Research Of Some Systems Based On Pan-Boolean Algebra

This research, basing on the Pan-Boolean Algebra, introduces the following two works: simulation work of the logic controller and design operators of two four-digit numbers in ternary system. The main content includes the simulation and study of different second-order, third-order plants and the design full adder and subtracter of two four-digit numbers in ternary system. So it makes further in specific application, enlarges the practical scope of the theory.The theory has been introduced by professor Zhang NanLun aiming at finding a rule which is different to the Boolean Algebra in the logic in the 80th. The Pan-Boolean algebra is basing on the obedient logical rule of multi mutual negative states, which exist in a factor. It has made people renew the universal and practicable three thought rules, which are the law of identity, the law of contradiction, the law of excluded middle, recognized causality and inductive inference. The primary character of the theory is that every factor only have one state in the multimode system and once the factor is determined, its corresponding state is one and only. Basing on the theory, the logical control has been put forward, the models and rules of which have been used for studying the control of mankind during the controlling action in application, furthermore, the nine-point controller has been set up.This paper introduces the nine-point controller, the nine-point-five-state controller, the twenty-seven-point-nine-state controller and their models and characters, respectively, the front two are controllers that adopt different control actions to attain demand based on the phase plane which is made up of the system of error, and the rate of error, the third controller adopt different control actions to attain demand based on the phase space which is made up of the system of error, the rate of error and the rate of the rate of error. The corresponding relation between the phase plane/space and responding curves are analyzed in the different actions. Given the responding control, the primarily basic capability targets (such as rise time, overshoot, steady-state error etc.) are obtained by adjusting the system in solo control, even the favorable capability can be kept no matter whether the process model is altered. The satisfied control effect are achieved to the various of the second-order, third-order plants through the control forces being analyzed to the different controllers, simulation analysis are respectively put up in the engineer application on the lagging system, high-order plants. Stability of simulation analysis to the nine-point-five-state controller, simulation analysis of the third-order plants to the twenty-seven-point-nine-state controller and the two controllers' application research make up of the paper's emphases.Additionally Basing on the theory, binary is expanded in the tradition Boolean Logic of [0, 1]. In the premise of the two restriction conditions of Pan-Booleanalgebra, the full adder and subtracter of two four-digit numbers in ternary system are designed and implemented respectively through CPLD.