﻿ 基于模糊滑模控制的磁流变半主动最优抗冲击技术
 舰船科学技术  2020, Vol. 42 Issue (6): 101-104    DOI: 10.3404/j.issn.1672-7649.2020.06.020 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 船舶与海洋学院，湖北 武汉 430033

Research on optimal design of the MR semi-active resistance system based on fuzzy sliding mode control
PAN Wei1, YAN Zheng-tao2, LOU Jing-jun2, ZHU Shi-jian2
1. College of Power Engineering, Naval University of Engineering, Wuhan 430033, China;
2. National Key Laboratory on Ship Vibration and Noise, Naval University of Engineering, Wuhan 430033, China
Abstract: To make up the defects in the shock isolation design of passive vibration isolation, a vibration and shock isolation system is designed according to the optimal shock isolation theory, which is composed of a magnetorheological damper and a vibration isolator. Aiming at the nonlinearity of magnetorheological damper, the short amplitude of impact time and the chattering of synovial control, a fuzzy sliding mode anti-impact controller is designed and simulated. The simulation on different resistance methods and the extreme situations shows that the semi-active MR optimal resistance design based on the fuzzy sliding mode control can decrease the impact acceleration and system displacement, which improve the impact resistance performance of the passive vibration isolation.
Key words: optimal shock isolation theory     fuzzy sliding mode control     magnetorheological damper     shock isolation
0 引　言

1 最优抗冲理论

2 隔振抗冲系统优化设计

1）初始阶段。

2）中间阶段。

3）结束阶段。

 图 1 磁流变阻尼器半主动抗冲击系统 Fig. 1 Semi-active shock isolation MRD system
3 磁流变阻尼器建模

MRD采用Bingham模型[6]建模，如下式：

 $f = {f_y}\operatorname{sgn} (\dot x) + {c_0}\dot x\;{\text{。}}$ (1)

 $\begin{array}{l} f = \left( {224.64I + 155.54} \right){\mathop{\rm sgn}} (\dot x)\;+\\ (3941.41 + 2482.21)\dot x\;{\text{。}} \end{array}$ (2)

4 模糊滑模控制器设计

 $m\ddot x + k(x - u) + c(\dot x - \dot u) + f = 0\;,$ (3)

 $m\ddot z + kz + c\dot z + f = - m\ddot u;\;,$ (4)
 $\ddot u(t) = \left\{ \begin{array}{l} U\sin ({\rm{{\text{π}}}} t/{t_m}),\\ 0\begin{array}{*{20}{c}} {\text{。}}&{} \end{array} \end{array} \right.$ (5)

 $\left\{ \begin{array}{l} {{\dot X}} = {{AX}} + {{BU}} ,\\ {{Y}} = {{CX}} + {{DU}} {\text{。}}\\ \end{array} \right.$ (5)

 ${{A}}=\left[\begin{array}{cccc} 0 & 1 & 0 & 0 \\ -\displaystyle\frac{k_{1}}{m_{1}} & -\displaystyle\frac{c_{1}}{m_{1}} & \displaystyle\frac{k_{2}}{m_{1}} & \displaystyle\frac{c_{2}}{m_{1}} \\ 0 & 0 & 0 & 1 \\ \displaystyle\frac{k_{1}}{m_{2}} & \displaystyle\frac{c_{1}}{m_{1}} & -\displaystyle\frac{k_{1}+k_{2}}{m_{2}} & -\displaystyle\frac{c_{1}+c_{2}}{m_{2}} \end{array}\right]\;{\text{，}}$ (7)
 ${{B}} = {[\begin{array}{*{20}{c}} 0&{ - 1}&0&{ - 1} \\ 0&{ - \displaystyle\frac{1}{{{m_1}}}}&0&{\displaystyle\frac{1}{{{m_2}}}} \end{array}]^{\rm{T}}}\;{\text{，}}$ (8)
 ${{C}} = [\begin{array}{*{20}{c}} { - \displaystyle\frac{{{k_1}}}{{{m_1}}}}&{ - \displaystyle\frac{{{c_1}}}{{{m_1}}}}&0&0 \end{array}]\;{\text{，}}$ (9)
 ${{D}} = [\begin{array}{*{20}{c}} { - 1}&{ - \displaystyle\frac{1}{{{m_1}}}} \end{array}]\;{\text{，}}$ (10)
 ${{U}} = {[\begin{array}{*{20}{c}} {\ddot u}&{{F_M}} \end{array}]^{\rm{T}}}\;{\text{。}}$ (11)

 $J = \int_{{t_0}}^t {\left[ {{{{e}}^{\rm{T}}}{{Qe}} + {{{u}}^{\rm{T}}}{{Ru}}} \right]} {\rm{d}}t\;{\text{。}}$ (12)

 ${\dot {\bar{ X}}} = {\bar{ A}{\bar {{X}}}} + {{\bar{ B}}{{U}}}\;{\text{，}}$ (13)

 $J = \int_{{t_0}}^t {\left[ {{{{\bar{ X}}}^{\rm{T}}}{{\bar{ Q}{\bar {{X}}}}} + {{{u}}^{\rm{T}}}{\bar{ R}}{{u}}} \right]} {\rm{d}}t\;。$ (14)

 $J = \int_{{t_0}}^t {\left[ {{{{\bar{ X}}}^{\rm{T}}}{{\bar{{ Q}}{\bar {{X}}}}}} \right]} {\rm{d}}t\;{\text{。}}$ (15)

 ${{\dot Z}} = {\bar {\bar{ A}}}{{Z}} + {\bar {\bar{ B}}}{{U}}$ (16)

