﻿ 低速水下航行器惯性调节系统的建模仿真
 舰船科学技术  2021, Vol. 43 Issue (7): 49-53    DOI: 10.3404/j.issn.1672-7649.2021.07.010 PDF

1. 海军装备部沈阳局驻葫芦岛地区军事代表室，辽宁 葫芦岛 125004;
2. 武汉第二船舶设计研究所，湖北 武汉 430205;
3. 华中师范大学，湖北 武汉 430079;
4. 武汉理工大学 汽车工程学院，湖北 武汉 430070

Modeling and simulation of low-speed underwater vessels using inertial-adjusting systems
TANG Xiong-hui1, LI Yu-sheng1, QIN Zi-ming2, YANG Yu-wan3, XIE Chao-jie4
1. Military Representative Office of Shenyang Naval Equipement Departement in Huludao Area, Huludao 125004, China;
2. Wuhan Second Ship Design and Research Institute, Wuhan 430205, China;
3. Central China Normal University, Wuhan 430079, China;
4. School of Automobile Engineering, Wuhan University of Technology, Wuhan 430070, China
Abstract: The rudder effect decreases dramatically when underwater vehicles move slowly. So inertial parameters changing method is used to adjust the movement attitudes, including injecting water or drainage for mass changing. A method based on AMESim and Simulink is used to model underwater vehicle’s inertial system for its fast modeling and simulation. This method is used to validate the feasibility of inertial changing method and the coupling dynamic characteristics between the vehicle and the inertial changing system. Taking a small vehicle as an example, a double-circle PID control method is demonstrated to maintain its depth with ocean wave and other disturbs.
Key words: low speed     underwater     ballast     simulation
0 引　言

1 水下航行器六自由度运动模型的建立 1.1 水下航行器六自由度运动方程

 图 1 两种运动坐标系 Fig. 1 Two kinds of movement coordinates

 $\begin{split} m(\dot u - rv + wq) =& \dfrac{1}{2}\rho {L^4}(X_{qq}'{q^2} + X_{rr}'{r^2} + X_{rp}'rp) + \\ &\dfrac{1}{2}\rho {L^3}\left(X_{\dot u}'\dot u + X_{vr}'vr + X_{wq}'wq\right) +\\ &\dfrac{1}{2}\rho {L^2}\left(X_{uu}'{u^2} + X_{vv}'{v^2}\right) + \\ &\dfrac{1}{2}\rho {L^2}{u^2}\left(X_{{\delta _r}{\delta _r}}'{\delta _r}^2 + X_{{\delta _s}{\delta _s}}'{\delta _s}^2 + X_{{\delta _b}{\delta _b}}'{\delta _b}^2\right) + \\ &{F_{xp}} + {F_x} \text{，} \\[-10pt]\end{split}$ (1)

 $\begin{split} m(\dot v - wp + ur) =& \dfrac{1}{2}\rho {L^4}\left(Y_{\dot r}'\dot r + Y_{\dot p}'\dot p + Y_{pq}'pq\right) + \\ &\dfrac{1}{2}\rho {L^3}\Biggr(Y_{\dot v}'\dot v + Y_r'ur + Y_p'up + Y_{wp}'wp +\\ &Y_{v\left| r \right|}'\dfrac{v}{{\left| v \right|}}{({v^2} + {w^2})^{\frac{1}{2}}}\left| r \right|\Biggr) + \\ &\dfrac{1}{2}\rho {L^2}\left(Y_v'uv + Y_{vw}'vw + Y_{v\left| v \right|}'{({v^2} + {w^2})^{\frac{1}{2}}}\right) +\\ &\frac{1}{2}\rho {L^2}\left(Y_{{\delta _r}}'{u^2}{\delta _r}\right) + {F_y} \text{，} \\ \\[-18pt]\end{split}$ (2)

 $\begin{split} m(\dot w - qu + pv) = &\dfrac{1}{2}\rho {L^4}\left(Z_{\dot q}'\dot q + Z_{rr}'{r^2} + Z_{rp}'rp\right) + \\ &\dfrac{1}{2}\rho {L^3}\Bigg(Z_{\dot w}'\dot w + Z_q'uq + Z_{vr}'vr + \\ & Z_{vp}'vp + Z_{w\left| q \right|}'\dfrac{w}{{\left| w \right|}}{\left({v^2} + {w^2}\right)^{\frac{1}{2}}}\left| q \right|\Bigg) +\\ &\dfrac{1}{2}\rho {L^2}\Bigr(Z_*'{u^2} + Z_w'uw + \\ &Z_{w\left| w \right|}'w{({v^2} + {w^2})^{\frac{1}{2}}} + Z_{vv}'{v^2}\Bigr) +\\ &\dfrac{1}{2}\rho {L^2}\left(Z_{{\delta _s}}'{u^2}{\delta _s} + Z_{{\delta _b}}'{u^2}{\delta _b}\right) \text{，} \\ \end{split}$ (3)

