基于FFT的波动方程VOFFLC控制

VOFFLC Control of Wave Equation Based on FFT

针对复杂波动方程的无穷维特性,基于Simulink平台利用FFT(Fast Fouri-er Transform)方法将其从时域PDE(Partial Differential Equations)模型转化为频域ODE(Ordinary Differential Equation)模型,并在频域上搭建类似于集中参数的控制系统。通过FFT和成熟FDM(Finite Difference Method)模拟实验结果的对比,证明采用FFT原理模拟PDE波动方程的思路正确;在频域ODE模型上施加自适应VOFFLC闭环控制,并设计了两种控制反馈规则。其中,采用乘法法则的VOFFLC控制时,波动呈现和原有形态一致、而周期缩短和振幅减小的现象;采用减法法则的VOFFLC控制时,可以实现类似边界控制的结果,然而在空间维度上可以实现向量级控制,即实现对该维度上任意函数形状、插值函数或者散点的向量级别控制,而这是边界控制做不到的。因而,基于FFT的波动方程VOFFLC控制有进一步的研究意义和广阔的实用价值。

The infinite-dimensional properties of complex wave equations is transformed from time-domain PDE model to frequency-domain ODE model using FFT method based on Simulink platform,and then a control system is created which is comparable to the centralized parameter in the frequency domain.It is demonstrated that the idea of using the FFT princi-ple to simulate the wave equation of a PDE is correct by comparing the experimental results of FFT and mature FDM simulation;adaptive VOFFLC closed-loop control is applied to the frequency domain ODE model,and two control feedback rules are designed.When VOFFLC control with a multiplication rule is applied to one of them,the wave has the same form as the original one,but the period is shortened and the amplitude is lowered.When VOFFLC control with the subtraction rule is used,it can achieve results similar to boundary control;however,vector-level control in the spatial dimension can be achieved,i.e.,vector-level control of any function shape,interpolation function,or scatter point in that dimension,which boundary con-trol cannot do.As a result,the FFT-based VOFFLC control of wave equations has significant research implications as well as extensive practical utility.