非线性系统的优化研究和稳定性分析

发布时间：2018-04-25 10:29

本文选题：极值搜索控制 + 非线性系统　；参考：《电子科技大学》2017年硕士论文

【摘要】：科学发展、技术创新是时代进步的标签,为了强大国家的军事实力和经济实力,同时也为了丰富人们的生产生活,智能化信息化的发展便成了迫在眉睫的问题。设备工艺的创新来自于设备核心技术的不断优化,在多样化的设备生产中,非线性系统则充斥着整个生产流程。因此如何优化非线性系统,最大化提高设备生产效率,始终是国内外学者热门研究问题之一。本论文提出了一种改进的极值搜索控制算法,针对非线性系统的输出量和参考输入量参考轨迹未知的情况进行优化,目的在于使控制系统在该算法作用下能够稳定收敛到系统最优值的同时,进一步提高原算法的优化效率。国内外针对非线性系统的优化算法很多,但大部分优化算法对于参考轨迹未知的非线性系统不适用。而极值搜索控制算法作为一种自适应控制方法,同时也是一种基于非模型的实时优化方法能够解决这类非线性系统的优化问题。因此本文基于极值搜索控制算法,设计了新的控制器,在通过霍尔维茨判据证明了整个控制系统的稳定性后,选取了不同的非线性系统模型验证改进算法的可靠性。本文首先分别针对单输入单输出的静态系统和动态系统,采用改进的牛顿极值搜索控制算法,在理论分析上证明改进控制算法具有稳定收敛性后,通过与原牛顿极值搜索控制算法的对比仿真实验,实现了对单输入单输出系统的优化目标,同时达到了提高原算法优化效率的目的。其次,本文针对极值搜索控制算法会陷入局部最优的局限性,设计了一种多峰值搜索控制算法,该优化算法将极值搜索控制算法与自动变输入步长的方式结合,能够实现将系统输出收敛到全局最优值的目的。同时,通过模拟局部遮阴的光伏阵列,采用多峰值搜索控制算法实现了光伏阵列全局最大功率的跟踪,体现了该优化算法的可靠性。最后扩充非线性系统的维数,针对多变量系统即多输入单输出的非线性系统,采用改进的牛顿极值搜索控制算法,通过严格的算法稳定性证明后,从与原算法的对比仿真结果可以看出,改进的牛顿极值搜索控制算法同样适用与多变量的非线性系统,而且提高了原算法的优化效率。
[Abstract]:The development of science and technology innovation are the label of the progress of the times. In order to enrich the military strength and economic strength of the powerful country and enrich the people's production and life, the development of intelligent information technology has become an urgent problem. The innovation of the equipment technology comes from the continuous optimization of the equipment core technology, and in the variety of equipment production, The linear system is full of the whole production process. Therefore, how to optimize the nonlinear system and maximize the production efficiency of the equipment is one of the hot research problems of the scholars at home and abroad. In this paper, an improved extreme search control algorithm is proposed, which is aimed at the output of the nonlinear system and the unknown reference trajectory of the reference input. The purpose of line optimization is to make the control system converge to the optimal value of the system under the action of the algorithm and improve the optimization efficiency of the original algorithm. There are many optimization algorithms for nonlinear systems at home and abroad, but most of the optimization algorithms are not applicable to the nonlinear systems with unknown reference trajectory. As an adaptive control method and a non model based real-time optimization method, the optimization problem of this kind of nonlinear system can be solved. Therefore, this paper designs a new controller based on the extremum search control algorithm. After proving the stability of the whole control system through the Holzer Witz criterion, different non lines are selected. The reliability of the improved algorithm is verified by the sexual system model. Firstly, the improved Newton extremum search control algorithm is adopted for the single input and single output static system and the dynamic system. On the theoretical analysis, it is proved that the improved control algorithm is stable and convergent, and the simulation experiments are compared with the original bull ton extremum search control algorithm. The goal of optimizing the single input and single output system is presented, and the aim of improving the optimization efficiency of the original algorithm is achieved. Secondly, in this paper, a multi peak search control algorithm is designed for the limitation of the extreme search control algorithm which will fall into the local optimal. The algorithm combines the extremum search control algorithm with the automatic variable input step length. In addition, it can achieve the goal of converging the output of the system to the global optimal value. At the same time, the global maximum power tracking of the photovoltaic array is realized by using the multi peak search and control algorithm by simulating the partially shaded photovoltaic array, and the reliability of the optimization algorithm is reflected. Finally, the dimension of the non linear system is expanded and the multivariable system is more lost. The improved Newton extremum search control algorithm is adopted for the nonlinear system entering the single output. After the rigorous proof of the stability of the algorithm, it can be seen from the comparison simulation results with the original algorithm that the improved Newton extremum search control algorithm is also applicable to the nonlinear system with multivariable, and the optimization efficiency of the original algorithm is improved.

【学位授予单位】：电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP13

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