Final value controller synthesis

A method is presented for synthesizing a type of control system designated as a final time controller. This device is a feedback control system that is designed to achieve a desired response at one time only, the response at earlier times being arbitrary within physical limits. In addition to the dynamic element, which has a response that is to be controlled, the control loop consists of a feedback element and a controller, both of which have characteristics derived by the synthesis procedure. The final time controller developed is a time varying, nonlinear system and the procedure is one of the few that are applicable to the synthesis of nonlinear controllers. Application of the procedure reduces analysis of the performance of the closed-loop system to the integration of a single, first order differential equation involving the impulse response of the controlled element.