Optimum Response of Full Third Order Systems with Contactor Control

IN THE FULL THIRD ORDER PROBLEM IT WAS DESIRABLE TO MODIFY THE ITERATION PROCEDURE USED IN THE PERIODIC APPROXIMATION METHOD THAT WAS DEVELOPED IN SOLVING THE OPTIMUM PROBLEM OF THE SECONDORDER VELOCITY CONTROLLED SYSTEM. A number of examples illustrate the new method. The examples were first constructed in reverse time by employing the true optimum switching times satisfying the optimum switching function which was developed by the methods of Pontrjagin. The obtained final values of error and error derivatives gave the initial values for the approximate method. Periodic approximations of the optimum switching times were then obtained. It was found that for less than three switchings the approximate method leads to identical results. Reasonably small differences occur when three or more switchings are needed to reduce the initial disturbance to zero. (Author).