﻿ 块处理的变步长自适应振动主动控制方法
 舰船科学技术  2023, Vol. 45 Issue (12): 40-46    DOI: 10.3404/j.issn.1672-7619.2023.12.008 PDF

1. 海军工程大学 动力工程学院，湖北 武汉 430033;
2. 海军工程大学 舰船与海洋学院，湖北 武汉 430033

Variable step adaptive vibration active control method based on block processing
XU Shiyu1, HE Qiwei2
1. College of Power Engineering, Naval University of Engineering, Wuhan 430033, China;
2. College of Naval Architecture and Ocean Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: In order to solve the problem of poor control effect caused by the interaction between secondary channel and control channel in active vibration control, an active vibration control method with variable step secondary channel online identification based on block processing is proposed.The variable step size for block processing of secondary channel identification and vibration control is improved according to the power changes of reference signal and expected signal. The step size is adjusted on-line to accelerate the convergence speed of algorithm, improve the identification accuracy and enhance the system stability.The simulation results show that, compared with the original algorithm, the algorithm has faster identification speed, higher accuracy and better system stability.The algorithm is experimentally studied with single-layer vibration isolation platform as control object.The results show that the algorithm has better control effect on vibration response of single-layer vibration isolation platform, and the effectiveness of the algorithm in actual control is verified.
Key words: active vibration control     secondary channel online identification     filtered least mean square algorithm     variable-step
0 引　言

Eriksson[6]提出引入随机白噪声作为次级通道的参考信号，但引入的白噪声信号会进入到控制通道中，对控制结果产生干扰，导致系统不稳定甚至发散。

Eriksson算法见图1 $P\left(z\right)$ 为初级通道，指振源到目标控制点的传递函数； $S\left(z\right)$ 为次级通道，指控制信号发生到目标控制点的传递函数； $x\left(n\right)$ 为振源信号，作为初级通道的参考信号； $e\left(n\right)$ 为误差信号； $v\left(n\right)$ 为引入的随机白噪声信号，作为次级通道的参考信号。

 图 1 Eriksson在线辨识次级通道算法框图 Fig. 1 Block diagram of Eriksson online identification secondary channel algorithm

 $w \left(n+1\right)=w\left(n\right)+{\mu }_{w}{x}'\left(n\right)e\left(n\right)，$ (1)
 ${s}'(n+1)={s}'\left(n\right)+{\mu }_{s}v\left(n\right)f\left(n\right)。$ (2)

 $f\left(n\right)=e\left(n\right)-{v}_{s}'\left(n\right)，$ (3)
 ${x}'\left(n\right)={{S}'}^{\rm{T}}\left(n\right){{X}}_{{L}}\left(n-1\right)，$ (4)
 ${{X}}_{{L}}(n-1)=[x\left(n\right),x\left(n-1\right),\cdots ,x(n-L+1){]}^{\rm{T}}。$ (5)

 ${v}_{s}\left(n\right)={{S}'}^{\mathbf{T}}\left(n\right){V}\left(n\right) ，$ (6)
 $\mathit{V}\left(n\right)=\left[v\right(n)\cdots v(n-L+1){]}^{\mathrm{T}} 。$ (7)

 $e\left(n\right)=\left[d\left(n\right)+{y}'\left(n\right)\right]-{v}'\left(n\right)。$ (8)

 $e\left(n\right)=\left[P\left(n\right)X\left(n\right)+S\left(n\right)Y\left(n\right)\right]-\left[s\left(n\right)v\left(n\right)\right]，$ (9)

 $f\left(n\right)=\left[S\left(n\right)V\left(n\right)-{S}'\left(n\right)V\left(n\right)\right]+\left[d\left(n\right)-{y}'\left(n\right)\right] 。$ (10)

1 基于块处理的改进型变步长LMS算法 1.1 变步长控制通道算法

 图 2 本文算法框图 Fig. 2 algorithm block diagram of this paper

 $\tau \left(n\right)=\frac{\parallel \mathit{X}\left(n\right)\parallel }{\alpha +\sqrt{\parallel \mathit{X}\left(n\right)\parallel \cdot \parallel \mathit{e}\left(n\right)\parallel }}。$ (11)

 ${\mu }_{w}\left(n\right)=\frac{\beta {\tau \left(n\right)}^{2}}{\sqrt{1+{\tau \left(n\right)}^{4}+\gamma {\tau \left(n\right)}^{2}}}。$ (12)

${\mu }_{w}\left(n\right)$ $\tau \left(n\right)$ 关系如图3所示，可根据控制对象和控制策略对步长上下限和调整速度快慢进行优化参数调整。

 图 3 ${\mathit{\mu }}_{\mathit{w}}\left(\mathit{n}\right)$ 与 $\mathit{\tau }\left(\mathit{n}\right)$ 函数关系图 Fig. 3 ${\mathit{\mu }}_{\mathit{w}}\left(\mathit{n}\right)$ and $\mathit{\tau }\left(\mathit{n}\right)$ function diagram
1.2 变步长辨识通道算法

 $\rho \left(n\right)=\frac{{P}_{v}\left(n\right)}{{P}_{e}\left(n\right)}，$ (13)

 ${P}_{v}(n+1)=a{P}_{v}\left(n\right)+\left(1-a\right){v}^{2}\left(n\right)，$ (14)
 ${P}_{e}(n+1)=a{P}_{e}\left(n\right)+\left(1-a\right){\parallel \mathit{e}\left(n\right)\parallel }^{2} 。$ (15)

 ${\mu }_{s1}\left(n\right)=\rho \left(n\right){\mu }_{min}+[1-\rho (n\left)\right]{\mu }_{max}。$ (16)

 ${\mu }_{s2}\left(n\right)=b{\mu }_{s2}(n-1)+c\left(1-\mathrm{e}\mathrm{x}\mathrm{p}\left({\rho }^{2}\left(n\right)\right)\right) 。$ (17)

2 算法仿真

 $\mathrm{\Delta }S\left(n\right)=10\mathrm{lg}\left\{\frac{{∥S\left(n\right)-{S}'\left(n\right)∥}^{2}}{\parallel S\left(n\right){\parallel }^{2}}\right\}，$ (18)

 $R\left(n\right)=10\mathrm{l}\mathrm{g}\left\{\frac{\sum e(n{)}^{2}}{\sum d(n{)}^{2}}\right\}。$ (19)

$\mathrm{\Delta }S\left(n\right)$ 的值越小，表征辨识精度越高， $R\left(n\right)$ 的值越小，表征系统的减振性能越好。

 图 4 仿真模型幅值特性图 Fig. 4 Amplitude characteristic diagram of simulation model

2.1 双频振动信号控制算例仿真

 图 5 本文算法与Akhtar算法仿真结果比较 Fig. 5 Comparison of simulation results between this algorithm and Akhtar algorithm

2.2 次级通道突变算例仿真

 图 6 突变后次级通道幅值特性图 Fig. 6 Amplitude characteristic diagram of secondary channel after sudden change

 图 7 次级通道突变仿真结果比较 Fig. 7 Comparison of simulation results of secondary channel mutation
3 实验研究

 图 8 单层隔振平台实验示意图 Fig. 8 Schematic diagram of single-layer vibration isolation platform experiment

 图 9 单层隔振平台实验结果 Fig. 9 Experimental results of single-layer vibration isolation platform
4 结　语

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