Synthesis of closed loop systems using curvilinear squares to predict root location

THIS paper introduces a procedure for synthesizing servomechanisms whereby the roots of the characteristic equation can be predicted. Given a specified location in the s plane for the roots, the open-loop transfer function parameters and gain can be calculated to give those roots. Since the roots of the characteristic equation are the exponents in the expression for the transient response, it is thus possible to synthesize a system from the standpoint of desired transient response. Inherent in this procedure is the ability to determine whether such a response is physically possible for a particular system. Throughout this paper the term transient response means transient response to a step input.