 $\begin{split}{I}_{x}\dot{p}\!+\!({I}_{x}\!-\!{I}_{y})qr\!=\!&\dfrac{1}{2}\rho {L}^{5}\bigg({K}_{\dot{p}}'\dot{p}+{K}_{\dot{r}}'\dot{r}+{K}_{\left|p\right|p}'p\left|p\right|+{K}_{qr}'qr\bigg)+\\ &\dfrac{1}{2}\rho {L}^{4}\left({K}_{\dot{v}}'\dot{v}+{K}_{p}'up\right) +\dfrac{1}{2}\rho {L}^{3}\Bigg({K}_{v}'uv+\\ &{K}_{vw}'vw+{K}_{\left|v\right|v}'v({{v^2} +{w^2})^{\frac{1}{2}}}\Bigg)+\\ &\frac{1}{2}\rho {L}^{3}\left({K}_{{\delta }_{r}}'{u}^{2}{\delta }_{r}\right)-mgh\mathrm{cos}\theta \mathrm{sin}\phi +{M}_{x}\text{，}\\[-12pt]\end{split}$ (4)

 $\begin{split} {I_y}\dot q + ({I_x} - {I_z})rp =& \dfrac{1}{2}\rho {L^5}\left(M_{\dot q}'\dot q + M_{rr}'{r^2} + M_{rp}'rp\right) + \\ &\dfrac{1}{2}\rho {L^4}\bigg(M_{\dot w}'\dot w + M_{vr}'vr + M_{vp}'vp + \\ &M_{\left| w \right|q}'{({v^2} + {w^2})^{\tfrac{1}{2}}}q + M_q'uq\bigg) +\\ &\frac{1}{2}\rho {L^3}\bigg(M_*'{u^2} + M_w'uw + M_{w\left| w \right|}'{({v^2} + {w^2})^{\frac{1}{2}}} + \\ &M_{vv}'{v^2}\bigg) + \dfrac{1}{2}\rho {L^3}\left(M_{{\delta _s}}'{u^2}{\delta _s} + M_{{\delta _b}}'{u^2}{\delta _b}\right) -\\ & mgh\sin \theta + {M_y} \text{，} \\ \\[-12pt]\end{split}$ (5)

 $\begin{split} {I_z}\dot r + ({I_y} - {I_x})pq = &\dfrac{1}{2}\rho {L^5}\left(N_{\dot p}'\dot p + N_{\dot r}'\dot r + N_{pq}'pq\right) + \dfrac{1}{2}\rho {L^4}\bigg(N_{\dot v}'\dot v +\\ & N_p'up + N_r'ur + N_{wp}'wp\bigg) + N_{\left| v \right|r}'{({v^2} + {w^2})^{\frac{1}{2}}}) +\\ & \dfrac{1}{2}\rho {L^3}\bigg(N_v'uv + N_{vw}'vw + N_{\left| v \right|v}'v{({v^2} + {w^2})^{\frac{1}{2}}}\bigg) + \\ &\frac{1}{2}\rho {L^3}\left(N_{{\delta _r}}'{u^2}{\delta _r}\right) + {M_z}\text{。} \\ \\[-18pt]\end{split}$ (6)

 $\dot \psi = q\frac{{\sin \varphi }}{{\cos \theta }} + r\frac{{\cos \varphi }}{{\cos \theta }}\text{，}$ (7)
 $\dot \varphi = p + q\tan \theta \sin \varphi + r\tan \theta \cos \varphi \text{，}$ (8)
 $\dot \theta = q\cos \varphi - r\sin \varphi \text{，}$ (9)
 $\begin{split} \dot \xi =& u\cos \psi \cos \theta + v(\cos \psi \sin \theta \sin \varphi - \sin \psi \cos \varphi ) + \\ & w(\cos \psi \sin \theta \cos \varphi + \sin \psi \sin \varphi ) \text{，} \\ \end{split}$ (10)
 $\begin{split} \dot \eta =& u\sin \psi \cos \theta + v(\sin \psi \sin \theta \sin \varphi + \cos \psi \cos \varphi ) + \\ &w(\sin \psi \sin \theta \cos \varphi - \cos \psi \sin \varphi )\text{，} \\ \end{split}$ (11)
 $\dot \zeta = - u\sin \theta + v\cos \theta \sin \varphi + w\cos \theta \cos \varphi \text{。}$ (12)