 $J = \frac{1}{2}\int_{{t_0}}^t {\left[ {{{{z}}_1}^{\rm{T}}{{{\bar{ Q}}}_{11}}{{{z}}_1} + 2{{{z}}_1}^{\rm{T}}{{{\bar{\bf Q}}}_{12}}{{{z}}_2} + {{{z}}_2}^{\rm{T}}{{{\bar{ Q}}}_{22}}{{{z}}_2}} \right]} {\rm{d}}t\;{\text{。}}$ (17)

 $J = \int_{{t_0}}^t {\left[ {{{{z}}_1}^{\rm{T}}\left( {{{{\bar{ Q}}}_{11}} - {{{\bar{ Q}}}_{12}}{{{\bar{ Q}}}_{22}}^{ - 1}{{{\bar{ Q}}}_{12}}^{\rm{T}}} \right){{{z}}_1} + {{{h}}^{\rm{T}}}{{{\bar{ Q}}}_{22}}{{h}}} \right]} {\rm{d}}t\;{\text{，}}$ (18)

 ${{{\dot z}}_1} = \left( {{{{\bar{ A}}}_{11}} - {{{\bar{ A}}}_{12}}{{{\bar{ Q}}}_{22}}^{ - 1}{{{\bar{ Q}}}_{12}}^{\rm{T}}} \right){{{z}}_1} + {{\bar{ A}}_{12}}{{h}}\;{\text{，}}$ (19)

 ${{ S}}\left( t \right) = {{{ K} \bar { X}}} = \left( {{{{{\bar { Q}}}}_{22}}^{ - 1}\left( {{{{}}_{12}}^{\rm{T}} + {{{{\bar { A}}}}_{12}}^{\rm{T}}{{ P}}} \right),{{{ I}}_m}} \right){{{ M}}^{ - 1}}{{ \bar { X}}}\;{\text{。}}$ (20)

 \begin{aligned} & {{P}}\left( {{{{\bar{ A}}}_{11}} - {{{\bar{ A}}}_{12}}{{{\bar{ Q}}}_{22}}^{ - 1}{{{\bar{ Q}}}_{12}}^{\rm{T}}} \right) \;+\\ & \quad \quad {\left( {{{{\bar{ A}}}_{11}} - {{{\bar{ A}}}_{12}}{{{\bar{ Q}}}_{22}}^{ - 1}{{{\bar{ Q}}}_{12}}^{\rm{T}}} \right)^{\rm{T}}}{{P}} \;-\\ & \quad \quad {{P}}{{{\bar{ A}}}_{12}}{{{\bar{ Q}}}_{22}}^{ - 1}{{{\bar{ Q}}}_{12}}^{\rm{T}}{{P}} \;+\\ & \quad \quad \left( {{{{\bar{ Q}}}_{11}} - {{{\bar{ Q}}}_{12}}{{{\bar{ Q}}}_{22}}^{ - 1}{{{\bar{ Q}}}_{12}}^{\rm{T}}} \right) = 0 \end{aligned} (21)

 ${{\dot S}}(t) = \alpha {{S}}(t) + \beta sign\left( {{{S}}(t)} \right),\;\;\alpha < 0,\beta < 0\;{\text{。}}$ (22)

 ${{u}}\left( t \right) = - {\left( {{{K}}}{\bar {\bar {{B}}}} \right)^{{\rm{ - 1}}}}\left( {{{K}}{{\bar {\bar {{A}}}}{\bar {{X}} }}+ \alpha {{S}}(t) + \beta sign\left( {{{S}}(t)} \right)} \right)\;{\text{。}}$ (23)

1）确定输入输出变量

2）数字量模糊化

 图 2 输隶属度函数曲线 Fig. 2 The membership function

3）利用模糊规则进行模糊推理

4）解模糊还原输出

 图 3 系统控制示意图 Fig. 3 The system control schematic diagram
5 仿真分析

 图 4 加速度对比 Fig. 4 Comparison of acceleration

 图 5 相对位移对比 Fig. 5 Comparison of relative displacement

 ${J_1}{J_2}/{V_0}^2 \geqslant \frac{1}{2}\;{\text{。}}$ (24)

 图 6 极限性能对比 Fig. 6 Comparison of limiting performance

6 结　语

 [1] 汪玉, 华宏星. 舰船现代冲击理论及应用[M]. 北京: 科学出版社, 2005: 1-16, 66-68. [2] 胡铂. 基于磁流变阻尼器的半主动悬架控制策略研究[D]. 杭州: 浙江大学, 2017. [3] 周文亮, 王强. 冲击隔离发展浅谈[J]. 噪声与振动控制, 2002(5): 22-25. DOI:10.3969/j.issn.1006-1355.2002.05.006 [4] 陈昭晖, 陈宝春. 斜拉索-磁流变阻尼器系统的频域自适应控制[J]. 福州大学学报(自然科学版), 2017(04): 459-465. [5] 于漪丁. 小型磁流变飞机起落架建模与缓冲控制研究[D]. 沈阳: 沈阳航空航天大学, 2018. [6] 张磊. 基于磁流变阻尼器的飞机起落架控制方法研究[D]. 天津: 中国民航大学, 2017. [7] SEVIN E, PILKEV W D. Optimum shock and vibration isolation[M]. Shock and Vibration Information Analysis Center, Washington, DC, 1971. [8] 刘金锟. 滑模变结构控制MATLAB仿真[M]. 北京: 清华大学出版社, 2005. [9] 孙静. 模糊滑模控制的研究[M]. 北京: 北京化工大学, 2003.