PRESENT STATE OF THE ART IN THE SPECIFICATION OF NONLINEAR CONTROL SYSTEMS

This report is concerned primarily with assessing the state of the art of nonlinear control as a prelude to the solution of the actual specification problem. As an introduction, the classical methods of nonlinear analysis are discussed, and the reasons for the inadequacy of these techniques for automatic control systems are explained. The two generally known methods of analyzing the stability of autonomous nonlinear control systems, namely phase plane analysis and the describing function, are discussed. The concept of the state variable and the state space is introduced in some detail. The stability of the nonautonomous system and the response of autonomous and nonautonomous systems are covered. As a criterion for specification, the time optimum system is stressed, and distinction is made between the solution of the time optimum problem as a performance index and the synthesis of the optimum switching boundaries. The phase plane is discussed for forced systems and the work of Wiener is mentioned in connection with the response of nonlinear systems to random inputs.