Parametric Controller Design Of The Nonlinear System Based On Symbolic Computation

With the processing objects become more and more complicated, the primary approach which used linear system to simulate nonlinear system has been difficult to satisfy the accuracy requirement of the practical production and theoretical studies. Therefore, in order to achieve the satisfactory control effect, you have to take the nonlinearity of system and uncertainty of the system into account. At the same time, you should also think about the external noise, interference or other unknown factors, because all these things may influence the performance of system. Polynomial nonlinear system is one kind of typical nonlinear system, which is widely used in industry, agriculture, manufacturing, transportation, aerospace industry and many other engineering technical departments, at the same time, the general nonlinear system can also be better expressed by polynomial nonlinear system. So this paper mainly studies the parametric controller design of polynomial nonlinear system.Although the study of parametric controller of the polynomial nonlinear system has achieved a lot of excellent achievements, there still have some places that are worth to further research:(1)There does not have a general method to design the parametric controller;(2) During the design of parametric controller, as to the complexity of the calculation, people used to consider a part of the parameter range, not all of the parameter range;(3)The existing research of parametric controller in some works, few people consider the parameter optimization problem.For these problems and research needs, this paper introduced the key research in the following four aspects:(1) Through the study to the parametric controller design of the polynomial nonlinear systems, this paper puts forward an approach to design a parametric controller, and proposes a general form of the parametric controller.(2) This paper applies the method of symbolic computation to design parametric controller, it effectively solves the problem of the complicated calculation during the design process, and obtains the complete solution of the parameters in a sense.(3) This paper creatively applies the concept of attenuation coefficient to the parametric controller design, and presents a way to determine the optimal parameters of the controller.(4) This paper also introduces the problems of the domain of attraction of the system and circuit simulation of the system, which proves the correctness of the parametric controller that designed in this paper.In the third and fourth chapter, I choose two different actual systems to verify the effectiveness of the theoretical design. The results show that:(1) Controller designed in this paper can make the system stable and the approach proposed to design a parametric controller is universal.(2) The range of the parameters obtained in this paper can make the system stable which is a complete solution for the parameters of the controller.(3) In this paper, under the attenuation significance the best parameters of the controller are sought out, and the method to determinate the optimal parameters are proved feasible.