Optimization And Stability Analysis Of Nonlinear Systems

The development of science and technology innovation is a label of the progression of the times,in order to keep strong both national military and economic strength,and diversify people's life and production,the development of intelligent information becomes the imminent problem.The equipment innovation comes from the constant optimization of the core technology,the nonlinear system is filled with the entire production process in the whole variety manufacturing process.So how to optimize the nonlinear system and maximize the efficiency of production equipment are always hot topics for domestic and overseas scholars.In this paper,a modified extremum seeking control algorithm is proposed to optimize the non-linear system,which the reference trajectory between system input and output is unknown.The purpose of the algorithm is to make the control system converge to the optimal value,and improve the optimization efficiency of the original algorithm.There are many algorithms for optimization of nonlinear systems around the world,but most of them are not suitable for non-linear systems with unknown reference trajectories.But this problem can be solved by extreme seeking control algorithm.It is an adaptive algorithm,and a kind of real-time optimization based on the non-model method.Therefore,based on the extremum seeking algorithm,a new controller is designed.After the stability of the whole control system is proved by the Hurwitz criterion,the reliability of the modified algorithm is verified by different nonlinear system models.In this paper,firstly,the modified Newton extremum seeking control algorithm is used for single-input single-output static system and dynamic system respectively.The stability of control system is verified,and the output can converge to the optimal value.Also the efficiency of original algorithm is improved by contrast experiments.Secondly,a multi-peak seeking control algorithm is designed to avoid falling into the local optimum under the extremum seeking algorithm.It can converge to the global optimal value by combining extremum seeking algorithm with the automatic variable input step.At the same time,the multi-peak seeking control algorithm is reliably used to realize the global maximum power tracking,through the simulation of PV array with the partial shade.Finally,the dimension of the non-linear system is extended.The modified Newton extreme seeking algorithm is used for a multiple-input single-output non-linear system.The algorithm stability can be proved strictly.Moreover,the modified Newton extreme seeking control algorithm is also applicable to multivariable nonlinear systems by contrast experiments.At the same time,it improves the efficiency of the original algorithm.