This method is not restricted to cases of intermittently applied constant torque as in previous treatments but is applicable to any controlled object whose unilateral transfer function can be written, as for example a motor, a vacuum-tube circuit, or a complete servomechanism loop.