Computer-aided nonlinear system design and simulation

Abstract

To explain a phenomenon in a nonlinear system and to find its function, a useful method is to construct the nonlinear system in a dialogue form with a computer and to obtain its characteristics. This paper introduces the software commands to design a nonlinear system by using a dialogue form with a computer, and the method of a simulation of the subsystem constructed. The procedure of the specifications of the design of the nonlinear system is as follows: a block-line diagram consisting of a linear system and nonlinear subsystems is constructed for the subsystems within the system, and the simulation is carried out based on this diagram. A simulation-system command, simulation-execution command, and supporting commands were developed for the dialogue-type commands required for the design. Then if a subsystem is linear, its input response is specified by the z-transformation equation; and if a subsystem is nonlinear, this is specified by the form of a polynomial of the input variables of the system. Three types of combination of the subsystems within the whole system were discussed: the series connection, parallel connection, and feedback connection. A white noise was fed into the input of the system constructed, and the first- and second-order Wiener kernels, which were obtained as the Wiener-functional and showed the characteristic of the system, were shown.