文章以一道二阶线性微分方程为例,归纳出六种不同的解题方法,分别是常数变易法、微分算子法、Laplace变换、配凑法、待定系数法、程序法,并进一步阐述微分方程的一题多解,有利于学生搭建完整的知识体系结构,从多个角度体会解题方法和技巧,提高学生的发散思维和创新能力。Taking a second-order linear differential equation as an example, this paper summarizes six different problem-solving methods, namely the method of variation of constants, the differential operator method, the Laplace transform method, the method of assembling and matching, the method of undetermined coefficients, and the programming method. Furthermore, it elaborates that multiple solutions to one differential equation problem are beneficial for students to build a complete knowledge system structure, experience problem-solving methods and techniques from multiple perspectives, and improve students’ divergent thinking and innovative abilities.
为使独立光伏储能系统(independent photovoltaic energy storage system,IPESS)能够更好地适应各类外部条件变化,提出了一种基于模糊二阶线性自抗扰控制(fuzzy second-order linear active disturbance rejection control,FS-LADRC)的双向DC-DC变换器(bidirectional DC-DC converter,BDC)控制策略.构建了独立光伏储能系统线性模型,基于储能侧双向DC-DC变换器控制特性,采用常规双闭环控制,电流环采用PI控制,对电压环采用二阶线性自抗扰控制,将模糊自适应逻辑与线性状态误差反馈控制率(linear state error feedback,LSEF)结合,使系统有更高的控制精度.与传统PI控制和传统线性自抗扰控制(LADRC)作对比,通过改变光伏发电辐照度的强度,分析了三种控制策略在应对各类条件变化时的直流母线电压的稳定性和系统的发电性能.仿真实验验证得出FS-LADRC在提升直流母线电压的稳定性和系统的发电性能以及系统的鲁棒性方面要优于传统PI和LADRC控制策略.