1.2 海浪干扰力的计算

1阶波浪力呈高频周期振荡形式，在其作用下航行器主要做摇荡运动，即垂荡、纵摇以及横摇运动等。计算波浪的1阶摇荡力的近似公式估算法有海勒默等，理论计算方法主要有细长体法、切片法、三维面元法等，模拟时可以运用数值解法。2阶波浪力呈小幅值长周期形式，通常在同周期内为常值，主要与波高及深度有关，被称为波吸引力。对于近水面运动，当海浪为长波，航行器顺着海浪方向运动时，趋于随浪逐流，其深度变化较大；在海浪为短波时，航行器的垂直位置几乎不受浪涌的影响。

 ${X_w} = {X_{wf}}\text{，}$ (13)
 ${Y_w} = {Y_{wf}}\text{，}$ (14)
 ${Z_w} = {Z_{wu}} + \;{Z_{ws}}{\rm{ + }}{Z_{wf}}\text{，}$ (15)
 ${K_w} = {K_{wf}}\text{，}$ (16)
 ${M_w} = {M_{wf}}\text{，}$ (17)
 ${N_w} = {N_{wu}} + {N_{ws}} + {N_{wf}}\text{。}$ (18)

 ${{\rm{Z}}_{wu}} = {U_w}^2{\cos ^2}\psi \,{C_z}\text{，}$ (19)
 ${N_{wu}} = {U_w}^2{\cos ^2}\psi \,{m_z}\text{。}$ (20)

 ${{\rm{Z}}_{ws}} = {Z_s}{{\rm{e}}^{{b_w}({\zeta _R} - \zeta )}}\text{，}$ (21)
 ${N_{ws}} = {N_s}{{\rm{e}}^{{b_w}({\zeta _R} - \zeta )}}\text{。}$ (22)

1阶波浪力通常采用多个正弦波叠加的方式进行逼近，正弦波参数包括频率和相位差。1阶波浪力也随着深度的变化而衰减，衰减系数与2阶波浪力相同。故所受的1阶波浪力的模型可表示为：

 ${X_{wf}} = {e^{bw\left( {{\zeta _R} - \zeta } \right)}}\sum\limits_{i = 1}^4 {\alpha _x^i\sin \left[ {{\omega _i}t + {\phi _i}} \right]} \text{，}$ (23)
 ${Y_{wf}} = {e^{bw\left( {{\zeta _R} - \zeta } \right)}}\sum\limits_{i = 1}^4 {\alpha _y^i\sin \left[ {{\omega _i}t + {\phi _i}} \right]} \text{，}$ (24)
 ${Z_{wf}} = {e^{bw\left( {{\zeta _R} - \zeta } \right)}}\sum\limits_{i = 1}^4 {\alpha _z^i\sin \left[ {{\omega _i}t + {\phi _i}} \right]}\text{，}$ (25)
 ${K_{wf}} = {e^{bw\left( {{\zeta _R} - \zeta } \right)}}\sum\limits_{i = 1}^4 {\alpha _K^i\sin \left[ {{\omega _i}t + {\phi _i}} \right]} \text{，}$ (26)
 ${M_{wf}} = {e^{bw\left( {{\zeta _R} - \zeta } \right)}}\sum\limits_{i = 1}^4 {\alpha _M^i\sin \left[ {{\omega _i}t + {\phi _i}} \right]} \text{，}$ (27)
 ${N_{wf}} = {e^{bw\left( {{\zeta _R} - \zeta } \right)}}\sum\limits_{i = 1}^4 {\alpha _N^i\sin \left[ {{\omega _i}t + {\phi _i}} \right]}\text{。}$ (28)

2 运动姿态惯性调节系统动力学建模 2.1 基于AMESim的运动姿态惯性调节系统模型建立 2.1.1 水系统建模

 图 2 水系统模型 Fig. 2 Water system modeling
2.1.2 气系统建模

 图 3 气系统模型 Fig. 3 Air system modeling
2.2 面向多领域联合仿真的AMESim压载系统模型编译

3 基于多领域联合的低速水下航行器深度调节系统仿真

 图 4 典型工况下的位移曲线（m） Fig. 4 Movement curve under typical condition

 图 5 典型工况下的速度曲线（m/s） Fig. 5 Speed curve under typical condition

 图 6 典型工况下的水舱压力曲线（bar） Fig. 6 Tank pressure curve under typical condition
4 结　语

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